From 3d9de25f9166816497b20de677c6ff046d119f48 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Wed, 1 Sep 2021 11:44:59 +0200 Subject: [PATCH 01/58] Refactorin ongoing. Snapshot --- .gitignore | 2 + examples/loss_it2.png | Bin 253257 -> 249477 bytes examples/loss_it3.png | Bin 254075 -> 285566 bytes src/CausticsEngineering.jl | 1 + src/create_mesh.jl | 586 ++++++++++++++++--------------------- src/parameters.jl | 21 ++ src/utilities.jl | 145 +++++++-- 7 files changed, 401 insertions(+), 354 deletions(-) create mode 100644 src/parameters.jl diff --git a/.gitignore b/.gitignore index a45d4bb..049a072 100644 --- a/.gitignore +++ b/.gitignore @@ -1,3 +1,5 @@ +.vscode + # Files generated by invoking Julia with --code-coverage *.jl.cov *.jl.*.cov diff --git a/examples/loss_it2.png b/examples/loss_it2.png index 3188ba73c7dc8164a59bfbb67ff8066aa77e63c1..48221c353adf88288811943ab2bf83b97ceb49d1 100644 GIT binary patch literal 249477 zcmXtg2{_d2`+j{bjWsijeVNRRee5HEak=!&^FHr=-_QNLA6d?h)&jheyhn~45wO8qxE?w3 zKk()MjzA7SB}tk;0G~KRaSpg6N1E^O9RzTJ*GEaN)~Am=9F|@OFAza^SBE1<5*3ad zxt@09$WQRC>uX1jT+%#px%eid*od9z!w>|kW~@2;* 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zHmmDCeNG*SH~t&F+O+$`-fDPUF&K)OQ2KogxVNm#+K51eb7?wk{F<~h9ZT+uGbpjquyoqgm)9Tnr(ejB z+uOurQAuq}?*_s#Km@6mw^Ly*KEwA+VWaEtIpl)X9@CT5W!Z)T{dv%F<`0KWCb@0R z&ef8`xZ9@80)e?6eWOf;!t{tC3$LF^3%B*`h6DZ8NK1Ar=FS%$8u&Z2kowL(di zFwrhDwQBOB(K`Q^@t3o3HyzD`LmO2Y3|uA*xpcp*e-)RCfr@)DjZpaag@tjP?A z>lsUKjoGz&KhGL41BB?%L9G=UGyi3uK)0tVm#>28vR8g3zGg6UMX+Cv}In tnDeDRDa9vg@toBq{i{1SiAgUxy=KP;onUN@x^oWrArUC}Q B + t_vB - u1 = dp2.x - dp1.x - v1 = dp2.y - dp1.y + # To make the calculation simpler, everything is translated so that A is at the + # origin of the plane and its velocity is nil. + Bx = p2.x - p1.x; By = p2.y - p1.y + Cx = p3.x - p1.x; Cy = p3.y - p1.y - u2 = dp3.x - dp1.x - v2 = dp3.y - dp1.y + t_vBx = p2.vx - p1.vx; t_vBy = p2.vy - p1.vy + t_vCx = p3.vx - p1.vx; t_vCy = p3.vy - p1.vy - a = u1 * v2 - u2 * v1 - b = x1 * v1 + y2 * u1 - x2 * v1 - y1 * u2 - c = x1 * y2 - x2 * y1 + # After this, given that Ax = Ay = 0, the area is nil iff + # Bx Cy - Cx By = 0. + # After expansion and reshuffling to have a quadratic equation where t + # is the variable, the coefficients of that equation are: - if a != 0 - quotient = b^2 - 4a * c - if quotient >= 0 - d = sqrt(quotient) + a = t_vBy * t_vCx - t_vCy * t_vBx + b = By * t_vCx + Cx * t_vBy - (Bx * t_vCy + Cy * t_vBx) + c = Cx * By - Bx * Cy + + # if a = 0, this is just a linear equation. + if a == 0 + # Fingers crossed that b != 0 + return -c / b, -c / b + else + + discriminant = b^2 - 4a * c + + # If there is a solution + if discriminant >= 0 + d = sqrt(discriminant) return (-b - d) / 2a, (-b + d) / 2a else - return -123.0, -123.0 - end - else + # There can be no solution if, after translation, B abd C move in parallel direction. + # C will never end up on the line AB.result_mesh.rectangles[row, col].z = height_map[row, col] + result_mesh.rectangles[row, col].z = height_map[row, col] - # cool, there just isn't any dependence on t^2, but there is still on t! - return -c / b, -c / b + # Very unlikely with Float64. + return missing, missing + end end end @@ -106,7 +90,7 @@ $(SIGNATURES) This function saves the mesh object in stl format. """ -function saveObj!( +function save_stl!( mesh::Mesh, filename::String; scale = 1.0, @@ -114,26 +98,37 @@ function saveObj!( reverse = false, flipxy = false, ) + + height, width = size(mesh.rectangles) + open(filename, "w") do io - for vertex in mesh.nodes + for row ∈ 1:height, col ∈ 1:width + n = mesh.topNodes[row, col] if flipxy - println( - io, - "v $(vertex.y * scale) $(vertex.x * scale) $(vertex.z * scalez)", - ) + println(io,"v $(n.y * scale) $(n.x * scale) $(n.z * scalez)") else - println( - io, - "v $(vertex.x * scale) $(vertex.y * scale) $(vertex.z * scalez)", - ) + println(io,"v $(n.x * scale) $(n.y * scale) $(n.z * scalez)") end - end - for face in mesh.triangles + t = mesh.topTriangles[row, col] if reverse - println(io, "f $(face.pt3) $(face.pt2) $(face.pt1)") + println(io, "f $(t.pt3) $(t.pt2) $(t.pt1)") else - println(io, "f $(face.pt1) $(face.pt2) $(face.pt3)") + println(io, "f $(t.pt1) $(t.pt2) $(t.pt3)") + end + + n = mesh.botNodes[row, col] + if flipxy + println(io,"v $(n.y * scale) $(n.x * scale) $(n.z * scalez)") + else + println(io,"v $(n.x * scale) $(n.y * scale) $(n.z * scalez)") + end + + t = mesh.botTriangles[row, col] + if reverse + println(io, "f $(t.pt3) $(t.pt2) $(t.pt1)") + else + println(io, "f $(t.pt1) $(t.pt2) $(t.pt3)") end end @@ -144,29 +139,31 @@ end """ $(SIGNATURES) + +TO REFACTOR. """ -function Obj2Mesh(filename) +function stl_2_mesh(filename) lines = readlines(filename) vertexLines = [l for l in lines if startswith(l, "v")] nodeList = Vector{Point3D}(undef, size(vertexLines)) - count = 1 + count = 0 for line in vertexLines + count += 1 elements = split(line, " ") x = parse(Float64, elements[2]) y = parse(Float64, elements[3]) z = parse(Float64, elements[4]) * 10 pt = Point3D(x, y, z, 0, 0) nodeList[count] = pt - count += 1 end faceLines = [l for l in lines if startswith(l, "f")] triangles = Vector{Triangle}(undef, size(faceLines)) for line in faceLines elements = split(line, " ") - triangle = Triangle( + triangles[line] = Triangle( parse(Int64, elements[2]), parse(Int64, elements[3]), parse(Int64, elements[4]), @@ -183,18 +180,18 @@ end """ $(SIGNATURES) """ -function ∇(f::Matrix{Float64}) +function ∇(ϕ::Matrix{Float64}) width, height = size(f) - ∇fᵤ = zeros(Float64, width, height) # the right edge will be filled with zeros - ∇fᵥ = zeros(Float64, width, height) # the buttom edge will be filled with zeros + ∇ϕᵤ = zeros(Float64, width, height) # the right edge will be filled with zeros + ∇ϕᵥ = zeros(Float64, width, height) # the buttom edge will be filled with zeros - for x = 1:width, y = 1:height - ∇fᵤ[x, y] = (x == width ? 0 : f[x+1, y] - f[x, y]) - ∇fᵥ[x, y] = (y == height ? 0 : f[x, y+1] - f[x, y]) + for x = 1:width-1, y = 1:height-1 + ∇ϕᵤ[x, y] = ϕ[x+1, y] - ϕ[x, y] + ∇ϕᵥ[x, y] = ϕ[x, y+1] - ϕ[x, y] end - return ∇fᵤ, ∇fᵥ + return ∇ϕᵤ, ∇ϕᵥ end @@ -204,15 +201,11 @@ $(SIGNATURES) function getPixelArea(mesh::Mesh) # A Mesh is a grid of 3D points. The X and Y coordinates are not necessarily aligned or square # The Z coordinate represents the value. brightness is just proportional to area. - pixelAreas = Matrix{Float64}(undef, mesh.width - 1, mesh.height - 1) + height, width = size(mesh.rectangles) - for x = 1:mesh.width-1, y = 1:mesh.height-1 - upperLeft = mesh.nodeArray[x, y] - upperRight = mesh.nodeArray[x+1, y] - - lowerLeft = mesh.nodeArray[x, y+1] - lowerRight = mesh.nodeArray[x+1, y+1] + pixelAreas = zeros(Float64, height, width) + for row = 1:mesh.height, col = 1:width #= *------* | / | @@ -221,108 +214,49 @@ function getPixelArea(mesh::Mesh) | / | *------* =# - pixelAreas[x, y] = - triangle_area(lowerLeft, upperRight, upperLeft) + - triangle_area(lowerLeft, lowerRight, upperRight) + pixelAreas[width, col] = + triangle_area(mesh.topTriangles[height, width]) + + triangle_area(mesh.botTriangles[height, width]) end - return pixelAreas + return topPixelAreas end """ $(SIGNATURES) """ -function relax!(matrix::Matrix{Float64}, D::Matrix{Float64}) - - ω = 1.99 # ω = 2 / (1 + π / width) - +function relax!(height_map::Matrix{Float64}, D::Matrix{Float64}) # This function implements successive over relaxation for a matrix and its associated error matrix # There is a hardcoded assumption of Neumann boundary conditions--that the derivative across the # boundary must be zero in all cases. See: # https://math.stackexchange.com/questions/3790299/how-to-iteratively-solve-poissons-equation-with-no-boundary-conditions - width, height = size(matrix) - - max_update = 0.0 - for x = 1:width, y = 1:height - val = matrix[x, y] - - if x == 1 && y == 1 - # Top left corner - val_down = matrix[x, y+1] - val_right = matrix[x+1, y] - delta = 1 / 2 * (val_down + val_right - D[x, y]) - continue # To skip the matrix[x, y] increment - - elseif x == 1 && y == height - # Bottom left corner - val_up = matrix[x, y-1] - val_right = matrix[x+1, y] - delta = 1 / 2 * (val_up + val_right - D[x, y]) - - elseif x == width && y == 1 - # Top right corner - val_down = matrix[x, y+1] - val_left = matrix[x-1, y] - delta = 1 / 2 * (val_down + val_left - D[x, y]) - - elseif x == width && y == height - # Bottom right corner - val_up = matrix[x, y-1] - val_left = matrix[x-1, y] - delta = 1 / 2 * (val_up + val_left - D[x, y]) - - elseif x == 1 - # Along the left edge, but not the top or buttom corner - val_up = matrix[x, y-1] - val_down = matrix[x, y+1] - val_right = matrix[x+1, y] - delta = 1 / 3 * (val_up + val_down + val_right - D[x, y]) - - elseif x == width - # Along the right edge, but not the top or buttom corner - val_up = matrix[x, y-1] - val_down = matrix[x, y+1] - val_left = matrix[x-1, y] - delta = 1 / 3 * (val_up + val_down + val_left - D[x, y]) - - elseif y == 1 - # Along the top edge, but not the left or right corner - val_down = matrix[x, y+1] - val_left = matrix[x-1, y] - val_right = matrix[x+1, y] - delta = 1 / 3 * (val_down + val_left + val_right - D[x, y]) - - elseif y == height - # Along the bottom edge, but not the left or right corner - val_up = matrix[x, y-1] - val_left = matrix[x-1, y] - val_right = matrix[x+1, y] - delta = 1 / 3 * (val_up + val_left + val_right - D[x, y]) + width, height = size(height_map) + val_average = sum(height_map) / (width * height) - else - # The new way - # ∇x₁ = [TODO] - - # The old way - val_up = matrix[x, y-1] - val_down = matrix[x, y+1] - val_left = matrix[x-1, y] - val_right = matrix[x+1, y] - delta = 1 / 4 * (val_up + val_down + val_left + val_right - D[x, y]) - end + # Embed matrix within a larger matrix for better vectorization + embedding = zeros(Float64, height + 2, width + 2) - delta = ω * (delta - val) - matrix[x, y] += delta + embedding[:, :] .= val_average + embedding[2:height+1, 2:height+1] .= height_map[:, :] - max_update = max(max_update, abs(delta)) + val_up = embedding[1:height, 2:width+1] + val_down = embedding[3:height+2, 2:width+1] + val_left = embedding[2:height+1, 1:width] + val_right = embedding[2:height+1, 3:width+2] - # node.z = .25 * (node_up.z + node_down.z + node_left.z + node_right.z) # simple averaging - # node.z += ω/4 * (node_up.z + node_down.z + node_left.z + node_right.z - 4 * node.z) + delta = (val_up + val_down + val_left + val_right - D) ./ 4.0 + delta = ω .* (delta - height_map) + height_map += delta + + max_update = maximum(abs.(delta)) - # matrix[x, y] += ω/4 * (val_up + val_down + val_left + val_right - 4 * val - D[x, y]) - end + + # node.z = .25 * (node_up.z + node_down.z + node_left.z + node_right.z) # simple averaging + # node.z += ω/4 * (node_up.z + node_down.z + node_left.z + node_right.z - 4 * node.z) + + # matrix[x, y] += ω/4 * (val_up + val_down + val_left + val_right - 4 * val - D[x, y]) return max_update end @@ -331,21 +265,24 @@ end """ $(SIGNATURES) -This function will take a `grid_definition x grid_definition` matrix and returns a `grid_definition x grid_definition` mesh. - -It currently takes the size of the matrix passed as argument. +This function will take a `grid_definition x grid_definition` matrix and returns a +`grid_definition x grid_definition` mesh. """ -function matrix_to_mesh(matrix::Matrix{Float64}) - w, h = size(matrix) +function matrix_to_mesh(height_map::Matrix{Float64}) + height, width = size(height_map) - retval = squareMesh(w, h) - for x = 1:w, y = 1:h - index = (y - 1) * retval.width + x - node = retval.nodes[index] - node.z = matrix[x, y] + result_mesh = create_mesh(height, width) + for row = 1:height, col = 1:width + result_mesh.rectangles[row, col].z = height_map[row, col] + + result_mesh.topPixelAreas[row, col].pt1.z = height_map[row, col] + result_mesh.topNodes[row, col].z = height_map[row, col] + + result_mesh.botPixelAreas[row, col].pt1.z = height_map[row, col] + result_mesh.botNodes[row, col].z = height_map[row, col] end - return retval + return result_mesh end @@ -355,15 +292,14 @@ $(SIGNATURES) function marchMesh!(mesh::Mesh, ϕ::Matrix{Float64}) ∇ϕᵤ, ∇ϕᵥ = ∇(ϕ) - imgWidth, imgHeight = size(ϕ) # should be grid_definitionxgrid_definition + height, imgHeight = size(mesh.rectangles) # For each point in the mesh we need to figure out its velocity - velocities = Matrix{Point3D}(undef, mesh.width, mesh.height) - for x = 1:mesh.width, y = 1:mesh.height + for x = 1:height, y = 1:mesh.height # XY coordinates in the mesh ARE XY coordinates in the image. The mesh just needs an extra row and column - # at the bottom right edge so that the triangles can be closed + # at the bottom right edge so that the triangles can be closed (a triangle per pixel) - if x == mesh.width + if x == height u = 0 else u = (y == mesh.height ? ∇ϕᵤ[x, y-1] : ∇ϕᵤ[x, y]) @@ -372,39 +308,48 @@ function marchMesh!(mesh::Mesh, ϕ::Matrix{Float64}) if y == mesh.height v = 0 else - v = (x == mesh.width ? ∇ϕᵥ[x-1, y] : ∇ϕᵥ[x, y]) + v = (x == height ? ∇ϕᵥ[x-1, y] : ∇ϕᵥ[x, y]) end velocities[x, y] = Point3D(-u, -v, 0, 0, 0) end - min_t = 10000 - triangleCount = 1 - for triangle in mesh.triangles - p1 = mesh.nodes[triangle.pt1] - p2 = mesh.nodes[triangle.pt2] - p3 = mesh.nodes[triangle.pt3] + # Basically infinity time to shrink a triangle to zip. + min_t = 10_000.0 + + for i ∈ 1:length(mesh.topTriangles) + triangle = mesh.topTriangles[i] + + p1 = mesh.topNodes[triangle.pt1] + p2 = mesh.topNodes[triangle.pt2] + p3 = mesh.topNodes[triangle.pt3] v1 = velocities[p1.ix, p1.iy] v2 = velocities[p2.ix, p2.iy] v3 = velocities[p3.ix, p3.iy] - t1, t2 = findT(p1, p2, p3, v1, v2, v3) + # Get the time, at that velocity, for the area of the triangle to be nil. + t1, t2 = find_maximum_t(p1, p2, p3, v1, v2, v3) - if 0 < t1 < min_t - min_t = t1 - end + # We are only interested in positive times. + if !ismissing(t1) + if 0 < t1 < min_t + min_t = t1 + end - if 0 < t2 < min_t - min_t = t2 + if 0 < t2 < min_t + min_t = t2 + end end - triangleCount += 1 end println("Overall min_t:", min_t) + + # Modify the mesh triangles but ensuring that we are far from destroying any of them. δ = min_t / 2 - for point in mesh.nodes + + for point in mesh.topNodes v = velocities[point.ix, point.iy] point.x = v.x * δ + point.x point.y = v.y * δ + point.y @@ -419,13 +364,11 @@ $(SIGNATURES) """ function quantifyLoss!(D, suffix, img) println("Loss:") - println("Minimum: $(minimum(D))") - println("Maximum: $(maximum(D))") + println("\tMinimum: $(minimum(D))") + println("\tMaximum: $(maximum(D))") - blue = zeros(size(D)) - blue[D.>0] = D[D.>0] - red = zeros(size(D)) - red[D.<0] = -D[D.<0] + blue = zeros(size(D)); blue[D.>0] = D[D.>0] + red = zeros(size(D)); red[D.<0] = -D[D.<0] green = zeros(size(D)) println(size(blue)) @@ -469,7 +412,7 @@ function oneIteration(meshy, img, suffix) ϕ = Matrix{Float64}(undef, width, height) - for i = 1:10240/2 + for i = 1:Grid_Definition * 10 max_update = relax!(ϕ, D) i % 500 == 0 && println(max_update) @@ -479,7 +422,7 @@ function oneIteration(meshy, img, suffix) break end - saveObj!( + save_stl!( matrix_to_mesh(ϕ * 0.02), "./examples/phi_$(suffix).obj", reverse = false, @@ -490,7 +433,7 @@ function oneIteration(meshy, img, suffix) # Now we need to march the x,y locations in our mesh according to this gradient! marchMesh!(meshy, ϕ) - saveObj!(meshy, "./examples/mesh_$(suffix).obj", flipxy = true) + save_stl!(meshy, "./examples/mesh_$(suffix).obj", flipxy = true) end @@ -504,7 +447,7 @@ function setHeights!(mesh, heights, heightScale = 1.0, heightOffset = 50) mesh.nodeArray[x, y].z = heights[x, y] * heightScale + heightOffset if x == 100 && y == 100 println( - "Example heights: $(heights[x, y]) and $(heights[x, y] * heightScale) and $(heights[x, y] * heightScale + heightOffset)", + "Example heights: $(heights[x, y]) and $(heights[x, y] * heightScale) and $(heights[x, y] * heightScale + heightOffset)", ) end end @@ -514,12 +457,11 @@ function setHeights!(mesh, heights, heightScale = 1.0, heightOffset = 50) mesh.nodeArray[width+1, y].z = mesh.nodeArray[width, y].z end - # get the bottom edge + # get the bottom edge including the pesky corner for x = 1:width+1 mesh.nodeArray[x, height+1].z = mesh.nodeArray[x, height].z end - # # get the pesky corner! # mesh.nodeArray[width + 1, height + 1].z = mesh.nodeArray[width, height].z end @@ -528,26 +470,23 @@ end """ $(SIGNATURES) """ -function setHeights(mesh, heights) +function setHeights(mesh, heightmap) width = mesh.width height = mesh.height nodes = Vector{Point3D}(undef, size(mesh.nodes)) nodeArray = Matrix{Point3D}(undef, 0, 0) triangles = Vector{Triangle}(undef, size(mesh.triangles)) - scale = 1 + scale = 1.0 - count = 1 - w, h = size(heights) - for y = 1:height - for x = 1:width - count += 1 - point = mesh.nodes[count] + count = 0 + w, h = size(heightmap) + for y = 1:height, x = 1:width + count += 1 + point = mesh.nodes[count] - z = heights[x, y] + z = heightmap[x, y] - newPoint = Point3D(point.x * scale, point.y * scale, z * scale, 0, 0) - nodes[count] = newPoint - end + nodes[count] = Point3D(point.x * scale, point.y * scale, z * scale, 0, 0) end return Mesh(nodes, nodeArray, triangles, width, height) @@ -561,6 +500,7 @@ function solidify(inputMesh, offset = 100) width = inputMesh.width height = inputMesh.height totalNodes = width * height * 2 + nodeList = Vector{Point3D}(undef, totalNodes) nodeArrayTop = Matrix{Point3D}(undef, width, height) nodeArrayBottom = Matrix{Point3D}(undef, width, height) @@ -568,8 +508,7 @@ function solidify(inputMesh, offset = 100) # imagine a 4x4 image. 4 * 2 + 2 * 2 = 12 numEdgeNodes = width * 2 + (height - 2) * 2 - numTrianglesTop = (width - 1) * (height - 1) * 2 - numTrianglesBottom = numTrianglesTop + numTrianglesBottom = numTrianglesTop = (width - 1) * (height - 1) * 2 numTrianglesEdges = numEdgeNodes * 2 totalTriangles = numTrianglesBottom + numTrianglesTop + numTrianglesEdges @@ -579,77 +518,68 @@ function solidify(inputMesh, offset = 100) ) # Build the bottom surface - count = 1 - for y = 1:height - for x = 1:width - newPoint = Point3D(x, y, -offset, x, y) - nodeList[count] = newPoint - nodeArrayBottom[x, y] = newPoint - count += 1 - end + count = 0 + for y = 1:height, x = 1:width + count += 1 + newPoint = Point3D(x, y, -offset, x, y) + nodeList[count] = newPoint + nodeArrayBottom[x, y] = newPoint end # Copy in the top surface - for y = 1:height - for x = 1:width - node = inputMesh.nodeArray[x, y] - copiedPoint = Point3D(node.x, node.y, node.z, node.ix, node.iy) - if node.ix != x - println("OH NO POINTS NOT MATCHED $(x) vs $(node.ix)") - end - if node.iy != y - println("OH NO POINTS NOT MATCHED $(y) vs $(node.iy)") - end - - nodeList[count] = copiedPoint - nodeArrayTop[x, y] = copiedPoint - count += 1 + for y = 1:height, x = 1:width + count += 1 + node = inputMesh.nodeArray[x, y] + copiedPoint = Point3D(node.x, node.y, node.z, node.ix, node.iy) + if node.ix != x + println("OH NO POINTS NOT MATCHED $(x) vs $(node.ix)") end + if node.iy != y + println("OH NO POINTS NOT MATCHED $(y) vs $(node.iy)") + end + + nodeList[count] = copiedPoint + nodeArrayTop[x, y] = copiedPoint end println("We now have $(count-1) valid nodes") # Build the triangles for the bottom surface triangles = Vector{Triangle}(undef, totalTriangles) - count = 1 - for y = 1:(height-1) - for x = 1:(width-1) - # here x and y establish the column of squares we're in - index_ul = (y - 1) * width + x - index_ur = index_ul + 1 - - index_ll = y * width + x - index_lr = index_ll + 1 - - triangles[count] = Triangle(index_ul, index_ll, index_ur) - count += 1 - triangles[count] = Triangle(index_lr, index_ur, index_ll) - count += 1 - end + count = 0 + for y = 1:(height-1), x = 1:(width-1) + count += 1 + # here x and y establish the column of squares we're in + index_ul = (y - 1) * width + x + index_ur = index_ul + 1 + + index_ll = y * width + x + index_lr = index_ll + 1 + + triangles[2*count-1] = Triangle(index_ul, index_ll, index_ur) + triangles[2*count] = Triangle(index_lr, index_ur, index_ll) end println("We've filled up $(count-1) triangles") - if count != numTrianglesBottom + 1 + if 2*count != numTrianglesBottom println( - "Hmm aren't count and triangles bottom equal? $(count) vs $(numTrianglesBottom + 1)", + "Hmm aren't count and triangles bottom equal? $(count) vs $(numTrianglesBottom)", ) end # Build the triangles for the top surface - for y = 1:(height-1) - for x = 1:(width-1) - # here x and y establish the column of squares we're in - index_ul = (y - 1) * width + x + totalNodes / 2 - index_ur = index_ul + 1 - - index_ll = y * width + x + totalNodes / 2 - index_lr = index_ll + 1 - - triangles[count] = Triangle(index_ul, index_ur, index_ll) - count += 1 - triangles[count] = Triangle(index_lr, index_ll, index_ur) - count += 1 - end + for y = 1:(height-1), x = 1:(width-1) + count += 1 + + # here x and y establish the column of squares we're in + index_ul = (y - 1) * width + x + totalNodes / 2 + index_ur = index_ul + 1 + + index_ll = y * width + x + totalNodes / 2 + index_lr = index_ll + 1 + + triangles[2*count-1] = Triangle(index_ul, index_ur, index_ll) + triangles[2*count] = Triangle(index_lr, index_ll, index_ur) end println("We've filled up $(count-1) triangles") @@ -657,50 +587,50 @@ function solidify(inputMesh, offset = 100) # Build the triangles to close the mesh x = 1 for y = 1:(height-1) + count += 1 + ll = (y - 1) * width + x ul = ll + totalNodes / 2 lr = y * width + x ur = lr + totalNodes / 2 - triangles[count] = Triangle(ll, ul, ur) - count += 1 - triangles[count] = Triangle(ur, lr, ll) - count += 1 + triangles[2*count-1] = Triangle(ll, ul, ur) + triangles[2*count] = Triangle(ur, lr, ll) end x = width for y = 1:(height-1) + count += 1 + ll = (y - 1) * width + x ul = ll + totalNodes / 2 lr = y * width + x ur = lr + totalNodes / 2 - triangles[count] = Triangle(ll, ur, ul) - count += 1 - triangles[count] = Triangle(ur, ll, lr) - count += 1 + triangles[2*count-1] = Triangle(ll, ur, ul) + triangles[2*count] = Triangle(ur, ll, lr) end y = 1 for x = 2:width + count += 1 + ll = (y - 1) * width + x ul = ll + totalNodes / 2 lr = (y - 1) * width + (x - 1) ur = lr + totalNodes / 2 - triangles[count] = Triangle(ll, ul, ur) - count += 1 - triangles[count] = Triangle(ur, lr, ll) - count += 1 + triangles[2*count-1] = Triangle(ll, ul, ur) + triangles[2*count] = Triangle(ur, lr, ll) end y = height for x = 2:width + count += 1 + ll = (y - 1) * width + x ul = ll + totalNodes / 2 lr = (y - 1) * width + (x - 1) ur = lr + totalNodes / 2 - triangles[count] = Triangle(ll, ur, ul) - count += 1 - triangles[count] = Triangle(ur, ll, lr) - count += 1 + triangles[2*count-1] = Triangle(ll, ur, ul) + triangles[2*count] = Triangle(ur, ll, lr) end return Mesh(nodeList, nodeArrayBottom, triangles, width, height) @@ -719,9 +649,6 @@ function findSurface(mesh, image, f, imgWidth) metersPerPixel = imgWidth / width println(metersPerPixel) - # η = 1.49 - n₂ = 1 - n₁ = 1.49 Nx = zeros(Float64, width + 1, height + 1) Ny = zeros(Float64, width + 1, height + 1) @@ -738,8 +665,8 @@ function findSurface(mesh, image, f, imgWidth) # k = η * sqrt(dx * dx + dy * dy + H_minus_h * H_minus_h) - H_minus_h # Nx[i, j] = 1/k * dx # Ny[i, j] = 1/k * dy - Ny[i, j] = tan(atan(dy / dz) / (n₁ - 1)) - Nx[i, j] = tan(atan(dx / dz) / (n₁ - 1)) + Ny[i, j] = tan(atan(dy / dz) / (n₁ - n₂)) + Nx[i, j] = tan(atan(dx / dz) / (n₁ - n₂)) end @@ -757,7 +684,7 @@ function findSurface(mesh, image, f, imgWidth) h = zeros(Float64, width, height) max_update = 0 - for i = 1:10240/4 + for i = 1:Grid_Definition * 10 / 2 max_update = relax!(h, divergence) i % 100 == 0 && println(max_update) @@ -774,7 +701,7 @@ end $(SIGNATURES) """ function testSquareMesh!() - mesh = squareMesh(100, 50) + mesh = create_mesh(100, 50) println(mesh.nodeArray[1, 1]) println(mesh.nodes[1]) @@ -786,7 +713,6 @@ function testSquareMesh!() mesh.nodes[1].y += 12 println(mesh.nodeArray[1, 1]) println(mesh.nodes[1]) - end @@ -797,7 +723,7 @@ function testSolidify!() println("Testing solidification") width = 100 height = 100 - origMesh = squareMesh(width, height) + origMesh = create_mesh(width, height) for y = 1:height, x = 1:width x2 = (x - width / 2) / width @@ -806,9 +732,9 @@ function testSolidify!() origMesh.nodeArray[x, y].z = 15 - value * 25 end - saveObj!(origMesh, "./examples/testSolidify.obj") + save_stl!(origMesh, "./examples/testSolidify.obj") solidMesh = solidify(origMesh, 0) - saveObj!(solidMesh, "./examples/testSolidify2.obj") + save_stl!(solidMesh, "./examples/testSolidify2.obj") end @@ -824,6 +750,7 @@ function plotAsQuiver( reversey = false, reversex = false, ) + h, w = size(g) xs = Float64[] ys = Float64[] @@ -896,8 +823,9 @@ function engineer_caustics(img) img2 = permutedims(img) * 1.0 width, height = size(img2) - # meshy is the same size as the image - meshy = squareMesh(width + 1, height + 1) + # meshy is the same size as the image with an extra row/column to have coordinates to + # cover each image pixel with a triangle. + meshy = create_mesh(width + 1, height + 1) # We need to boost the brightness of the image so that its sum and the sum of the area are equal mesh_sum = width * height @@ -916,19 +844,17 @@ function engineer_caustics(img) # oneIteration(meshy, img3, "it5") # oneIteration(meshy, img3, "it6") - artifactSize = 0.15 # meters - - h, metersPerPixel = findSurface(meshy, img3, 1.0, artifactSize) + h, metersPerPixel = findSurface(meshy, img3, 1.0, Artifact_Size) setHeights!(meshy, h, 1.0) # newMesh = setHeights(meshy, h) solidMesh = solidify(meshy) - saveObj!( + save_stl!( solidMesh, "./examples/original_image.obj", - scale = 1 / grid_definition * artifactSize, - scalez = 1 / 512.0 * artifactSize, + scale = Float64(1 / Grid_Definition * Artifact_Size), + scalez = Float64(1 / Grid_Definition * Artifact_Size) ) return meshy, img3 @@ -941,7 +867,7 @@ $(SIGNATURES) function main() @assert size(ARGS) == (1,) "Intented usage is: julia create_mesh.jl image.png" - img = load(ARGS[1]) + img = Images.load(ARGS[1]) return engineer_caustics(img) end diff --git a/src/parameters.jl b/src/parameters.jl new file mode 100644 index 0000000..de6dc3a --- /dev/null +++ b/src/parameters.jl @@ -0,0 +1,21 @@ +# Constants + +## Materials +const n₁ = 1.49 # acrylate +const n₂ = 1.00 # air + +## Optics +const Focal_Length = 1.0 # meters +const Artifact_Size = 0.15 # meters + +# Defined as parameters +# Currently unused. +global Grid_Definition = 512 +global Grid_Width = Grid_Definition +global Grid_Height = Grid_Definition + +const ω = 2 / (1 + π / Grid_Width) + + + + diff --git a/src/utilities.jl b/src/utilities.jl index 0cc97f4..8663b72 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -7,9 +7,11 @@ mutable struct Point3D y::Float64 z::Float64 - # Velocity at those coordinates - ix::Int - iy::Int + # Calculated velocity at those coordinates (velocity along z not necessary) + vx::Float64 + vy::Float64 + + Point3D() = new(0.0, 0.0,0.0,0.0,0.0) end @@ -19,7 +21,8 @@ $(SIGNATURES) function dist(p1::Point3D, p2::Point3D) dx = p2.x - p1.x dy = p2.y - p1.y - return sqrt(dx * dx + dy * dy) + dz = p2.z - p1.z + return sqrt(dx^2 + dy^2 + dz^2) end @@ -29,7 +32,7 @@ $(SIGNATURES) A midpoint is the average between two points """ midpoint(p1::Point3D, p2::Point3D) = - Point3D(0.5p1.x + 0.5p2.x, 0.5p1.y + 0.5p2.y, 0.5p1.z + 0.5p2.z, 0, 0) + Point3D((p1.x + p2.x )/ 2.0, (p1.y + p2.y )/ 2.0, (p1.z + p2.z )/ 2.0, 0, 0) """ @@ -46,51 +49,145 @@ centroid(p1::Point3D, p2::Point3D, p3::Point3D) = Point3D( ) +""" +$(SIGNATURES) +""" +function triangle_area(p1::Point3D, p2::Point3D, p3::Point3D) + a = dist(p1, p2) + b = dist(p2, p3) + c = dist(p3, p1) + s = (a + b + c) / 2.0 + + return sqrt(s * (s - a) * (s - b) * (s - c)) +end + + """ $(TYPEDEF) """ struct Triangle - pt1::Int64 - pt2::Int64 - pt3::Int64 + pt1::Point3D + pt2::Point3D + pt3::Point3D - Triangle() = new(0, 0, 0) + Triangle() = new(Point3D(), Point3D(), Point3D()) Triangle(pt1, pt2, pt3) = new(pt1, pt2, pt3) end +""" +$(SIGNATURES) +""" +centroid(t::Triangle) = centroid(t.p1, t.p2, t.p3) + +""" +$(SIGNATURES) +""" +triangle_area(t::Triangle) = triangle_area(t.p1, t.p2, t.p3) + + + """ $(TYPEDEF) + +A mesh is represents a single surface. First the surface is split into rectangles of size (width, height). Then, +each rectangle is broken into a top-left triangle and a bottom-right triangle. + +`arrays` represents the matrix of rectangles. Since each corner is shared by 4 rectangles, it is enough to +only record the top-left corner of each. +`nodes` contains the point at the center of a triangle of a given triangle. """ struct Mesh - nodes::Vector{Point3D} - nodeArray::Matrix{Point3D} - triangles::Vector{Triangle} - width::Int + rectangles::Matrix{Point3D} + + topTriangles::Matrix{Triangle} + topNodes::Matrix{Point3D} + + botTriangles::Matrix{Triangle} + botNodes::Matrix{Point3D} + + Mesh(height::Int, width::Int) = new( + Matrix{Point3D}(undef, height, width), + + Matrix{Triangle}(undef, height, width), + Matrix{Point3D}(undef, height, width), + + Matrix{Triangle}(undef, height, width), + Matrix{Point3D}(undef, height, width)) +end + +""" +$(TYPEDEF) + +Meshes representing the block of acrylate. Bottom is facing the light source; Top is facing the caustics. +""" +struct TopBottomMeshes height::Int + width::Int + + bottomMesh::Mesh + topMesh::Mesh + + TopBottomMeshes(height::Int, width::Int) = new(height, width, Mesh(height, width), Mesh(height, width)) end +""" +$(SIGNATURES) +""" +function top_triangle_area(mesh::Mesh, height::Int, width::Int) + triangle = mesh.topTriangles[height, width] + pt1 = mesh.topNodes[triangle.pt1] + pt2 = mesh.topNodes[triangle.pt2] + pt3 = mesh.topNodes[triangle.pt3] + + return top_triangle_area(pt1, pt2, pt3) +end """ $(SIGNATURES) """ -function triangle_area(mesh::Mesh, index::Int) - triangle = mesh.triangles[index] - pt1 = mesh.nodes[triangle.pt1] - pt2 = mesh.nodes[triangle.pt2] - pt3 = mesh.nodes[triangle.pt3] +function bot_triangle_area(mesh::Mesh, height::Int, width::Int) + triangle = mesh.topTriangles[height, width] + pt1 = triangle.pt1 + pt2 = triangle.pt2 + pt3 = triangle.pt3 return triangle_area(pt1, pt2, pt3) end +""" +$(SIGNATURES) +""" +function top_triangle_area(mesh::Mesh, height::Int, width::Int) + mesh_height, _ = size(mesh.topTriangles) + index = height + width * mesh_height + + return top_triangle_area(mesh, index) +end + """ $(SIGNATURES) + +Warning: not guaranteed to work in 3D? """ -function triangle_area(p1::Point3D, p2::Point3D, p3::Point3D) - a = dist(p1, p2) - b = dist(p2, p3) - c = dist(p3, p1) - s = (a + b + c) / 2.0 +function centroid(mesh::Mesh, index::Int) + triangle = mesh.topTriangles[index] + p1 = mesh.topNodes[triangle.pt1] + p2 = mesh.topNodes[triangle.pt2] + p3 = mesh.topNodes[triangle.pt3] - return sqrt(s * (s - a) * (s - b) * (s - c)) + return centroid(p1, p2, p3) end + +""" +$(SIGNATURES) +""" +function centroid(mesh::Mesh, height::Int, width::Int) + mesh_height, _ = size(mesh.topTriangles) + index = height + width * mesh_height + + return centroid(mesh, index) +end + + + From c56c6f192404463e68000843e51862a1522e7135 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Wed, 1 Sep 2021 11:46:00 +0200 Subject: [PATCH 02/58] Refactorin ongoing. Snapshot --- src/create_mesh.jl | 60 ++++++++++++++++++++++++---------------------- src/parameters.jl | 4 ---- src/utilities.jl | 15 +++++------- 3 files changed, 38 insertions(+), 41 deletions(-) diff --git a/src/create_mesh.jl b/src/create_mesh.jl index e550546..2f3e06f 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -13,14 +13,16 @@ function create_mesh(width::Int, height::Int) new_mesh.topTriangles[row, col] = Triangle( Point3D(Float64(row), Float64(col), 0.0, 0.0, 0.0), - Point3D(Float64(row+1), Float64(col), 0.0, 0.0, 0.0), - Point3D(Float64(row), Float64(col+1), 0.0, 0.0, 0.0)) + Point3D(Float64(row + 1), Float64(col), 0.0, 0.0, 0.0), + Point3D(Float64(row), Float64(col + 1), 0.0, 0.0, 0.0), + ) new_mesh.topNodes[row, col] = centroid(new_mesh.topTriangles[row, col]) new_mesh.botTriangles[row, col] = Triangle( - Point3D(Float64(row), Float64(col+1), 0.0, 0.0, 0.0), - Point3D(Float64(row+1), Float64(col), 0.0, 0.0, 0.0), - Point3D(Float64(row+1), Float64(col+1), 0.0, 0.0, 0.0)) + Point3D(Float64(row), Float64(col + 1), 0.0, 0.0, 0.0), + Point3D(Float64(row + 1), Float64(col), 0.0, 0.0, 0.0), + Point3D(Float64(row + 1), Float64(col + 1), 0.0, 0.0, 0.0), + ) new_mesh.botNodes[row, col] = centroid(new_mesh.botTriangles[row, col]) end @@ -33,11 +35,7 @@ $(SIGNATURES) Given 3 points and 3 velocities, calculate the `t` required to bring the area of that triangle to zero """ -function find_maximum_t( - p1::Point3D, - p2::Point3D, - p3::Point3D, -) +function find_maximum_t(p1::Point3D, p2::Point3D, p3::Point3D) # The area of a triangle is 1/2 * [ Ax (By - Cy) + Bx (Cy - Ay) + Cx (Ay - By)] # where each point of the triangle is where it will be after time t @@ -46,11 +44,15 @@ function find_maximum_t( # To make the calculation simpler, everything is translated so that A is at the # origin of the plane and its velocity is nil. - Bx = p2.x - p1.x; By = p2.y - p1.y - Cx = p3.x - p1.x; Cy = p3.y - p1.y + Bx = p2.x - p1.x + By = p2.y - p1.y + Cx = p3.x - p1.x + Cy = p3.y - p1.y - t_vBx = p2.vx - p1.vx; t_vBy = p2.vy - p1.vy - t_vCx = p3.vx - p1.vx; t_vCy = p3.vy - p1.vy + t_vBx = p2.vx - p1.vx + t_vBy = p2.vy - p1.vy + t_vCx = p3.vx - p1.vx + t_vCy = p3.vy - p1.vy # After this, given that Ax = Ay = 0, the area is nil iff # Bx Cy - Cx By = 0. @@ -76,7 +78,7 @@ function find_maximum_t( else # There can be no solution if, after translation, B abd C move in parallel direction. # C will never end up on the line AB.result_mesh.rectangles[row, col].z = height_map[row, col] - result_mesh.rectangles[row, col].z = height_map[row, col] + result_mesh.rectangles[row, col].z = height_map[row, col] # Very unlikely with Float64. return missing, missing @@ -105,9 +107,9 @@ function save_stl!( for row ∈ 1:height, col ∈ 1:width n = mesh.topNodes[row, col] if flipxy - println(io,"v $(n.y * scale) $(n.x * scale) $(n.z * scalez)") + println(io, "v $(n.y * scale) $(n.x * scale) $(n.z * scalez)") else - println(io,"v $(n.x * scale) $(n.y * scale) $(n.z * scalez)") + println(io, "v $(n.x * scale) $(n.y * scale) $(n.z * scalez)") end t = mesh.topTriangles[row, col] @@ -119,9 +121,9 @@ function save_stl!( n = mesh.botNodes[row, col] if flipxy - println(io,"v $(n.y * scale) $(n.x * scale) $(n.z * scalez)") + println(io, "v $(n.y * scale) $(n.x * scale) $(n.z * scalez)") else - println(io,"v $(n.x * scale) $(n.y * scale) $(n.z * scalez)") + println(io, "v $(n.x * scale) $(n.y * scale) $(n.z * scalez)") end t = mesh.botTriangles[row, col] @@ -241,9 +243,9 @@ function relax!(height_map::Matrix{Float64}, D::Matrix{Float64}) embedding[:, :] .= val_average embedding[2:height+1, 2:height+1] .= height_map[:, :] - val_up = embedding[1:height, 2:width+1] - val_down = embedding[3:height+2, 2:width+1] - val_left = embedding[2:height+1, 1:width] + val_up = embedding[1:height, 2:width+1] + val_down = embedding[3:height+2, 2:width+1] + val_left = embedding[2:height+1, 1:width] val_right = embedding[2:height+1, 3:width+2] delta = (val_up + val_down + val_left + val_right - D) ./ 4.0 @@ -367,8 +369,10 @@ function quantifyLoss!(D, suffix, img) println("\tMinimum: $(minimum(D))") println("\tMaximum: $(maximum(D))") - blue = zeros(size(D)); blue[D.>0] = D[D.>0] - red = zeros(size(D)); red[D.<0] = -D[D.<0] + blue = zeros(size(D)) + blue[D.>0] = D[D.>0] + red = zeros(size(D)) + red[D.<0] = -D[D.<0] green = zeros(size(D)) println(size(blue)) @@ -412,7 +416,7 @@ function oneIteration(meshy, img, suffix) ϕ = Matrix{Float64}(undef, width, height) - for i = 1:Grid_Definition * 10 + for i = 1:Grid_Definition*10 max_update = relax!(ϕ, D) i % 500 == 0 && println(max_update) @@ -561,7 +565,7 @@ function solidify(inputMesh, offset = 100) end println("We've filled up $(count-1) triangles") - if 2*count != numTrianglesBottom + if 2 * count != numTrianglesBottom println( "Hmm aren't count and triangles bottom equal? $(count) vs $(numTrianglesBottom)", ) @@ -684,7 +688,7 @@ function findSurface(mesh, image, f, imgWidth) h = zeros(Float64, width, height) max_update = 0 - for i = 1:Grid_Definition * 10 / 2 + for i = 1:Grid_Definition*10/2 max_update = relax!(h, divergence) i % 100 == 0 && println(max_update) @@ -854,7 +858,7 @@ function engineer_caustics(img) solidMesh, "./examples/original_image.obj", scale = Float64(1 / Grid_Definition * Artifact_Size), - scalez = Float64(1 / Grid_Definition * Artifact_Size) + scalez = Float64(1 / Grid_Definition * Artifact_Size), ) return meshy, img3 diff --git a/src/parameters.jl b/src/parameters.jl index de6dc3a..da715a3 100644 --- a/src/parameters.jl +++ b/src/parameters.jl @@ -15,7 +15,3 @@ global Grid_Width = Grid_Definition global Grid_Height = Grid_Definition const ω = 2 / (1 + π / Grid_Width) - - - - diff --git a/src/utilities.jl b/src/utilities.jl index 8663b72..03a7694 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -11,7 +11,7 @@ mutable struct Point3D vx::Float64 vy::Float64 - Point3D() = new(0.0, 0.0,0.0,0.0,0.0) + Point3D() = new(0.0, 0.0, 0.0, 0.0, 0.0) end @@ -32,7 +32,7 @@ $(SIGNATURES) A midpoint is the average between two points """ midpoint(p1::Point3D, p2::Point3D) = - Point3D((p1.x + p2.x )/ 2.0, (p1.y + p2.y )/ 2.0, (p1.z + p2.z )/ 2.0, 0, 0) + Point3D((p1.x + p2.x) / 2.0, (p1.y + p2.y) / 2.0, (p1.z + p2.z) / 2.0, 0, 0) """ @@ -107,12 +107,11 @@ struct Mesh Mesh(height::Int, width::Int) = new( Matrix{Point3D}(undef, height, width), - Matrix{Triangle}(undef, height, width), Matrix{Point3D}(undef, height, width), - Matrix{Triangle}(undef, height, width), - Matrix{Point3D}(undef, height, width)) + Matrix{Point3D}(undef, height, width), + ) end """ @@ -127,7 +126,8 @@ struct TopBottomMeshes bottomMesh::Mesh topMesh::Mesh - TopBottomMeshes(height::Int, width::Int) = new(height, width, Mesh(height, width), Mesh(height, width)) + TopBottomMeshes(height::Int, width::Int) = + new(height, width, Mesh(height, width), Mesh(height, width)) end """ @@ -188,6 +188,3 @@ function centroid(mesh::Mesh, height::Int, width::Int) return centroid(mesh, index) end - - - From d975aaa901d596b716d1053bcd87a818338aaad5 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Wed, 1 Sep 2021 15:00:48 +0200 Subject: [PATCH 03/58] Refactorig. Snapshot 2 --- src/create_mesh.jl | 186 +++++++++++++++++++++++++++------------------ src/utilities.jl | 59 ++------------ 2 files changed, 117 insertions(+), 128 deletions(-) diff --git a/src/create_mesh.jl b/src/create_mesh.jl index 2f3e06f..ace87e0 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -1,4 +1,3 @@ - """ $(SIGNATURES) @@ -8,22 +7,8 @@ function create_mesh(width::Int, height::Int) new_mesh = Mesh(height, width) - for row = 1:height, col = 1:width + for row = 1:height+1, col = 1:width+1 new_mesh.rectangles[row, col] = Point3D(Float64(row), Float64(col), 0.0, 0.0, 0.0) - - new_mesh.topTriangles[row, col] = Triangle( - Point3D(Float64(row), Float64(col), 0.0, 0.0, 0.0), - Point3D(Float64(row + 1), Float64(col), 0.0, 0.0, 0.0), - Point3D(Float64(row), Float64(col + 1), 0.0, 0.0, 0.0), - ) - new_mesh.topNodes[row, col] = centroid(new_mesh.topTriangles[row, col]) - - new_mesh.botTriangles[row, col] = Triangle( - Point3D(Float64(row), Float64(col + 1), 0.0, 0.0, 0.0), - Point3D(Float64(row + 1), Float64(col), 0.0, 0.0, 0.0), - Point3D(Float64(row + 1), Float64(col + 1), 0.0, 0.0, 0.0), - ) - new_mesh.botNodes[row, col] = centroid(new_mesh.botTriangles[row, col]) end return new_mesh @@ -105,36 +90,49 @@ function save_stl!( open(filename, "w") do io for row ∈ 1:height, col ∈ 1:width - n = mesh.topNodes[row, col] + + # Top triangle + top_triangle_1 = mesh.rectangles[row, col] + top_triangle_2 = mesh.rectangles[row+1, col] + top_triangle_3 = mesh.rectangles[row, col+1] + + n = centroid(top_triangle_1, top_triangle_2, top_triangle_3) if flipxy println(io, "v $(n.y * scale) $(n.x * scale) $(n.z * scalez)") else println(io, "v $(n.x * scale) $(n.y * scale) $(n.z * scalez)") end - t = mesh.topTriangles[row, col] - if reverse - println(io, "f $(t.pt3) $(t.pt2) $(t.pt1)") + if flipxy + println(io, "v $(n.y * scale) $(n.x * scale) $(n.z * scalez)") else - println(io, "f $(t.pt1) $(t.pt2) $(t.pt3)") + println(io, "v $(n.x * scale) $(n.y * scale) $(n.z * scalez)") end - n = mesh.botNodes[row, col] + + # Bottom triangle + bot_triangle_1 = mesh.rectangles[row, col+1] + bot_triangle_2 = mesh.rectangles[row+1, col] + bot_triangle_3 = mesh.rectangles[row+1, col+1] + + n = centroid(bot_triangle_1, bot_triangle_2, bot_triangle_3) if flipxy println(io, "v $(n.y * scale) $(n.x * scale) $(n.z * scalez)") else println(io, "v $(n.x * scale) $(n.y * scale) $(n.z * scalez)") end - t = mesh.botTriangles[row, col] - if reverse - println(io, "f $(t.pt3) $(t.pt2) $(t.pt1)") + if flipxy + println(io, "v $(n.y * scale) $(n.x * scale) $(n.z * scalez)") else - println(io, "f $(t.pt1) $(t.pt2) $(t.pt3)") + println(io, "v $(n.x * scale) $(n.y * scale) $(n.z * scalez)") end + + end - println(io, "dims $(mesh.width) $(mesh.height)") + # CHECK + println(io, "dims $(2*mesh.width) $(2*mesh.height)") end end @@ -188,9 +186,9 @@ function ∇(ϕ::Matrix{Float64}) ∇ϕᵤ = zeros(Float64, width, height) # the right edge will be filled with zeros ∇ϕᵥ = zeros(Float64, width, height) # the buttom edge will be filled with zeros - for x = 1:width-1, y = 1:height-1 - ∇ϕᵤ[x, y] = ϕ[x+1, y] - ϕ[x, y] - ∇ϕᵥ[x, y] = ϕ[x, y+1] - ϕ[x, y] + for row = 1:height, col = 1:width + ∇ϕᵤ[row, col] = ϕ[row+1, col] - ϕ[row, col] + ∇ϕᵥ[row, col] = ϕ[row, col+1] - ϕ[row, col] end return ∇ϕᵤ, ∇ϕᵥ @@ -203,11 +201,13 @@ $(SIGNATURES) function getPixelArea(mesh::Mesh) # A Mesh is a grid of 3D points. The X and Y coordinates are not necessarily aligned or square # The Z coordinate represents the value. brightness is just proportional to area. - height, width = size(mesh.rectangles) + height_plus_1, width_plus_1 = size(mesh.rectangles) + height = height_plus_1 - 1 + width = width_plus_1 - 1 pixelAreas = zeros(Float64, height, width) - for row = 1:mesh.height, col = 1:width + for row = 1:height, col = 1:width #= *------* | / | @@ -216,12 +216,21 @@ function getPixelArea(mesh::Mesh) | / | *------* =# + + top_triangle_1 = mesh.rectangles[row, col] + top_triangle_2 = mesh.rectangles[row+1, col] + top_triangle_3 = mesh.rectangles[row, col+1] + + bot_triangle_1 = mesh.rectangles[row, col+1] + bot_triangle_2 = mesh.rectangles[row+1, col] + bot_triangle_3 = mesh.rectangles[row+1, col+1] + pixelAreas[width, col] = - triangle_area(mesh.topTriangles[height, width]) + - triangle_area(mesh.botTriangles[height, width]) + triangle_area(top_triangle_1, top_triangle_2, top_triangle_3) + + triangle_area(bot_triangle_1, bot_triangle_2, bot_triangle_3) end - return topPixelAreas + return pixelAreas end @@ -234,10 +243,11 @@ function relax!(height_map::Matrix{Float64}, D::Matrix{Float64}) # boundary must be zero in all cases. See: # https://math.stackexchange.com/questions/3790299/how-to-iteratively-solve-poissons-equation-with-no-boundary-conditions - width, height = size(height_map) - val_average = sum(height_map) / (width * height) + height, width = size(height_map) + n_pixels = height * width + val_average = sum(height_map) / n_pixels - # Embed matrix within a larger matrix for better vectorization + # Embed matrix within a larger matrix for better vectorization and avoid duplicated code embedding = zeros(Float64, height + 2, width + 2) embedding[:, :] .= val_average @@ -252,15 +262,7 @@ function relax!(height_map::Matrix{Float64}, D::Matrix{Float64}) delta = ω .* (delta - height_map) height_map += delta - max_update = maximum(abs.(delta)) - - - # node.z = .25 * (node_up.z + node_down.z + node_left.z + node_right.z) # simple averaging - # node.z += ω/4 * (node_up.z + node_down.z + node_left.z + node_right.z - 4 * node.z) - - # matrix[x, y] += ω/4 * (val_up + val_down + val_left + val_right - 4 * val - D[x, y]) - - return max_update + return maximum(abs.(delta)) end @@ -274,13 +276,14 @@ function matrix_to_mesh(height_map::Matrix{Float64}) height, width = size(height_map) result_mesh = create_mesh(height, width) + for row = 1:height, col = 1:width result_mesh.rectangles[row, col].z = height_map[row, col] - result_mesh.topPixelAreas[row, col].pt1.z = height_map[row, col] + result_mesh.topTriangles[row, col].pt1.z = height_map[row, col] result_mesh.topNodes[row, col].z = height_map[row, col] - result_mesh.botPixelAreas[row, col].pt1.z = height_map[row, col] + result_mesh.botTriangles[row, col].pt1.z = height_map[row, col] result_mesh.botNodes[row, col].z = height_map[row, col] end @@ -294,41 +297,46 @@ $(SIGNATURES) function marchMesh!(mesh::Mesh, ϕ::Matrix{Float64}) ∇ϕᵤ, ∇ϕᵥ = ∇(ϕ) - height, imgHeight = size(mesh.rectangles) + height, width = size(mesh.rectangles) # For each point in the mesh we need to figure out its velocity - for x = 1:height, y = 1:mesh.height + # However all velocities on points located at a border will never move + # I.e. velocity (Vx, Vy) = (0, 0) and the square of acrylate will remain + # of the same size. + + for row ∈ 1:height, col ∈ 1:width # XY coordinates in the mesh ARE XY coordinates in the image. The mesh just needs an extra row and column # at the bottom right edge so that the triangles can be closed (a triangle per pixel) - if x == height - u = 0 - else - u = (y == mesh.height ? ∇ϕᵤ[x, y-1] : ∇ϕᵤ[x, y]) - end - - if y == mesh.height - v = 0 - else - v = (x == height ? ∇ϕᵥ[x-1, y] : ∇ϕᵥ[x, y]) - end + Vx = ∇ϕᵤ[x, y] + Vy = ∇ϕᵥ[x, y] - velocities[x, y] = Point3D(-u, -v, 0, 0, 0) + mesh.velocities[row, col].vx = -Vx + mesh.velocities[row, col].vy = -Vy end + # The velocity matrix was initialized with zeros everywhere. We nevertheless ovewrite them just in case... + mesh.velocities[:, 1].vx .= 0.0 + mesh.velocities[:, width].vy = 0.0 + + mesh.velocities[1, :].vx .= 0.0 + mesh.velocities[width, :].vy = 0.0 + + # Basically infinity time to shrink a triangle to zip. min_t = 10_000.0 - for i ∈ 1:length(mesh.topTriangles) - triangle = mesh.topTriangles[i] + for row ∈ 1:height, col ∈ 1:width + top_triangle = mesh.topTriangles[row, col] - p1 = mesh.topNodes[triangle.pt1] - p2 = mesh.topNodes[triangle.pt2] - p3 = mesh.topNodes[triangle.pt3] + p1 = top_triangle.pt1 + p2 = top_triangle.pt2 + p3 = top_triangle.pt3 - v1 = velocities[p1.ix, p1.iy] - v2 = velocities[p2.ix, p2.iy] - v3 = velocities[p3.ix, p3.iy] + # Remember the order of the triangle corners + v1 = mesh.velocities[row, col] + v2 = mesh.velocities[row+1, col] + v3 = mesh.velocities[row, col+1] # Get the time, at that velocity, for the area of the triangle to be nil. t1, t2 = find_maximum_t(p1, p2, p3, v1, v2, v3) @@ -343,6 +351,33 @@ function marchMesh!(mesh::Mesh, ϕ::Matrix{Float64}) min_t = t2 end end + + + bot_triangle = mesh.botTriangles[row, col] + + p1 = bot_triangle.pt1 + p2 = bot_triangle.pt2 + p3 = bot_triangle.pt3 + + # Remember the order of the triangle corners + v1 = mesh.velocities[row, col+1] + v2 = mesh.velocities[row+1, col] + v3 = mesh.velocities[row+1, col+1] + + # Get the time, at that velocity, for the area of the triangle to be nil. + t1, t2 = find_maximum_t(p1, p2, p3, v1, v2, v3) + + # We are only interested in positive times. + if !ismissing(t1) + if 0 < t1 < min_t + min_t = t1 + end + + if 0 < t2 < min_t + min_t = t2 + end + end + end println("Overall min_t:", min_t) @@ -350,11 +385,12 @@ function marchMesh!(mesh::Mesh, ϕ::Matrix{Float64}) # Modify the mesh triangles but ensuring that we are far from destroying any of them. δ = min_t / 2 + for row ∈ 1:height, col ∈ 1:width + Vx = velocities[row, col].vx + Vy = velocities[row, col].vy - for point in mesh.topNodes - v = velocities[point.ix, point.iy] - point.x = v.x * δ + point.x - point.y = v.y * δ + point.y + mesh.topTriangles[row, col].pt1.x += δ * Vx + mesh.topTriangles[row, col].pt1.x += δ * Vx end # saveObj(mesh, "gateau.obj") diff --git a/src/utilities.jl b/src/utilities.jl index 03a7694..067301b 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -7,14 +7,13 @@ mutable struct Point3D y::Float64 z::Float64 - # Calculated velocity at those coordinates (velocity along z not necessary) + # Velocity vector (velocity along z not necessary) vx::Float64 vy::Float64 Point3D() = new(0.0, 0.0, 0.0, 0.0, 0.0) end - """ $(SIGNATURES) """ @@ -32,7 +31,7 @@ $(SIGNATURES) A midpoint is the average between two points """ midpoint(p1::Point3D, p2::Point3D) = - Point3D((p1.x + p2.x) / 2.0, (p1.y + p2.y) / 2.0, (p1.z + p2.z) / 2.0, 0, 0) + Point3D((p1.x + p2.x) / 2.0, (p1.y + p2.y) / 2.0, (p1.z + p2.z) / 2.0, 0.0, 0.0) """ @@ -92,32 +91,20 @@ $(TYPEDEF) A mesh is represents a single surface. First the surface is split into rectangles of size (width, height). Then, each rectangle is broken into a top-left triangle and a bottom-right triangle. -`arrays` represents the matrix of rectangles. Since each corner is shared by 4 rectangles, it is enough to +`rectangles` represents the matrix of rectangles. Since each corner is shared by 4 rectangles, it is enough to only record the top-left corner of each. -`nodes` contains the point at the center of a triangle of a given triangle. """ struct Mesh rectangles::Matrix{Point3D} - - topTriangles::Matrix{Triangle} - topNodes::Matrix{Point3D} - - botTriangles::Matrix{Triangle} - botNodes::Matrix{Point3D} - - Mesh(height::Int, width::Int) = new( - Matrix{Point3D}(undef, height, width), - Matrix{Triangle}(undef, height, width), - Matrix{Point3D}(undef, height, width), - Matrix{Triangle}(undef, height, width), - Matrix{Point3D}(undef, height, width), - ) + Mesh(height::Int, width::Int) = new(Matrix{Point3D}(undef, height + 1, width + 1)) end """ $(TYPEDEF) + Meshes representing the block of acrylate. Bottom is facing the light source; Top is facing the caustics. +CHECK whether bottomMesh is at all useful. """ struct TopBottomMeshes height::Int @@ -130,40 +117,6 @@ struct TopBottomMeshes new(height, width, Mesh(height, width), Mesh(height, width)) end -""" -$(SIGNATURES) -""" -function top_triangle_area(mesh::Mesh, height::Int, width::Int) - triangle = mesh.topTriangles[height, width] - pt1 = mesh.topNodes[triangle.pt1] - pt2 = mesh.topNodes[triangle.pt2] - pt3 = mesh.topNodes[triangle.pt3] - - return top_triangle_area(pt1, pt2, pt3) -end - -""" -$(SIGNATURES) -""" -function bot_triangle_area(mesh::Mesh, height::Int, width::Int) - triangle = mesh.topTriangles[height, width] - pt1 = triangle.pt1 - pt2 = triangle.pt2 - pt3 = triangle.pt3 - - return triangle_area(pt1, pt2, pt3) -end - -""" -$(SIGNATURES) -""" -function top_triangle_area(mesh::Mesh, height::Int, width::Int) - mesh_height, _ = size(mesh.topTriangles) - index = height + width * mesh_height - - return top_triangle_area(mesh, index) -end - """ $(SIGNATURES) From 624fbefbf2819ed4d741e8e92df3ecee6c88dede Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Wed, 1 Sep 2021 19:44:51 +0200 Subject: [PATCH 04/58] Refactorig. Snapshot 3 --- src/create_mesh.jl | 421 ++++++++++++------------------------------ src/parameters.jl | 12 +- src/plots.jl | 74 ++++++++ src/test_functions.jl | 42 +++++ src/utilities.jl | 74 +++++--- 5 files changed, 298 insertions(+), 325 deletions(-) create mode 100644 src/plots.jl create mode 100644 src/test_functions.jl diff --git a/src/create_mesh.jl b/src/create_mesh.jl index ace87e0..037f82e 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -3,12 +3,13 @@ $(SIGNATURES) This func returns a square mesh, centered on zero, with (width * height) nodes """ -function create_mesh(width::Int, height::Int) +function create_mesh(height::Int, width::Int) new_mesh = Mesh(height, width) for row = 1:height+1, col = 1:width+1 - new_mesh.rectangles[row, col] = Point3D(Float64(row), Float64(col), 0.0, 0.0, 0.0) + new_mesh.rectangles[row, col] = + Point3D(Float64(row), Float64(col), Height_Offset, 0.0, 0.0) end return new_mesh @@ -18,10 +19,9 @@ end """ $(SIGNATURES) -Given 3 points and 3 velocities, calculate the `t` required to bring the area of that triangle to zero +Given 3 points and their velocities, calculate the time `t` required to bring the area of that triangle to zero """ function find_maximum_t(p1::Point3D, p2::Point3D, p3::Point3D) - # The area of a triangle is 1/2 * [ Ax (By - Cy) + Bx (Cy - Ay) + Cx (Ay - By)] # where each point of the triangle is where it will be after time t # i.e. a point goes from P to P+tV where V is the velocity of that point. @@ -39,8 +39,8 @@ function find_maximum_t(p1::Point3D, p2::Point3D, p3::Point3D) t_vCx = p3.vx - p1.vx t_vCy = p3.vy - p1.vy - # After this, given that Ax = Ay = 0, the area is nil iff - # Bx Cy - Cx By = 0. + # After this, given that Ax = Ay = t_vAx = t_vAy = 0, the area is nil iff + # (Bx + t_vBx) (Cy + t_vCy )- (Cx + t_vCx) (By + t_vBy) = 0. # After expansion and reshuffling to have a quadratic equation where t # is the variable, the coefficients of that equation are: @@ -50,7 +50,7 @@ function find_maximum_t(p1::Point3D, p2::Point3D, p3::Point3D) # if a = 0, this is just a linear equation. if a == 0 - # Fingers crossed that b != 0 + # Fingers crossed that b != 0 but extremely unlikely since B is a Float64. return -c / b, -c / b else @@ -86,7 +86,7 @@ function save_stl!( flipxy = false, ) - height, width = size(mesh.rectangles) + height, width = size(mesh) open(filename, "w") do io for row ∈ 1:height, col ∈ 1:width @@ -95,8 +95,8 @@ function save_stl!( top_triangle_1 = mesh.rectangles[row, col] top_triangle_2 = mesh.rectangles[row+1, col] top_triangle_3 = mesh.rectangles[row, col+1] - n = centroid(top_triangle_1, top_triangle_2, top_triangle_3) + if flipxy println(io, "v $(n.y * scale) $(n.x * scale) $(n.z * scalez)") else @@ -114,8 +114,8 @@ function save_stl!( bot_triangle_1 = mesh.rectangles[row, col+1] bot_triangle_2 = mesh.rectangles[row+1, col] bot_triangle_3 = mesh.rectangles[row+1, col+1] - n = centroid(bot_triangle_1, bot_triangle_2, bot_triangle_3) + if flipxy println(io, "v $(n.y * scale) $(n.x * scale) $(n.z * scalez)") else @@ -131,7 +131,7 @@ function save_stl!( end - # CHECK + # CHECK what dims exactly represents. Number of triangles? println(io, "dims $(2*mesh.width) $(2*mesh.height)") end end @@ -198,36 +198,25 @@ end """ $(SIGNATURES) """ -function getPixelArea(mesh::Mesh) +function get_pixel_area(mesh::Mesh) # A Mesh is a grid of 3D points. The X and Y coordinates are not necessarily aligned or square # The Z coordinate represents the value. brightness is just proportional to area. - height_plus_1, width_plus_1 = size(mesh.rectangles) - height = height_plus_1 - 1 - width = width_plus_1 - 1 + height, width = size(mesh) pixelAreas = zeros(Float64, height, width) for row = 1:height, col = 1:width - #= - *------* - | / | - | / | - | / | - | / | - *------* - =# - - top_triangle_1 = mesh.rectangles[row, col] - top_triangle_2 = mesh.rectangles[row+1, col] - top_triangle_3 = mesh.rectangles[row, col+1] - - bot_triangle_1 = mesh.rectangles[row, col+1] - bot_triangle_2 = mesh.rectangles[row+1, col] - bot_triangle_3 = mesh.rectangles[row+1, col+1] - - pixelAreas[width, col] = - triangle_area(top_triangle_1, top_triangle_2, top_triangle_3) + - triangle_area(bot_triangle_1, bot_triangle_2, bot_triangle_3) + # + # *------* + # | TOP/ | + # | / | + # | / | + # | /BOT | + # *------* + # + pixelAreas[row, col] = + triangle_area(top_triangle(mesh, row, col)) + + triangle_area(bottom_triangle(mesh, row, col)) end return pixelAreas @@ -236,31 +225,31 @@ end """ $(SIGNATURES) -""" -function relax!(height_map::Matrix{Float64}, D::Matrix{Float64}) - # This function implements successive over relaxation for a matrix and its associated error matrix - # There is a hardcoded assumption of Neumann boundary conditions--that the derivative across the - # boundary must be zero in all cases. See: - # https://math.stackexchange.com/questions/3790299/how-to-iteratively-solve-poissons-equation-with-no-boundary-conditions +This function implements successive over relaxation for a matrix and its associated error matrix +There is a hardcoded assumption of Neumann boundary conditions--that the derivative across the +boundary must be zero in all cases. See: +https://math.stackexchange.com/questions/3790299/how-to-iteratively-solve-poissons-equation-with-no-boundary-conditions + +""" +function relax!(height_map::Matrix{Float64}, divergence::Matrix{Float64}) height, width = size(height_map) n_pixels = height * width val_average = sum(height_map) / n_pixels # Embed matrix within a larger matrix for better vectorization and avoid duplicated code - embedding = zeros(Float64, height + 2, width + 2) + container = zeros(Float64, height + 2, width + 2) - embedding[:, :] .= val_average - embedding[2:height+1, 2:height+1] .= height_map[:, :] + container[:, :] .= val_average + container[2:height+1, 2:height+1] .= height_map[:, :] - val_up = embedding[1:height, 2:width+1] - val_down = embedding[3:height+2, 2:width+1] - val_left = embedding[2:height+1, 1:width] - val_right = embedding[2:height+1, 3:width+2] + val_up = container[1:height, 2:width+1] + val_down = container[3:height+2, 2:width+1] + val_left = container[2:height+1, 1:width] + val_right = embcontaineredding[2:height+1, 3:width+2] - delta = (val_up + val_down + val_left + val_right - D) ./ 4.0 - delta = ω .* (delta - height_map) - height_map += delta + delta = (val_up + val_down + val_left + val_right - divergence) ./ 4.0 + height_map = height_map + ω .* (delta - height_map) return maximum(abs.(delta)) end @@ -271,6 +260,7 @@ $(SIGNATURES) This function will take a `grid_definition x grid_definition` matrix and returns a `grid_definition x grid_definition` mesh. + """ function matrix_to_mesh(height_map::Matrix{Float64}) height, width = size(height_map) @@ -279,14 +269,14 @@ function matrix_to_mesh(height_map::Matrix{Float64}) for row = 1:height, col = 1:width result_mesh.rectangles[row, col].z = height_map[row, col] - - result_mesh.topTriangles[row, col].pt1.z = height_map[row, col] - result_mesh.topNodes[row, col].z = height_map[row, col] - - result_mesh.botTriangles[row, col].pt1.z = height_map[row, col] - result_mesh.botNodes[row, col].z = height_map[row, col] end + # The borders height is forced at 0. + result_mesh.rectangles[:, 1].z .= 0.0 + result_mesh.rectangles[:, end].z .= 0.0 + result_mesh.rectangles[1, :].z .= 0.0 + result_mesh.rectangles[end, :].z .= 0.0 + return result_mesh end @@ -294,20 +284,16 @@ end """ $(SIGNATURES) """ -function marchMesh!(mesh::Mesh, ϕ::Matrix{Float64}) +function march_mesh!(mesh::Mesh, ϕ::Matrix{Float64}) ∇ϕᵤ, ∇ϕᵥ = ∇(ϕ) - height, width = size(mesh.rectangles) + height, width = size(mesh) # For each point in the mesh we need to figure out its velocity - # However all velocities on points located at a border will never move + # However all the nodes located at a border will never move # I.e. velocity (Vx, Vy) = (0, 0) and the square of acrylate will remain # of the same size. - for row ∈ 1:height, col ∈ 1:width - # XY coordinates in the mesh ARE XY coordinates in the image. The mesh just needs an extra row and column - # at the bottom right edge so that the triangles can be closed (a triangle per pixel) - Vx = ∇ϕᵤ[x, y] Vy = ∇ϕᵥ[x, y] @@ -317,64 +303,42 @@ function marchMesh!(mesh::Mesh, ϕ::Matrix{Float64}) # The velocity matrix was initialized with zeros everywhere. We nevertheless ovewrite them just in case... mesh.velocities[:, 1].vx .= 0.0 - mesh.velocities[:, width].vy = 0.0 + mesh.velocities[:, end].vy = 0.0 mesh.velocities[1, :].vx .= 0.0 - mesh.velocities[width, :].vy = 0.0 + mesh.velocities[end, :].vy = 0.0 # Basically infinity time to shrink a triangle to zip. min_t = 10_000.0 for row ∈ 1:height, col ∈ 1:width - top_triangle = mesh.topTriangles[row, col] - + top_triangle = top_triangle[row, col] p1 = top_triangle.pt1 p2 = top_triangle.pt2 p3 = top_triangle.pt3 - # Remember the order of the triangle corners - v1 = mesh.velocities[row, col] - v2 = mesh.velocities[row+1, col] - v3 = mesh.velocities[row, col+1] - # Get the time, at that velocity, for the area of the triangle to be nil. - t1, t2 = find_maximum_t(p1, p2, p3, v1, v2, v3) - # We are only interested in positive times. - if !ismissing(t1) - if 0 < t1 < min_t - min_t = t1 - end - - if 0 < t2 < min_t - min_t = t2 + t1, t2 = find_maximum_t(p1, p2, p3) + for t ∈ [t1, t2] + if (!ismissing(t)) && (0 < t < min_t) + min_t = t end end - bot_triangle = mesh.botTriangles[row, col] - + bot_triangle = bottom_triangle[row, col] p1 = bot_triangle.pt1 p2 = bot_triangle.pt2 p3 = bot_triangle.pt3 - # Remember the order of the triangle corners - v1 = mesh.velocities[row, col+1] - v2 = mesh.velocities[row+1, col] - v3 = mesh.velocities[row+1, col+1] - # Get the time, at that velocity, for the area of the triangle to be nil. - t1, t2 = find_maximum_t(p1, p2, p3, v1, v2, v3) - # We are only interested in positive times. - if !ismissing(t1) - if 0 < t1 < min_t - min_t = t1 - end - - if 0 < t2 < min_t - min_t = t2 + t1, t2 = find_maximum_t(p1, p2, p3) + for t ∈ [t1, t2] + if (!ismissing(t)) && (0 < t < min_t) + min_t = t end end @@ -382,15 +346,15 @@ function marchMesh!(mesh::Mesh, ϕ::Matrix{Float64}) println("Overall min_t:", min_t) - # Modify the mesh triangles but ensuring that we are far from destroying any of them. + # Modify the mesh triangles but ensuring that we are far from destroying any of them with a nil area. δ = min_t / 2 for row ∈ 1:height, col ∈ 1:width - Vx = velocities[row, col].vx - Vy = velocities[row, col].vy + Vx = mesh.rectangles[row, col].vx + Vy = mesh.rectangles[row, col].vy - mesh.topTriangles[row, col].pt1.x += δ * Vx - mesh.topTriangles[row, col].pt1.x += δ * Vx + mesh.rectangles[row, col].x += δ * Vx + mesh.rectangles[row, col].y += δ * Vy end # saveObj(mesh, "gateau.obj") @@ -430,10 +394,10 @@ end """ $(SIGNATURES) """ -function oneIteration(meshy, img, suffix) +function single_iteration!(mesh, img, suffix) # Remember meshy is (will be) `grid_definition x grid_definition` just like the image # `grid_definition x grid_definition`, so LJ is `grid_definition x grid_definition`. - LJ = getPixelArea(meshy) + LJ = get_pixel_area(mesh) D = Float64.(LJ - img) # Save the loss image as a png @@ -441,25 +405,18 @@ function oneIteration(meshy, img, suffix) println(maximum(D)) quantifyLoss!(D, suffix, img) - # ∇Lᵤ, ∇Lᵥ = ∇(D) - # plotVAsQuiver(∇Lᵤ, ∇Lᵥ, stride=10, scale=10, max_length=200) - # println("okay") - # return - - # save("./examples/loss_$(suffix).png", colorview(Gray, D)) - # return width, height = size(img) ϕ = Matrix{Float64}(undef, width, height) - for i = 1:Grid_Definition*10 + for i = 1:N_Iterations_Convergence max_update = relax!(ϕ, D) i % 500 == 0 && println(max_update) - max_update < 0.00001 && - println("Convergence reached at step $(i) with max_update of $(max_update)") - break + max_update < 0.00001 && ( + println("Convergence reached at step $(i) with max_update of $(max_update)"); break + ) end save_stl!( @@ -472,64 +429,43 @@ function oneIteration(meshy, img, suffix) # saveObj(matrix_to_mesh(D * 10), "D_$(suffix).obj") # Now we need to march the x,y locations in our mesh according to this gradient! - marchMesh!(meshy, ϕ) - save_stl!(meshy, "./examples/mesh_$(suffix).obj", flipxy = true) + march_mesh!(mesh, ϕ) + save_stl!(mesh, "./examples/mesh_$(suffix).obj", flipxy = true) end """ $(SIGNATURES) """ -function setHeights!(mesh, heights, heightScale = 1.0, heightOffset = 50) - width, height = size(heights) +function set_heights!(mesh, height_map, height_scale = 1.0) + width, height = size(height_map) + + for row ∈ 1:height, col ∈ 1:width + mesh.rectangles[row, col].z = height_map[x, y] * height_scale + Height_Offset - for y = 1:height, x = 1:width - mesh.nodeArray[x, y].z = heights[x, y] * heightScale + heightOffset if x == 100 && y == 100 println( - "Example heights: $(heights[x, y]) and $(heights[x, y] * heightScale) and $(heights[x, y] * heightScale + heightOffset)", + "Example heights: $(height_map[x, y]) and $(height_map[x, y] * heightScale) and $(height_map[x, y] * heightScale + heightOffset)", ) end end - # get the side edge - for y = 1:height - mesh.nodeArray[width+1, y].z = mesh.nodeArray[width, y].z - end - - # get the bottom edge including the pesky corner - for x = 1:width+1 - mesh.nodeArray[x, height+1].z = mesh.nodeArray[x, height].z - end - - # # get the pesky corner! - # mesh.nodeArray[width + 1, height + 1].z = mesh.nodeArray[width, height].z + # Forces the borders at Height_Offset. They will never change because nil velocity. + mesh.rectangles[1, :] .= Height_Offset + mesh.rectangles[end, :] .= Height_Offset + mesh.rectangles[:, 1] .= Height_Offset + mesh.rectangles[:, end] .= Height_Offset end """ $(SIGNATURES) """ -function setHeights(mesh, heightmap) - width = mesh.width - height = mesh.height - nodes = Vector{Point3D}(undef, size(mesh.nodes)) - nodeArray = Matrix{Point3D}(undef, 0, 0) - triangles = Vector{Triangle}(undef, size(mesh.triangles)) - scale = 1.0 - - count = 0 - w, h = size(heightmap) - for y = 1:height, x = 1:width - count += 1 - point = mesh.nodes[count] - - z = heightmap[x, y] - - nodes[count] = Point3D(point.x * scale, point.y * scale, z * scale, 0, 0) - end +function set_heights(height_map, height_scale = 1.0) + height, width = size(height_map) + mesh = create_mesh(height, width) - return Mesh(nodes, nodeArray, triangles, width, height) + return set_heights!(mesh, height_map, height_scale = 1.0) end @@ -537,11 +473,11 @@ end $(SIGNATURES) """ function solidify(inputMesh, offset = 100) - width = inputMesh.width - height = inputMesh.height - totalNodes = width * height * 2 + height, width = size(inputMesh) + totalNodes = width * height * 2 nodeList = Vector{Point3D}(undef, totalNodes) + nodeArrayTop = Matrix{Point3D}(undef, width, height) nodeArrayBottom = Matrix{Point3D}(undef, width, height) @@ -680,20 +616,18 @@ end """ $(SIGNATURES) """ -function findSurface(mesh, image, f, imgWidth) - width, height = size(image) +function find_surface(mesh, image, f = Focal_Length, picture_width = Picture_Side) + height, width = size(image) - # imgWidth = .1 # m - # f = 1.0 # m H = f - metersPerPixel = imgWidth / width + metersPerPixel = picture_width / width println(metersPerPixel) - Nx = zeros(Float64, width + 1, height + 1) - Ny = zeros(Float64, width + 1, height + 1) + Nx = zeros(Float64, height + 1, width + 1) + Ny = zeros(Float64, height + 1, width + 1) - for j = 1:height, i = 1:width - node = mesh.nodeArray[i, j] + for row ∈ 1:height, col ∈ 1:width + node = mesh.nodeArray[row, col] dx = (node.ix - node.x) * metersPerPixel dy = (node.iy - node.y) * metersPerPixel @@ -701,10 +635,7 @@ function findSurface(mesh, image, f, imgWidth) H_minus_h = H - little_h dz = H_minus_h - # k = η * sqrt(dx * dx + dy * dy + H_minus_h * H_minus_h) - H_minus_h - # Nx[i, j] = 1/k * dx - # Ny[i, j] = 1/k * dy Ny[i, j] = tan(atan(dy / dz) / (n₁ - n₂)) Nx[i, j] = tan(atan(dx / dz) / (n₁ - n₂)) end @@ -713,7 +644,7 @@ function findSurface(mesh, image, f, imgWidth) # We need to find the divergence of the Vector field described by Nx and Ny divergence = zeros(Float64, width, height) - for j = 1:height, i = 1:width + for row ∈ 1:height, col ∈ 1:width δx = (Nx[i+1, j] - Nx[i, j]) δy = (Ny[i, j+1] - Ny[i, j]) divergence[i, j] = δx + δy @@ -722,137 +653,21 @@ function findSurface(mesh, image, f, imgWidth) end println("Have all the divergences") - h = zeros(Float64, width, height) + h = zeros(Float64, height, width) max_update = 0 - for i = 1:Grid_Definition*10/2 + for i = 1:N_Iterations_Convergence max_update = relax!(h, divergence) i % 100 == 0 && println(max_update) - max_update < 0.00001 && - println("Convergence reached at step $(i) with max_update of $(max_update)") - break + max_update < 0.00001 && ( + println("Convergence reached at step $(i) with max_update of $(max_update)"); break + ) end # saveObj(matrix_to_mesh(h / 10), "./examples/heightmap.obj") return h, metersPerPixel end -""" -$(SIGNATURES) -""" -function testSquareMesh!() - mesh = create_mesh(100, 50) - - println(mesh.nodeArray[1, 1]) - println(mesh.nodes[1]) - - mesh.nodeArray[1, 1].x = 8 - println(mesh.nodeArray[1, 1]) - println(mesh.nodes[1]) - - mesh.nodes[1].y += 12 - println(mesh.nodeArray[1, 1]) - println(mesh.nodes[1]) -end - - -""" -$(SIGNATURES) -""" -function testSolidify!() - println("Testing solidification") - width = 100 - height = 100 - origMesh = create_mesh(width, height) - - for y = 1:height, x = 1:width - x2 = (x - width / 2) / width - y2 = (y - height / 2) / height - value = x2 * x2 + y2 * y2 - origMesh.nodeArray[x, y].z = 15 - value * 25 - end - - save_stl!(origMesh, "./examples/testSolidify.obj") - solidMesh = solidify(origMesh, 0) - save_stl!(solidMesh, "./examples/testSolidify2.obj") -end - - -""" -$(SIGNATURES) -""" -function plotAsQuiver( - g; - stride = 4, - scale = 300, - max_length = 2, - flipxy = false, - reversey = false, - reversex = false, -) - - h, w = size(g) - xs = Float64[] - ys = Float64[] - us = Float64[] - vs = Float64[] - - for x = 1:stride:w, y = 1:stride:h - reversex ? push!(xs, x) : push!(xs, -x) - reversey ? push!(ys, -y) : push!(ys, y) - - p1 = g[y, x] - u = (g[y, x+1] - g[y, x]) * scale - v = (g[y+1, x] - g[y, x]) * scale - - u = -u - - reversey && (v = -v) - reversex && (u = -u) - - # println(u, v) - u >= 0 ? push!(us, min(u, max_length)) : push!(us, max(u, -max_length)) - v >= 0 ? push!(vs, min(v, max_length)) : push!(vs, max(v, -max_length)) - end - - q = - flipxy ? quiver(ys, xs, quiver = (vs, us), aspect_ratio = :equal) : - quiver(xs, ys, quiver = (us, vs), aspect_ratio = :equal) - - display(q) - readline() -end - - -""" -$(SIGNATURES) -""" -function plotVAsQuiver(vx, vy; stride = 4, scale = 300, max_length = 2) - h, w = size(vx) - - xs = Float64[] - ys = Float64[] - us = Float64[] - vs = Float64[] - - for x = 1:stride:w, y = 1:stride:h - push!(xs, x) - push!(ys, h - y) - - u = max(vx[x, y], 0.001) - v = max(vy[x, y], 0.001) - - push!(us, u) - push!(vs, v) - # println(u, ": ", v) - end - - # readline() - q = quiver(xs, ys, quiver = (us, vs), aspect_ratio = :equal) - display(q) - readline() -end - """ @@ -865,7 +680,7 @@ function engineer_caustics(img) # meshy is the same size as the image with an extra row/column to have coordinates to # cover each image pixel with a triangle. - meshy = create_mesh(width + 1, height + 1) + mesh = create_mesh(width + 1, height + 1) # We need to boost the brightness of the image so that its sum and the sum of the area are equal mesh_sum = width * height @@ -876,20 +691,20 @@ function engineer_caustics(img) # original image. img3 = img2 .* boost_ratio - oneIteration(meshy, img3, "it1") - oneIteration(meshy, img3, "it2") - oneIteration(meshy, img3, "it3") + single_iteration!(mesh, img3, "it1") + single_iteration!(mesh, img3, "it2") + single_iteration!(mesh, img3, "it3") + + # single_teration(meshy, img3, "it4") + # single_teration(meshy, img3, "it5") + # single_teration(meshy, img3, "it6") - # oneIteration(meshy, img3, "it4") - # oneIteration(meshy, img3, "it5") - # oneIteration(meshy, img3, "it6") - h, metersPerPixel = findSurface(meshy, img3, 1.0, Artifact_Size) + h, metersPerPixel = find_surface(mesh, img3, 1.0, Artifact_Size) - setHeights!(meshy, h, 1.0) - # newMesh = setHeights(meshy, h) + set_heights!(mesh, h) - solidMesh = solidify(meshy) + solidMesh = solidify(mesh) save_stl!( solidMesh, "./examples/original_image.obj", @@ -897,7 +712,7 @@ function engineer_caustics(img) scalez = Float64(1 / Grid_Definition * Artifact_Size), ) - return meshy, img3 + return mesh, img3 end diff --git a/src/parameters.jl b/src/parameters.jl index da715a3..36da97e 100644 --- a/src/parameters.jl +++ b/src/parameters.jl @@ -4,11 +4,21 @@ const n₁ = 1.49 # acrylate const n₂ = 1.00 # air +const Height_Offset = 5.0 + ## Optics const Focal_Length = 1.0 # meters const Artifact_Size = 0.15 # meters -# Defined as parameters +# Caustics picture +const Picture_Side = 0.1 # m +const Picture_Height = Picture_Side +const Picture_Width = Picture_Side + + +# calculation +global n_iterations_convergence = 10_000 # CHECK: What is a reasonable number of iterations? + # Currently unused. global Grid_Definition = 512 global Grid_Width = Grid_Definition diff --git a/src/plots.jl b/src/plots.jl new file mode 100644 index 0000000..aa5fa06 --- /dev/null +++ b/src/plots.jl @@ -0,0 +1,74 @@ +""" +$(SIGNATURES) +""" +function plot_as_quiver( + g; + stride = 4, + scale = 300, + max_length = 2, + flipxy = false, + reversey = false, + reversex = false, +) + + h, w = size(g) + xs = Float64[] + ys = Float64[] + us = Float64[] + vs = Float64[] + + for x = 1:stride:w, y = 1:stride:h + reversex ? push!(xs, x) : push!(xs, -x) + reversey ? push!(ys, -y) : push!(ys, y) + + p1 = g[y, x] + u = (g[y, x+1] - g[y, x]) * scale + v = (g[y+1, x] - g[y, x]) * scale + + u = -u + + reversey && (v = -v) + reversex && (u = -u) + + # println(u, v) + u >= 0 ? push!(us, min(u, max_length)) : push!(us, max(u, -max_length)) + v >= 0 ? push!(vs, min(v, max_length)) : push!(vs, max(v, -max_length)) + end + + q = + flipxy ? quiver(ys, xs, quiver = (vs, us), aspect_ratio = :equal) : + quiver(xs, ys, quiver = (us, vs), aspect_ratio = :equal) + + display(q) + readline() +end + + +""" +$(SIGNATURES) +""" +function plot_velocities_as_quiver(vx, vy; stride = 4, scale = 300, max_length = 2) + h, w = size(vx) + + xs = Float64[] + ys = Float64[] + us = Float64[] + vs = Float64[] + + for x = 1:stride:w, y = 1:stride:h + push!(xs, x) + push!(ys, h - y) + + u = max(vx[x, y], 0.001) + v = max(vy[x, y], 0.001) + + push!(us, u) + push!(vs, v) + # println(u, ": ", v) + end + + # readline() + q = quiver(xs, ys, quiver = (us, vs), aspect_ratio = :equal) + display(q) + readline() +end diff --git a/src/test_functions.jl b/src/test_functions.jl new file mode 100644 index 0000000..2003bbd --- /dev/null +++ b/src/test_functions.jl @@ -0,0 +1,42 @@ +""" +$(SIGNATURES) + +""" +function testSquareMesh!() + mesh = create_mesh(100, 50) + + println(mesh.nodeArray[1, 1]) + println(mesh.nodes[1]) + + mesh.nodeArray[1, 1].x = 8 + println(mesh.nodeArray[1, 1]) + println(mesh.nodes[1]) + + mesh.nodes[1].y += 12 + println(mesh.nodeArray[1, 1]) + println(mesh.nodes[1]) +end + + +""" +$(SIGNATURES) + +TO REFACTOR. +""" +function testSolidify!() + println("Testing solidification") + width = 100 + height = 100 + origMesh = create_mesh(width, height) + + for y = 1:height, x = 1:width + x2 = (x - width / 2) / width + y2 = (y - height / 2) / height + value = x2 * x2 + y2 * y2 + origMesh.nodeArray[x, y].z = 15 - value * 25 + end + + save_stl!(origMesh, "./examples/testSolidify.obj") + solidMesh = solidify(origMesh, 0) + save_stl!(solidMesh, "./examples/testSolidify2.obj") +end diff --git a/src/utilities.jl b/src/utilities.jl index 067301b..66df98a 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -11,7 +11,7 @@ mutable struct Point3D vx::Float64 vy::Float64 - Point3D() = new(0.0, 0.0, 0.0, 0.0, 0.0) + Point3D() = new(0.0, 0.0, Height_Offset, 0.0, 0.0) end """ @@ -63,6 +63,25 @@ end """ $(TYPEDEF) + +The algorithm works by allocating a rectangle from the exit mesh (the face where the light exits the block +of acrylate). Initially, each rectangle representsa single pixel on that face and faces s single pixel on +the caustics picture. + +Each rectangle is split into 2 trangles: one upper-left, the other bottom-right like: + +` +*------* +| / | +| / | +| / | +| / | +*------* +` + + +Although the corners of each triangle match corners of the rectangles, it is sometimes easier to think in terms +of triangles rather than corners coming from different rectangles. """ struct Triangle pt1::Point3D @@ -96,28 +115,22 @@ only record the top-left corner of each. """ struct Mesh rectangles::Matrix{Point3D} + Mesh(height::Int, width::Int) = new(Matrix{Point3D}(undef, height + 1, width + 1)) end -""" -$(TYPEDEF) -Meshes representing the block of acrylate. Bottom is facing the light source; Top is facing the caustics. -CHECK whether bottomMesh is at all useful. """ -struct TopBottomMeshes - height::Int - width::Int - - bottomMesh::Mesh - topMesh::Mesh +$(SIGNATURES) - TopBottomMeshes(height::Int, width::Int) = - new(height, width, Mesh(height, width), Mesh(height, width)) +Return the dimension of the mesh as the number of rectangles. It does not return the number of corner points. +""" +function base.size(mesh::Mesh) + height, width = size(mesh.rectangles) + return height - 1, width - 1 end - """ $(SIGNATURES) @@ -132,12 +145,31 @@ function centroid(mesh::Mesh, index::Int) return centroid(p1, p2, p3) end -""" -$(SIGNATURES) -""" -function centroid(mesh::Mesh, height::Int, width::Int) - mesh_height, _ = size(mesh.topTriangles) - index = height + width * mesh_height - return centroid(mesh, index) +function top_triangle(mesh::Mesh, row::Int, col::Int) + height, width = size(mesh) + + if (1 <= row <= height) && (1 <= col <= width) + # The order is important + pt1 = mesh.rectangles[row, col] + pt2 = mesh.rectangles[row+1, col] + pt3 = mesh.rectangles[row, col+1] + return Triangle(pt1, pt2, pt3) + else + return nothing + end +end + +function bottom_triangle(mesh::Mesh, row::Int, col::Int) + height, width = size(mesh) + + if (1 <= row <= height) && (1 <= col <= width) + # The order is important + pt1 = mesh.rectangles[row, col+1] + pt2 = mesh.rectangles[row+1, col] + pt3 = mesh.rectangles[row+1, col+1] + return Triangle(pt1, pt2, pt3) + else + return nothing + end end From 311cd7a193b898940bf4f50aaf58f9880d01d4c9 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Thu, 2 Sep 2021 00:20:21 +0200 Subject: [PATCH 05/58] Refactorig. Snapshot 4 --- src/create_mesh.jl | 273 ++++++++++++++++++--------------------------- src/parameters.jl | 33 ++++-- src/utilities.jl | 129 +++++++++++---------- 3 files changed, 202 insertions(+), 233 deletions(-) diff --git a/src/create_mesh.jl b/src/create_mesh.jl index 037f82e..9c2acc7 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -1,27 +1,9 @@ """ $(SIGNATURES) -This func returns a square mesh, centered on zero, with (width * height) nodes -""" -function create_mesh(height::Int, width::Int) - - new_mesh = Mesh(height, width) - - for row = 1:height+1, col = 1:width+1 - new_mesh.rectangles[row, col] = - Point3D(Float64(row), Float64(col), Height_Offset, 0.0, 0.0) - end - - return new_mesh -end - - -""" -$(SIGNATURES) - Given 3 points and their velocities, calculate the time `t` required to bring the area of that triangle to zero """ -function find_maximum_t(p1::Point3D, p2::Point3D, p3::Point3D) +function find_maximum_t(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) # The area of a triangle is 1/2 * [ Ax (By - Cy) + Bx (Cy - Ay) + Cx (Ay - By)] # where each point of the triangle is where it will be after time t # i.e. a point goes from P to P+tV where V is the velocity of that point. @@ -43,7 +25,6 @@ function find_maximum_t(p1::Point3D, p2::Point3D, p3::Point3D) # (Bx + t_vBx) (Cy + t_vCy )- (Cx + t_vCx) (By + t_vBy) = 0. # After expansion and reshuffling to have a quadratic equation where t # is the variable, the coefficients of that equation are: - a = t_vBy * t_vCx - t_vCy * t_vBx b = By * t_vCx + Cx * t_vBy - (Bx * t_vCy + Cy * t_vBx) c = Cx * By - Bx * Cy @@ -61,6 +42,7 @@ function find_maximum_t(p1::Point3D, p2::Point3D, p3::Point3D) d = sqrt(discriminant) return (-b - d) / 2a, (-b + d) / 2a else + # There can be no solution if, after translation, B abd C move in parallel direction. # C will never end up on the line AB.result_mesh.rectangles[row, col].z = height_map[row, col] result_mesh.rectangles[row, col].z = height_map[row, col] @@ -78,7 +60,7 @@ $(SIGNATURES) This function saves the mesh object in stl format. """ function save_stl!( - mesh::Mesh, + mesh::RectangleMesh, filename::String; scale = 1.0, scalez = 1.0, @@ -92,10 +74,8 @@ function save_stl!( for row ∈ 1:height, col ∈ 1:width # Top triangle - top_triangle_1 = mesh.rectangles[row, col] - top_triangle_2 = mesh.rectangles[row+1, col] - top_triangle_3 = mesh.rectangles[row, col+1] - n = centroid(top_triangle_1, top_triangle_2, top_triangle_3) + top_triangle = top_triangle(mesh, row, col) + n = centroid(top_triangle) if flipxy println(io, "v $(n.y * scale) $(n.x * scale) $(n.z * scalez)") @@ -111,10 +91,8 @@ function save_stl!( # Bottom triangle - bot_triangle_1 = mesh.rectangles[row, col+1] - bot_triangle_2 = mesh.rectangles[row+1, col] - bot_triangle_3 = mesh.rectangles[row+1, col+1] - n = centroid(bot_triangle_1, bot_triangle_2, bot_triangle_3) + bot_triangle = bottom_triangle(mesh, row, col) + n = centroid(bot_triangle) if flipxy println(io, "v $(n.y * scale) $(n.x * scale) $(n.z * scalez)") @@ -146,7 +124,7 @@ function stl_2_mesh(filename) lines = readlines(filename) vertexLines = [l for l in lines if startswith(l, "v")] - nodeList = Vector{Point3D}(undef, size(vertexLines)) + nodeList = Vector{Vertex3D}(undef, size(vertexLines)) count = 0 for line in vertexLines @@ -155,7 +133,7 @@ function stl_2_mesh(filename) x = parse(Float64, elements[2]) y = parse(Float64, elements[3]) z = parse(Float64, elements[4]) * 10 - pt = Point3D(x, y, z, 0, 0) + pt = Vertex3D(x, y, z, 0, 0) nodeList[count] = pt end @@ -173,7 +151,12 @@ function stl_2_mesh(filename) dimsLines = [l for l in lines if startswith(l, "dims")] elements = split(dimsLines[1], " ") - return Mesh(nodeList, triangles, parse(Int64, elements[2]), parse(Int64, elements[3])) + return RectangleMesh( + nodeList, + triangles, + parse(Int64, elements[2]), + parse(Int64, elements[3]), + ) end @@ -198,7 +181,7 @@ end """ $(SIGNATURES) """ -function get_pixel_area(mesh::Mesh) +function get_pixel_area(mesh::RectangleMesh) # A Mesh is a grid of 3D points. The X and Y coordinates are not necessarily aligned or square # The Z coordinate represents the value. brightness is just proportional to area. height, width = size(mesh) @@ -215,7 +198,7 @@ function get_pixel_area(mesh::Mesh) # *------* # pixelAreas[row, col] = - triangle_area(top_triangle(mesh, row, col)) + + triangle_area(top_triangles(mesh, row, col)) + triangle_area(bottom_triangle(mesh, row, col)) end @@ -265,26 +248,31 @@ This function will take a `grid_definition x grid_definition` matrix and returns function matrix_to_mesh(height_map::Matrix{Float64}) height, width = size(height_map) - result_mesh = create_mesh(height, width) + mesh = RectangleMesh(height, width) - for row = 1:height, col = 1:width - result_mesh.rectangles[row, col].z = height_map[row, col] + for row ∈ 1:height, col ∈ 1:width + mesh.vertexList[mesh.to_index(row, col)].z = height_map[row, col] end # The borders height is forced at 0. - result_mesh.rectangles[:, 1].z .= 0.0 - result_mesh.rectangles[:, end].z .= 0.0 - result_mesh.rectangles[1, :].z .= 0.0 - result_mesh.rectangles[end, :].z .= 0.0 + for r ∈ 1:height+1 + mesh.vertexList[mesh.to_index(r, 1)].z = 0.0 + mesh.vertexList[mesh.to_index(r, width + 1)].z = 0.0 + end - return result_mesh + for c ∈ 1:width+1 + mesh.vertexList[mesh.to_index(1, c)].z = 0.0 + mesh.vertexList[mesh.to_index(height + 1, c)].z = 0.0 + end + + return mesh end """ $(SIGNATURES) """ -function march_mesh!(mesh::Mesh, ϕ::Matrix{Float64}) +function march_mesh!(mesh::RectangleMesh, ϕ::Matrix{Float64}) ∇ϕᵤ, ∇ϕᵥ = ∇(ϕ) height, width = size(mesh) @@ -297,26 +285,26 @@ function march_mesh!(mesh::Mesh, ϕ::Matrix{Float64}) Vx = ∇ϕᵤ[x, y] Vy = ∇ϕᵥ[x, y] - mesh.velocities[row, col].vx = -Vx - mesh.velocities[row, col].vy = -Vy + mesh.vertexList[mesh.to_index(row, col)].vx = -Vx + mesh.vertexList[mesh.to_index(row, col)].vy = -Vy end # The velocity matrix was initialized with zeros everywhere. We nevertheless ovewrite them just in case... - mesh.velocities[:, 1].vx .= 0.0 - mesh.velocities[:, end].vy = 0.0 + mesh.rectangles[:, 1].vx .= 0.0 + mesh.rectangles[:, end].vy = 0.0 - mesh.velocities[1, :].vx .= 0.0 - mesh.velocities[end, :].vy = 0.0 + mesh.rectangles[1, :].vx .= 0.0 + mesh.rectangles[end, :].vy = 0.0 # Basically infinity time to shrink a triangle to zip. min_t = 10_000.0 for row ∈ 1:height, col ∈ 1:width - top_triangle = top_triangle[row, col] - p1 = top_triangle.pt1 - p2 = top_triangle.pt2 - p3 = top_triangle.pt3 + top_tri = top_triangles(mesh, row, col) + p1 = top_tri.pt1 + p2 = top_tri.pt2 + p3 = top_tri.pt3 # Get the time, at that velocity, for the area of the triangle to be nil. # We are only interested in positive times. @@ -328,10 +316,10 @@ function march_mesh!(mesh::Mesh, ϕ::Matrix{Float64}) end - bot_triangle = bottom_triangle[row, col] - p1 = bot_triangle.pt1 - p2 = bot_triangle.pt2 - p3 = bot_triangle.pt3 + bottom_tri = bottom_triangle(mesh, row, col) + p1 = bottom_tri.pt1 + p2 = bottom_tri.pt2 + p3 = bottom_tri.pt3 # Get the time, at that velocity, for the area of the triangle to be nil. # We are only interested in positive times. @@ -394,18 +382,18 @@ end """ $(SIGNATURES) """ -function single_iteration!(mesh, img, suffix) +function single_iteration!(mesh, image, suffix) # Remember meshy is (will be) `grid_definition x grid_definition` just like the image # `grid_definition x grid_definition`, so LJ is `grid_definition x grid_definition`. LJ = get_pixel_area(mesh) - D = Float64.(LJ - img) + D = Float64.(LJ - image) # Save the loss image as a png println(minimum(D)) println(maximum(D)) - quantifyLoss!(D, suffix, img) + quantifyLoss!(D, suffix, image) - width, height = size(img) + width, height = size(image) ϕ = Matrix{Float64}(undef, width, height) @@ -437,11 +425,16 @@ end """ $(SIGNATURES) """ -function set_heights!(mesh, height_map, height_scale = 1.0) +function set_heights!( + mesh, + height_map, + height_scale = 1.0, + height_offset = Top_Offset / Meters_Per_Pixel, +) width, height = size(height_map) for row ∈ 1:height, col ∈ 1:width - mesh.rectangles[row, col].z = height_map[x, y] * height_scale + Height_Offset + mesh.rectangles[row, col].z = height_map[x, y] * height_scale + height_offset if x == 100 && y == 100 println( @@ -451,10 +444,10 @@ function set_heights!(mesh, height_map, height_scale = 1.0) end # Forces the borders at Height_Offset. They will never change because nil velocity. - mesh.rectangles[1, :] .= Height_Offset - mesh.rectangles[end, :] .= Height_Offset - mesh.rectangles[:, 1] .= Height_Offset - mesh.rectangles[:, end] .= Height_Offset + mesh.rectangles[1, :] .= height_offset + mesh.rectangles[end, :] .= height_offset + mesh.rectangles[:, 1] .= height_offset + mesh.rectangles[:, end] .= height_offset end @@ -463,7 +456,7 @@ $(SIGNATURES) """ function set_heights(height_map, height_scale = 1.0) height, width = size(height_map) - mesh = create_mesh(height, width) + mesh = RectangleMesh(height, width) return set_heights!(mesh, height_map, height_scale = 1.0) end @@ -472,94 +465,41 @@ end """ $(SIGNATURES) """ -function solidify(inputMesh, offset = 100) - height, width = size(inputMesh) - - totalNodes = width * height * 2 - nodeList = Vector{Point3D}(undef, totalNodes) - - nodeArrayTop = Matrix{Point3D}(undef, width, height) - nodeArrayBottom = Matrix{Point3D}(undef, width, height) +function create_solid(mesh, bottom_offset = Bottom_Offset / Meters_Per_Pixel) + height, width = size(mesh) - # imagine a 4x4 image. 4 * 2 + 2 * 2 = 12 - numEdgeNodes = width * 2 + (height - 2) * 2 + ### + ### Top mesh + ### + # List top mesh top triangles + list_triangles_top_top = [top_triangles(mesh, r, c) for r ∈ 1:height, c ∈ 1:width] - numTrianglesBottom = numTrianglesTop = (width - 1) * (height - 1) * 2 - numTrianglesEdges = numEdgeNodes * 2 + # List top mesh bottom triangles + list_triangles_top_bottom = [bottom_triangle(mesh, r, c) for r ∈ 1:height, c ∈ 1:width] - totalTriangles = numTrianglesBottom + numTrianglesTop + numTrianglesEdges - - println( - "Specs: $(width) $(height) $(totalNodes) $(numEdgeNodes) $(numTrianglesBottom) $(totalTriangles)", - ) + ### + ### Botttom mesh + ### # Build the bottom surface - count = 0 - for y = 1:height, x = 1:width - count += 1 - newPoint = Point3D(x, y, -offset, x, y) - nodeList[count] = newPoint - nodeArrayBottom[x, y] = newPoint - end - - # Copy in the top surface - for y = 1:height, x = 1:width - count += 1 - node = inputMesh.nodeArray[x, y] - copiedPoint = Point3D(node.x, node.y, node.z, node.ix, node.iy) - if node.ix != x - println("OH NO POINTS NOT MATCHED $(x) vs $(node.ix)") - end - if node.iy != y - println("OH NO POINTS NOT MATCHED $(y) vs $(node.iy)") - end - - nodeList[count] = copiedPoint - nodeArrayTop[x, y] = copiedPoint - end - - println("We now have $(count-1) valid nodes") - - # Build the triangles for the bottom surface - triangles = Vector{Triangle}(undef, totalTriangles) - count = 0 - for y = 1:(height-1), x = 1:(width-1) - count += 1 - # here x and y establish the column of squares we're in - index_ul = (y - 1) * width + x - index_ur = index_ul + 1 - - index_ll = y * width + x - index_lr = index_ll + 1 - - triangles[2*count-1] = Triangle(index_ul, index_ll, index_ur) - triangles[2*count] = Triangle(index_lr, index_ur, index_ll) - end - - println("We've filled up $(count-1) triangles") - if 2 * count != numTrianglesBottom - println( - "Hmm aren't count and triangles bottom equal? $(count) vs $(numTrianglesBottom)", - ) + bottom_mesh = RectangleMesh(height, width) + for row = 1:height+1, col = 1:width+1 + bottom_mesh.rectangles[row, col] = Vertex3D(row, col, -offset, 0.0, 0.0) end - # Build the triangles for the top surface - for y = 1:(height-1), x = 1:(width-1) - count += 1 + # List top mesh top triangles + list_triangles_bot_top = + [top_triangles(bottom_mesh, r, c) for r ∈ 1:height, c ∈ 1:width] - # here x and y establish the column of squares we're in - index_ul = (y - 1) * width + x + totalNodes / 2 - index_ur = index_ul + 1 + # List top mesh bottom triangles + list_triangles_bot_bottom = + [bottom_triangle(bottom_mesh, r, c) for r ∈ 1:height, c ∈ 1:width] - index_ll = y * width + x + totalNodes / 2 - index_lr = index_ll + 1 - triangles[2*count-1] = Triangle(index_ul, index_ur, index_ll) - triangles[2*count] = Triangle(index_lr, index_ll, index_ur) - end - - println("We've filled up $(count-1) triangles") + ### + ### Side meshes + ### # Build the triangles to close the mesh x = 1 for y = 1:(height-1) @@ -609,7 +549,7 @@ function solidify(inputMesh, offset = 100) triangles[2*count] = Triangle(ur, ll, lr) end - return Mesh(nodeList, nodeArrayBottom, triangles, width, height) + return RectangleMesh(nodeList, nodeArrayBottom, triangles, width, height) end @@ -617,12 +557,13 @@ end $(SIGNATURES) """ function find_surface(mesh, image, f = Focal_Length, picture_width = Picture_Side) - height, width = size(image) + height, width = size(mesh) H = f metersPerPixel = picture_width / width println(metersPerPixel) + # h(eight) indexes rows, w(idth) indexes columns Nx = zeros(Float64, height + 1, width + 1) Ny = zeros(Float64, height + 1, width + 1) @@ -636,8 +577,8 @@ function find_surface(mesh, image, f = Focal_Length, picture_width = Picture_Sid dz = H_minus_h # k = η * sqrt(dx * dx + dy * dy + H_minus_h * H_minus_h) - H_minus_h - Ny[i, j] = tan(atan(dy / dz) / (n₁ - n₂)) - Nx[i, j] = tan(atan(dx / dz) / (n₁ - n₂)) + Nx[row, col] = tan(atan(dx / dz) / (n₁ - n₂)) + Ny[row, col] = tan(atan(dy / dz) / (n₁ - n₂)) end @@ -645,26 +586,30 @@ function find_surface(mesh, image, f = Focal_Length, picture_width = Picture_Sid divergence = zeros(Float64, width, height) for row ∈ 1:height, col ∈ 1:width - δx = (Nx[i+1, j] - Nx[i, j]) - δy = (Ny[i, j+1] - Ny[i, j]) - divergence[i, j] = δx + δy + δx = Nx[row+1, col] - Nx[row, col] + δy = Ny[row, col+1] - Ny[row, col] + divergence[row, col] = δx + δy - i == 100 && j == 100 && println("div: $(divergence[i, j])") + (row % 100 == 0) && + (col % 100 == 0) && + println("div[$(row), $(col)]: $(divergence[row, col])") end println("Have all the divergences") - h = zeros(Float64, height, width) - max_update = 0 - for i = 1:N_Iterations_Convergence - max_update = relax!(h, divergence) + height_map = zeros(Float64, height, width) + max_update = 0.0 + for iter = 1:N_Iterations_Convergence + max_update = relax!(height_map, divergence) - i % 100 == 0 && println(max_update) - max_update < 0.00001 && ( - println("Convergence reached at step $(i) with max_update of $(max_update)"); break - ) + iter % 100 == 0 && println(max_update) + if max_update < 0.00001 + println("Convergence reached at step $(iter) with max_update of $(max_update)") + break + end end + # saveObj(matrix_to_mesh(h / 10), "./examples/heightmap.obj") - return h, metersPerPixel + return height_map, metersPerPixel end @@ -680,7 +625,7 @@ function engineer_caustics(img) # meshy is the same size as the image with an extra row/column to have coordinates to # cover each image pixel with a triangle. - mesh = create_mesh(width + 1, height + 1) + mesh = RectangleMesh(width + 1, height + 1) # We need to boost the brightness of the image so that its sum and the sum of the area are equal mesh_sum = width * height @@ -704,7 +649,7 @@ function engineer_caustics(img) set_heights!(mesh, h) - solidMesh = solidify(mesh) + solidMesh = create_solid(mesh) save_stl!( solidMesh, "./examples/original_image.obj", diff --git a/src/parameters.jl b/src/parameters.jl index 36da97e..349ce06 100644 --- a/src/parameters.jl +++ b/src/parameters.jl @@ -1,27 +1,36 @@ # Constants +# Physical parameters + ## Materials const n₁ = 1.49 # acrylate const n₂ = 1.00 # air -const Height_Offset = 5.0 +## The sides of the block to be carved +const Block_Side = 0.15 # meters +const Block_Height = Block_Side +const Block_Width = Block_Side + +## Depth parameters. If we imagine a reference place, the top face (facing the caustics) is at +## Top_Offset above it. The flat face facing the light source is Bottom below it. +const Top_Offset = 0.01 # 1 centimeters +const Bottom_Offset = 0.02 # 2 centimeters ## Optics const Focal_Length = 1.0 # meters -const Artifact_Size = 0.15 # meters + +const Caustics_Side = 0.1 # m +const Caustics_Height = Caustics_Side + # Caustics picture -const Picture_Side = 0.1 # m -const Picture_Height = Picture_Side -const Picture_Width = Picture_Side +const N_Pixel_Side = 512 +const N_Pixel_Height = N_Pixel_Side +const N_Pixel_Width = N_Pixel_Side + +global Meters_Per_Pixel = Caustics_Height / N_Pixel_Height # calculation +const ω = 2 / (1 + π / sqrt(N_Pixel_Height * N_Pixel_Width)) global n_iterations_convergence = 10_000 # CHECK: What is a reasonable number of iterations? - -# Currently unused. -global Grid_Definition = 512 -global Grid_Width = Grid_Definition -global Grid_Height = Grid_Definition - -const ω = 2 / (1 + π / Grid_Width) diff --git a/src/utilities.jl b/src/utilities.jl index 66df98a..ee7df1a 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -1,23 +1,32 @@ """ $(TYPEDEF) + +## Coordinates + +Origin is top left, going right and down .`x` goes horizontal and follows columns. x is within 1 and width +`y` goes vertical and follows rows. y is within 1 and height. + +# Velocity + +Velocity vector along `x` and `y` (velocity along z not necessary). + """ -mutable struct Point3D - # Coordinates +mutable struct Vertex3D x::Float64 y::Float64 z::Float64 - # Velocity vector (velocity along z not necessary) vx::Float64 vy::Float64 - Point3D() = new(0.0, 0.0, Height_Offset, 0.0, 0.0) + Vertex3D() = new(0.0, 0.0, Height_Offset, 0.0, 0.0) end + """ $(SIGNATURES) """ -function dist(p1::Point3D, p2::Point3D) +function dist(p1::Vertex3D, p2::Vertex3D) dx = p2.x - p1.x dy = p2.y - p1.y dz = p2.z - p1.z @@ -30,8 +39,8 @@ $(SIGNATURES) A midpoint is the average between two points """ -midpoint(p1::Point3D, p2::Point3D) = - Point3D((p1.x + p2.x) / 2.0, (p1.y + p2.y) / 2.0, (p1.z + p2.z) / 2.0, 0.0, 0.0) +midpoint(p1::Vertex3D, p2::Vertex3D) = + Vertex3D((p1.x + p2.x) / 2.0, (p1.y + p2.y) / 2.0, (p1.z + p2.z) / 2.0, 0.0, 0.0) """ @@ -39,7 +48,7 @@ $(SIGNATURES) Barycentre of three points. """ -centroid(p1::Point3D, p2::Point3D, p3::Point3D) = Point3D( +centroid(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) = Vertex3D( (p1.x + p2.x + p3.x) / 3.0, (p1.y + p2.y + p3.y) / 3.0, (p1.z + p2.z + p3.z) / 3.0, @@ -51,7 +60,7 @@ centroid(p1::Point3D, p2::Point3D, p3::Point3D) = Point3D( """ $(SIGNATURES) """ -function triangle_area(p1::Point3D, p2::Point3D, p3::Point3D) +function triangle_area(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) a = dist(p1, p2) b = dist(p2, p3) c = dist(p3, p1) @@ -70,53 +79,64 @@ the caustics picture. Each rectangle is split into 2 trangles: one upper-left, the other bottom-right like: -` +``` *------* | / | | / | | / | | / | *------* -` +``` Although the corners of each triangle match corners of the rectangles, it is sometimes easier to think in terms of triangles rather than corners coming from different rectangles. """ -struct Triangle - pt1::Point3D - pt2::Point3D - pt3::Point3D +Triangle = Tuple{UInt64,UInt64,UInt64} - Triangle() = new(Point3D(), Point3D(), Point3D()) - Triangle(pt1, pt2, pt3) = new(pt1, pt2, pt3) -end """ -$(SIGNATURES) -""" -centroid(t::Triangle) = centroid(t.p1, t.p2, t.p3) +$(TYPEDEF) +A Rectagle mesh represents a single face of the block. The most important face is the one facing the cautics. +First the surface is split into rectangles each associated with a pixel. Then, each rectangle is broken +into a top-left triangle and a bottom-right triangle. + +`VertexList` is the list of all the vertices (i.e. points) in the mesh. the list of triangles is split in 2. +Each triangle is a triplet of indices, each pointing to the relevant position in the list of vertices. + +The vertices are numbered by rows, then by columns. """ -$(SIGNATURES) -""" -triangle_area(t::Triangle) = triangle_area(t.p1, t.p2, t.p3) +struct RectangleMesh + height::UInt64 + width::UInt64 + vertexList::Vector{Vertex3D} + topTriangles::Matrix{Triangle} + botTriangles::Matrix{Triangle} + as_index::Function + function RectangleMesh(height::Int, width::Int) -""" -$(TYPEDEF) + to_index(r, c) = r + (c - 1) * (width + 1) -A mesh is represents a single surface. First the surface is split into rectangles of size (width, height). Then, -each rectangle is broken into a top-left triangle and a bottom-right triangle. + vertices = Vector{Vertex3D}(undef, (height + 1) * (width + 1)) + for row = 1:height+1, col = 1:width+1 + vertices[to_index(row, col)] = + Vertex3D(Float64(row), Float64(col), Height_Offset, 0.0, 0.0) + end -`rectangles` represents the matrix of rectangles. Since each corner is shared by 4 rectangles, it is enough to -only record the top-left corner of each. -""" -struct Mesh - rectangles::Matrix{Point3D} + top_triangles = Matrix{Triangle}(undef, height, width) + bot_triangles = Matrix{Triangle}(undef, height, width) + for row = 1:height, col = 1:width + top_triangles[row, col] = + (to_index(row, col), to_index(row + 1, col), to_index(row, col + 1)) + bot_triangles[row, col] = + (to_index(row, col + 1), to_index(row + 1, col), to_index(row + 1, col + 1)) + end - Mesh(height::Int, width::Int) = new(Matrix{Point3D}(undef, height + 1, width + 1)) + return new(height, width, vertexList, top_triangles, bot_triangles, to_index) + end end @@ -126,49 +146,44 @@ $(SIGNATURES) Return the dimension of the mesh as the number of rectangles. It does not return the number of corner points. """ -function base.size(mesh::Mesh) - height, width = size(mesh.rectangles) - return height - 1, width - 1 +function base.size(mesh::RectangleMesh) + return mesh.height, mesh.width end """ $(SIGNATURES) +""" +triangle3D(mesh::Mesh, t::Triangle) = + [mesh.vertexList(t[1]), mesh.vertexList(t[1]), mesh.vertexList(t[1])] -Warning: not guaranteed to work in 3D? """ -function centroid(mesh::Mesh, index::Int) - triangle = mesh.topTriangles[index] - p1 = mesh.topNodes[triangle.pt1] - p2 = mesh.topNodes[triangle.pt2] - p3 = mesh.topNodes[triangle.pt3] +$(SIGNATURES) +""" +centroid(mesh::Mesh, t::Triangle) = centroid(triangle3D(mesh, t)...) + + +""" +$(SIGNATURES) +""" +triangle_area(mesh::Mesh, t::Triangle) = triangle_area(triangle3D(mesh, t)...) - return centroid(p1, p2, p3) -end -function top_triangle(mesh::Mesh, row::Int, col::Int) +function top_triangle(mesh::RectangleMesh, row::Int, col::Int) height, width = size(mesh) if (1 <= row <= height) && (1 <= col <= width) - # The order is important - pt1 = mesh.rectangles[row, col] - pt2 = mesh.rectangles[row+1, col] - pt3 = mesh.rectangles[row, col+1] - return Triangle(pt1, pt2, pt3) + return mesh.topTriangles(row, col) else return nothing end end -function bottom_triangle(mesh::Mesh, row::Int, col::Int) +function bottom_triangle(mesh::RectangleMesh, row::Int, col::Int) height, width = size(mesh) if (1 <= row <= height) && (1 <= col <= width) - # The order is important - pt1 = mesh.rectangles[row, col+1] - pt2 = mesh.rectangles[row+1, col] - pt3 = mesh.rectangles[row+1, col+1] - return Triangle(pt1, pt2, pt3) + return mesh.botTriangles(row, col) else return nothing end From 9e12ce9c09a19c914a8b248e972910419493f1ad Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Thu, 2 Sep 2021 14:30:57 +0200 Subject: [PATCH 06/58] Refactorig. Snapshot 5 --- Project.toml | 3 + src/CausticsEngineering.jl | 2 + src/create_mesh.jl | 276 +++++++++---------------------------- src/io.jl | 113 +++++++++++++++ src/utilities.jl | 195 +++++++++++++++++--------- 5 files changed, 315 insertions(+), 274 deletions(-) create mode 100644 src/io.jl diff --git a/Project.toml b/Project.toml index 61a1bcf..2628409 100644 --- a/Project.toml +++ b/Project.toml @@ -7,8 +7,11 @@ version = "0.1.0" DocStringExtensions = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae" Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4" DocumenterTools = "35a29f4d-8980-5a13-9543-d66fff28ecb8" +FileIO = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549" Images = "916415d5-f1e6-5110-898d-aaa5f9f070e0" JuliaFormatter = "98e50ef6-434e-11e9-1051-2b60c6c9e899" +MeshIO = "7269a6da-0436-5bbc-96c2-40638cbb6118" +Meshes = "eacbb407-ea5a-433e-ab97-5258b1ca43fa" Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" [compat] diff --git a/src/CausticsEngineering.jl b/src/CausticsEngineering.jl index 3a1d8a3..a533737 100644 --- a/src/CausticsEngineering.jl +++ b/src/CausticsEngineering.jl @@ -2,6 +2,8 @@ module CausticsEngineering using DocStringExtensions +using meshes + using Images, Plots gr() diff --git a/src/create_mesh.jl b/src/create_mesh.jl index 9c2acc7..9f3bc57 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -54,111 +54,7 @@ function find_maximum_t(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) end -""" -$(SIGNATURES) - -This function saves the mesh object in stl format. -""" -function save_stl!( - mesh::RectangleMesh, - filename::String; - scale = 1.0, - scalez = 1.0, - reverse = false, - flipxy = false, -) - - height, width = size(mesh) - - open(filename, "w") do io - for row ∈ 1:height, col ∈ 1:width - - # Top triangle - top_triangle = top_triangle(mesh, row, col) - n = centroid(top_triangle) - - if flipxy - println(io, "v $(n.y * scale) $(n.x * scale) $(n.z * scalez)") - else - println(io, "v $(n.x * scale) $(n.y * scale) $(n.z * scalez)") - end - - if flipxy - println(io, "v $(n.y * scale) $(n.x * scale) $(n.z * scalez)") - else - println(io, "v $(n.x * scale) $(n.y * scale) $(n.z * scalez)") - end - - - # Bottom triangle - bot_triangle = bottom_triangle(mesh, row, col) - n = centroid(bot_triangle) - - if flipxy - println(io, "v $(n.y * scale) $(n.x * scale) $(n.z * scalez)") - else - println(io, "v $(n.x * scale) $(n.y * scale) $(n.z * scalez)") - end - - if flipxy - println(io, "v $(n.y * scale) $(n.x * scale) $(n.z * scalez)") - else - println(io, "v $(n.x * scale) $(n.y * scale) $(n.z * scalez)") - end - - - end - - # CHECK what dims exactly represents. Number of triangles? - println(io, "dims $(2*mesh.width) $(2*mesh.height)") - end -end - - -""" -$(SIGNATURES) - -TO REFACTOR. -""" -function stl_2_mesh(filename) - lines = readlines(filename) - - vertexLines = [l for l in lines if startswith(l, "v")] - nodeList = Vector{Vertex3D}(undef, size(vertexLines)) - - count = 0 - for line in vertexLines - count += 1 - elements = split(line, " ") - x = parse(Float64, elements[2]) - y = parse(Float64, elements[3]) - z = parse(Float64, elements[4]) * 10 - pt = Vertex3D(x, y, z, 0, 0) - nodeList[count] = pt - end - - faceLines = [l for l in lines if startswith(l, "f")] - triangles = Vector{Triangle}(undef, size(faceLines)) - for line in faceLines - elements = split(line, " ") - triangles[line] = Triangle( - parse(Int64, elements[2]), - parse(Int64, elements[3]), - parse(Int64, elements[4]), - ) - end - - dimsLines = [l for l in lines if startswith(l, "dims")] - elements = split(dimsLines[1], " ") - - return RectangleMesh( - nodeList, - triangles, - parse(Int64, elements[2]), - parse(Int64, elements[3]), - ) -end - +find_maximum_t(p::Tuple{Vertex3D,Vertex3D,Vertex3D}) = find_maximum_t(p[1], p[2], p[3]) """ $(SIGNATURES) @@ -169,9 +65,11 @@ function ∇(ϕ::Matrix{Float64}) ∇ϕᵤ = zeros(Float64, width, height) # the right edge will be filled with zeros ∇ϕᵥ = zeros(Float64, width, height) # the buttom edge will be filled with zeros - for row = 1:height, col = 1:width - ∇ϕᵤ[row, col] = ϕ[row+1, col] - ϕ[row, col] - ∇ϕᵥ[row, col] = ϕ[row, col+1] - ϕ[row, col] + for ci ∈ CartesianIndex(ϕ) + row = ci[1] + col = ci[2] + ∇ϕᵤ[ci] = ϕ[row+1, col] - ϕ[row, col] + ∇ϕᵥ[ci] = ϕ[row, col+1] - ϕ[row, col] end return ∇ϕᵤ, ∇ϕᵥ @@ -188,7 +86,7 @@ function get_pixel_area(mesh::RectangleMesh) pixelAreas = zeros(Float64, height, width) - for row = 1:height, col = 1:width + for ci ∈ CartesianIndex # # *------* # | TOP/ | @@ -197,9 +95,7 @@ function get_pixel_area(mesh::RectangleMesh) # | /BOT | # *------* # - pixelAreas[row, col] = - triangle_area(top_triangles(mesh, row, col)) + - triangle_area(bottom_triangle(mesh, row, col)) + pixelAreas[ci] = area(top_triangles(mesh, ci)) + area(bottom_triangle(mesh, ci)) end return pixelAreas @@ -223,7 +119,7 @@ function relax!(height_map::Matrix{Float64}, divergence::Matrix{Float64}) # Embed matrix within a larger matrix for better vectorization and avoid duplicated code container = zeros(Float64, height + 2, width + 2) - container[:, :] .= val_average + container .= val_average container[2:height+1, 2:height+1] .= height_map[:, :] val_up = container[1:height, 2:width+1] @@ -248,22 +144,15 @@ This function will take a `grid_definition x grid_definition` matrix and returns function matrix_to_mesh(height_map::Matrix{Float64}) height, width = size(height_map) - mesh = RectangleMesh(height, width) - - for row ∈ 1:height, col ∈ 1:width - mesh.vertexList[mesh.to_index(row, col)].z = height_map[row, col] - end + mesh = FaceMesh(height, width) + mesh.vertexList[:].z .= height_map[:] # The borders height is forced at 0. - for r ∈ 1:height+1 - mesh.vertexList[mesh.to_index(r, 1)].z = 0.0 - mesh.vertexList[mesh.to_index(r, width + 1)].z = 0.0 - end + mesh.topleft[CartesianIndex(:, 1)].z .= 0.0 + mesh.topleft[CartesianIndex(:, end)].z .= 0.0 - for c ∈ 1:width+1 - mesh.vertexList[mesh.to_index(1, c)].z = 0.0 - mesh.vertexList[mesh.to_index(height + 1, c)].z = 0.0 - end + mesh.topleft[CartesianIndex(1, :)].z .= 0.0 + mesh.topleft[CartesianIndex(end, :)].z .= 0.0 return mesh end @@ -272,7 +161,7 @@ end """ $(SIGNATURES) """ -function march_mesh!(mesh::RectangleMesh, ϕ::Matrix{Float64}) +function march_mesh!(mesh::FaceMesh, ϕ::Matrix{Float64}) ∇ϕᵤ, ∇ϕᵥ = ∇(ϕ) height, width = size(mesh) @@ -281,34 +170,30 @@ function march_mesh!(mesh::RectangleMesh, ϕ::Matrix{Float64}) # However all the nodes located at a border will never move # I.e. velocity (Vx, Vy) = (0, 0) and the square of acrylate will remain # of the same size. - for row ∈ 1:height, col ∈ 1:width - Vx = ∇ϕᵤ[x, y] - Vy = ∇ϕᵥ[x, y] - - mesh.vertexList[mesh.to_index(row, col)].vx = -Vx - mesh.vertexList[mesh.to_index(row, col)].vy = -Vy - end + mesh.topleft[:, :][1].vx .= -∇ϕᵤ[:, :] + mesh.topleft[:, :][1].vy .= -∇ϕᵥ[:, :] # The velocity matrix was initialized with zeros everywhere. We nevertheless ovewrite them just in case... - mesh.rectangles[:, 1].vx .= 0.0 - mesh.rectangles[:, end].vy = 0.0 + mesh.topleft[:, 1].vx .= 0.0 + mesh.topleft[:, 1].vy .= 0.0 + mesh.topleft[:, end].vx .= 0.0 + mesh.topleft[:, end].vy .= 0.0 - mesh.rectangles[1, :].vx .= 0.0 - mesh.rectangles[end, :].vy = 0.0 + mesh.topleft[1, :].vx .= 0.0 + mesh.topleft[1, :].vy .= 0.0 + mesh.topleft[end, :].vx = 0.0 + mesh.topleft[end, :].vy = 0.0 # Basically infinity time to shrink a triangle to zip. min_t = 10_000.0 - for row ∈ 1:height, col ∈ 1:width - top_tri = top_triangles(mesh, row, col) - p1 = top_tri.pt1 - p2 = top_tri.pt2 - p3 = top_tri.pt3 + for ci ∈ CartesianIndices(ϕ) + top_tri = top_triangles3D(mesh, ci) # Get the time, at that velocity, for the area of the triangle to be nil. # We are only interested in positive times. - t1, t2 = find_maximum_t(p1, p2, p3) + t1, t2 = find_maximum_t(top_tri) for t ∈ [t1, t2] if (!ismissing(t)) && (0 < t < min_t) min_t = t @@ -316,14 +201,11 @@ function march_mesh!(mesh::RectangleMesh, ϕ::Matrix{Float64}) end - bottom_tri = bottom_triangle(mesh, row, col) - p1 = bottom_tri.pt1 - p2 = bottom_tri.pt2 - p3 = bottom_tri.pt3 + bot_tri = bot_triangle3D(mesh, ci) # Get the time, at that velocity, for the area of the triangle to be nil. # We are only interested in positive times. - t1, t2 = find_maximum_t(p1, p2, p3) + t1, t2 = find_maximum_t(bot_tri) for t ∈ [t1, t2] if (!ismissing(t)) && (0 < t < min_t) min_t = t @@ -337,13 +219,8 @@ function march_mesh!(mesh::RectangleMesh, ϕ::Matrix{Float64}) # Modify the mesh triangles but ensuring that we are far from destroying any of them with a nil area. δ = min_t / 2 - for row ∈ 1:height, col ∈ 1:width - Vx = mesh.rectangles[row, col].vx - Vy = mesh.rectangles[row, col].vy - - mesh.rectangles[row, col].x += δ * Vx - mesh.rectangles[row, col].y += δ * Vy - end + mesh.topleft[:, :].x .+= δ * mesh.rectangles[:, :].vx + mesh.topleft[:, :].y .+= δ * mesh.rectangles[:, :].vy # saveObj(mesh, "gateau.obj") end @@ -433,15 +310,7 @@ function set_heights!( ) width, height = size(height_map) - for row ∈ 1:height, col ∈ 1:width - mesh.rectangles[row, col].z = height_map[x, y] * height_scale + height_offset - - if x == 100 && y == 100 - println( - "Example heights: $(height_map[x, y]) and $(height_map[x, y] * heightScale) and $(height_map[x, y] * heightScale + heightOffset)", - ) - end - end + mesh.rectangles[:, :].z .= height_map[:, :] * height_scale + height_offset # Forces the borders at Height_Offset. They will never change because nil velocity. mesh.rectangles[1, :] .= height_offset @@ -481,22 +350,14 @@ function create_solid(mesh, bottom_offset = Bottom_Offset / Meters_Per_Pixel) ### ### Botttom mesh ### - # Build the bottom surface - bottom_mesh = RectangleMesh(height, width) - for row = 1:height+1, col = 1:width+1 - bottom_mesh.rectangles[row, col] = Vertex3D(row, col, -offset, 0.0, 0.0) + # Build the bottom surface which is prepopulated by its constructor. However, its height is incorrect. + bottom_mesh = FaceMesh(height, width) + for ci ∈ CartesianIndices(bottom_mesh) + row = ci[1] + col = ci[2] + bottom_mesh.topleft[ci] = Vertex3D(row, col, -Bottom_Offset, 0.0, 0.0) end - # List top mesh top triangles - list_triangles_bot_top = - [top_triangles(bottom_mesh, r, c) for r ∈ 1:height, c ∈ 1:width] - - # List top mesh bottom triangles - list_triangles_bot_bottom = - [bottom_triangle(bottom_mesh, r, c) for r ∈ 1:height, c ∈ 1:width] - - - ### ### Side meshes ### @@ -556,44 +417,42 @@ end """ $(SIGNATURES) """ -function find_surface(mesh, image, f = Focal_Length, picture_width = Picture_Side) +function find_surface( + mesh::FaceMesh, + image, + f = Focal_Length, + picture_width = Caustics_Side, +) height, width = size(mesh) - H = f - metersPerPixel = picture_width / width - println(metersPerPixel) + # H is the initial distance from the surface of the carved face to the projection screen. + # H is constant and does not account for the change in heights due to carving. + # The focal length is in meters. H is in Pixels. + H = f / Meters_Per_Pixel # h(eight) indexes rows, w(idth) indexes columns Nx = zeros(Float64, height + 1, width + 1) Ny = zeros(Float64, height + 1, width + 1) - for row ∈ 1:height, col ∈ 1:width - node = mesh.nodeArray[row, col] - dx = (node.ix - node.x) * metersPerPixel - dy = (node.iy - node.y) * metersPerPixel + for ci ∈ CartesianIndices(mesh.nodeArray) + node = mesh.nodeArray[ci] + dx = (node.ix - node.x) + dy = (node.iy - node.y) - little_h = node.z * metersPerPixel - H_minus_h = H - little_h - dz = H_minus_h + true_H = H - node.z - # k = η * sqrt(dx * dx + dy * dy + H_minus_h * H_minus_h) - H_minus_h - Nx[row, col] = tan(atan(dx / dz) / (n₁ - n₂)) - Ny[row, col] = tan(atan(dy / dz) / (n₁ - n₂)) + Nx[ci] = tan(atan(dx / true_H) / (n₁ - n₂)) + Ny[ci] = tan(atan(dy / true_H) / (n₁ - n₂)) end - # We need to find the divergence of the Vector field described by Nx and Ny divergence = zeros(Float64, width, height) + δr = zeros(Float64, width, height) + δc = zeros(Float64, width, height) - for row ∈ 1:height, col ∈ 1:width - δx = Nx[row+1, col] - Nx[row, col] - δy = Ny[row, col+1] - Ny[row, col] - divergence[row, col] = δx + δy - - (row % 100 == 0) && - (col % 100 == 0) && - println("div[$(row), $(col)]: $(divergence[row, col])") - end + δr[:, :] .= Nx[2:end, 1:end-1] .- Nx[1:end-1, 1:end-1] + δc[:, :] .= Nx[1:end-1, 2:end] .- Ny[1:end-1, 1:end-1] + divergence = δx + δy println("Have all the divergences") height_map = zeros(Float64, height, width) @@ -609,7 +468,7 @@ function find_surface(mesh, image, f = Focal_Length, picture_width = Picture_Sid end # saveObj(matrix_to_mesh(h / 10), "./examples/heightmap.obj") - return height_map, metersPerPixel + return height_map end @@ -625,16 +484,15 @@ function engineer_caustics(img) # meshy is the same size as the image with an extra row/column to have coordinates to # cover each image pixel with a triangle. - mesh = RectangleMesh(width + 1, height + 1) + mesh = FaceMesh(width, height) # We need to boost the brightness of the image so that its sum and the sum of the area are equal - mesh_sum = width * height image_sum = sum(img2) - boost_ratio = mesh_sum / image_sum + average_intensity = image_sum / (width * height) # img3 is `grid_definition x grid_definition` and is normalised to the same (sort of) _energy_ as the # original image. - img3 = img2 .* boost_ratio + img3 = img2 ./ average_intensity single_iteration!(mesh, img3, "it1") single_iteration!(mesh, img3, "it2") @@ -645,7 +503,7 @@ function engineer_caustics(img) # single_teration(meshy, img3, "it6") - h, metersPerPixel = find_surface(mesh, img3, 1.0, Artifact_Size) + h = find_surface(mesh, img3, 1.0, Artifact_Size) set_heights!(mesh, h) diff --git a/src/io.jl b/src/io.jl new file mode 100644 index 0000000..cb3fe68 --- /dev/null +++ b/src/io.jl @@ -0,0 +1,113 @@ +using FileIO, MeshIO + +""" +$(SIGNATURES) + +This function saves the mesh object in stl format. + +The format difinition is sourced from [https://en.wikipedia.org/wiki/STL_(file_format)](). +""" +function save_stl!( + mesh::FaceMesh, + filename::String; + scale = 1.0, + scalez = 1.0, + reverse = false, + flipxy = false, +) + + height, width = size(mesh) + + open(filename, "w") do io + + println(io, "solid engineered_caustics") + + for row ∈ 1:height, col ∈ 1:width + + # Top triangle + top_triangle = top_triangle(mesh, row, col) + n = centroid(top_triangle) + + if flipxy + println(io, "v $(n.y * scale) $(n.x * scale) $(n.z * scalez)") + else + println(io, "v $(n.x * scale) $(n.y * scale) $(n.z * scalez)") + end + + if flipxy + println(io, "v $(n.y * scale) $(n.x * scale) $(n.z * scalez)") + else + println(io, "v $(n.x * scale) $(n.y * scale) $(n.z * scalez)") + end + + + # Bottom triangle + bot_triangle = bottom_triangle(mesh, row, col) + n = centroid(bot_triangle) + + if flipxy + println(io, "v $(n.y * scale) $(n.x * scale) $(n.z * scalez)") + else + println(io, "v $(n.x * scale) $(n.y * scale) $(n.z * scalez)") + end + + if flipxy + println(io, "v $(n.y * scale) $(n.x * scale) $(n.z * scalez)") + else + println(io, "v $(n.x * scale) $(n.y * scale) $(n.z * scalez)") + end + + + end + + # CHECK what dims exactly represents. Number of triangles? + println(io, "dims $(2*mesh.width) $(2*mesh.height)") + + println(io, "endsolid engineered_caustics") + end +end + + +""" +$(SIGNATURES) + +TO REFACTOR. +""" +function stl_2_mesh(filename) + lines = readlines(filename) + + vertexLines = [l for l in lines if startswith(l, "v")] + nodeList = Vector{Vertex3D}(undef, size(vertexLines)) + + count = 0 + for line in vertexLines + count += 1 + elements = split(line, " ") + x = parse(Float64, elements[2]) + y = parse(Float64, elements[3]) + z = parse(Float64, elements[4]) * 10 + pt = Vertex3D(x, y, z, 0, 0) + nodeList[count] = pt + end + + faceLines = [l for l in lines if startswith(l, "f")] + triangles = Vector{Triangle}(undef, size(faceLines)) + for line in faceLines + elements = split(line, " ") + triangles[line] = Triangle( + parse(Int64, elements[2]), + parse(Int64, elements[3]), + parse(Int64, elements[4]), + ) + end + + dimsLines = [l for l in lines if startswith(l, "dims")] + elements = split(dimsLines[1], " ") + + return RectangleMesh( + nodeList, + triangles, + parse(Int64, elements[2]), + parse(Int64, elements[3]), + ) +end diff --git a/src/utilities.jl b/src/utilities.jl index ee7df1a..f896a94 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -33,6 +33,13 @@ function dist(p1::Vertex3D, p2::Vertex3D) return sqrt(dx^2 + dy^2 + dz^2) end +""" +$(SIGNATURES) +""" +function dist(p1::Vec3f, p2::Vec3f) + v = p2 .- p1 + return sqrt(sum(v .^ 2)) +end """ $(SIGNATURES) @@ -57,19 +64,6 @@ centroid(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) = Vertex3D( ) -""" -$(SIGNATURES) -""" -function triangle_area(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) - a = dist(p1, p2) - b = dist(p2, p3) - c = dist(p3, p1) - s = (a + b + c) / 2.0 - - return sqrt(s * (s - a) * (s - b) * (s - c)) -end - - """ $(TYPEDEF) @@ -87,104 +81,175 @@ Each rectangle is split into 2 trangles: one upper-left, the other bottom-right | / | *------* ``` - - Although the corners of each triangle match corners of the rectangles, it is sometimes easier to think in terms of triangles rather than corners coming from different rectangles. """ -Triangle = Tuple{UInt64,UInt64,UInt64} +Rectangle = Nothing """ $(TYPEDEF) - -A Rectagle mesh represents a single face of the block. The most important face is the one facing the cautics. -First the surface is split into rectangles each associated with a pixel. Then, each rectangle is broken -into a top-left triangle and a bottom-right triangle. - -`VertexList` is the list of all the vertices (i.e. points) in the mesh. the list of triangles is split in 2. -Each triangle is a triplet of indices, each pointing to the relevant position in the list of vertices. - -The vertices are numbered by rows, then by columns. """ -struct RectangleMesh - height::UInt64 - width::UInt64 - vertexList::Vector{Vertex3D} - topTriangles::Matrix{Triangle} - botTriangles::Matrix{Triangle} +struct FaceMesh + size::Tuple{UInt,UInt} + topleft::AbstractMatrix{Vertex3D} + toptriangles::AbstractMatrix{Tuple{UInt,UInt,UInt}} + bottriangles::AbstractMatrix{Tuple{UInt,UInt,UInt}} as_index::Function - function RectangleMesh(height::Int, width::Int) - - to_index(r, c) = r + (c - 1) * (width + 1) + function FaceMesh(height::Int, width::Int) - vertices = Vector{Vertex3D}(undef, (height + 1) * (width + 1)) - for row = 1:height+1, col = 1:width+1 - vertices[to_index(row, col)] = - Vertex3D(Float64(row), Float64(col), Height_Offset, 0.0, 0.0) + function as_index(r, c) + if 1 <= r <= height + 1 && 1 <= c <= width + return r + (c - 1) * (width + 1) + else + return nothing + end end - top_triangles = Matrix{Triangle}(undef, height, width) - bot_triangles = Matrix{Triangle}(undef, height, width) - for row = 1:height, col = 1:width - top_triangles[row, col] = - (to_index(row, col), to_index(row + 1, col), to_index(row, col + 1)) - bot_triangles[row, col] = - (to_index(row, col + 1), to_index(row + 1, col), to_index(row + 1, col + 1)) + m_topleft = Matrix{Vertex3D}(undef, height, width) + t_triangles = Matrix{Tuple{UInt,UInt,UInt}}(undef, height, width) + b_triangles = Matrix{Tuple{UInt,UInt,UInt}}(undef, height, width) + for ci ∈ CartesianIndices(m_topleft) + row = ci[1] + col = ci[2] + + m_topleft .= (row, col, Top_Offset, 0.0, 0.0) + + t_triangles[ci] = + (as_index(row, col), as_index(row + 1, col), as_index(row, col + 1)) + b_triangles[ci] = + (as_index(row, col + 1), as_index(row + 1, col), as_index(row + 1, col + 1)) end - return new(height, width, vertexList, top_triangles, bot_triangles, to_index) + return new((height, width), m_topleft, t_triangles, b_triangles) end end +function convert(Meshes.SimpleMesh, mesh::FaceMesh) + height, width = size(mesh) + points = Meshes.Point3.([mesh.topleft[ci] for ci ∈ CartesianIndices(mesh.topleft)]) -""" -$(SIGNATURES) + top_connections = + [connect(mesh.toptriangles[ci]) for ci ∈ CartesianIndices(mesh.topleft)] + bot_connections = + [connect(mesh.bottriangles[ci]) for ci ∈ CartesianIndices(mesh.topleft)] -Return the dimension of the mesh as the number of rectangles. It does not return the number of corner points. + return SimpleMesh(points, vcat(top_connections, bot_connections)) +end + + +""" +$(TYPEDEF) """ -function base.size(mesh::RectangleMesh) - return mesh.height, mesh.width +struct Triangle + mesh::FaceMesh + points::Tuple{UInt,UInt,UInt} + + function Triangle(mesh::FaceMesh) + return Triangle( + mesh, + Tuple(mesh.as_index(1, 1), mesh.as_index(2, 1), mesh.as_index(1, 2)), + ) + end end + """ $(SIGNATURES) """ -triangle3D(mesh::Mesh, t::Triangle) = - [mesh.vertexList(t[1]), mesh.vertexList(t[1]), mesh.vertexList(t[1])] +function area(p1::Vec3f, p2::Vec3f, p3::Vec3f) + a = dist(p1, p2) + b = dist(p2, p3) + c = dist(p3, p1) + s = (a + b + c) / 2.0 + + return sqrt(s * (s - a) * (s - b) * (s - c)) +end + """ $(SIGNATURES) + +Return the dimension of the mesh as the number of rectangles. It does not return the number of corner points. """ -centroid(mesh::Mesh, t::Triangle) = centroid(triangle3D(mesh, t)...) +base.size(mesh::FaceMesh) = mesh.size """ $(SIGNATURES) + +Converts a triangle as a triplet of references to mesh vertices to a triplet of 3D coordinates. """ -triangle_area(mesh::Mesh, t::Triangle) = triangle_area(triangle3D(mesh, t)...) +function top_triangle3D(mesh::Mesh, ci::CartesianIndex) + if ci ∈ CartesianIndices(mesh.topleft) + t = mesh.top_triangle[ci] + p1 = mesh.topleft[t[1]] + p2 = mesh.topleft[t[2]] + p3 = mesh.topleft[t[3]] + return (p1, p2, p3) + else + return missing + end +end +top_triangle3D(mesh::Mesh, row::UInt, width::UInt) = + top_triangle3D(mesh, CartesianIndex(row, col)) +function bot_triangle3D(mesh::Mesh, ci::CartesianIndex) + if ci ∈ CartesianIndices(mesh.topleft) + t = mesh.bot_triangle[ci] + p1 = mesh.topleft[t[1]] + p2 = mesh.topleft[t[2]] + p3 = mesh.topleft[t[3]] + return (p1, p2, p3) + else + return missing + end +end -function top_triangle(mesh::RectangleMesh, row::Int, col::Int) - height, width = size(mesh) +bot_triangle3D(mesh::Mesh, row::UInt, width::UInt) = + bot_triangle3D(mesh, CartesianIndex(row, col)) - if (1 <= row <= height) && (1 <= col <= width) - return mesh.topTriangles(row, col) +function triangle3D(mesh::Mesh, ci::CartesianIndex; side = Union{:top,:bottom}) + if side == :top + return top_triangle3D(mesh, ci) + elseif side == :bottom + return bot_triangle3D(mesh, ci) else - return nothing + return missing end end -function bottom_triangle(mesh::RectangleMesh, row::Int, col::Int) - height, width = size(mesh) +triangle3D(mesh::Mesh, row::Uint, col::UInt; side = Union{:top,:bottom}) = + triangle3D(mesh, CartesianIndex(row, col); side) + + +""" +$(SIGNATURES) +""" +function centroid(mesh::Mesh, ci::CartesianIndex; side = Union{:top,:bottom}) + if side == :top + return centroid(top_triangle3D(mesh, row, col)...) + elseif side == :bottom + return centroid(bot_triangle3D(mesh, row, col)...) + else + return missing + end +end - if (1 <= row <= height) && (1 <= col <= width) - return mesh.botTriangles(row, col) + +""" +$(SIGNATURES) +""" +function area(mesh::Mesh, ci::CartesianIndex; side = Union{:top,:bottom}) + if side == :top + return area(top_triangle3D(mesh, ci)...) + elseif side == :bottom + return area(top_triangle3D(mesh, ci)...) else - return nothing + return missing end end From 8adb7c5594d36c4c188a3cf5519e45e4eac81afd Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Fri, 3 Sep 2021 11:54:41 +0200 Subject: [PATCH 07/58] Refactoring. Snapshot 5 --- Project.toml | 2 + examples/loss_it2.png | Bin 249477 -> 248791 bytes examples/loss_it3.png | Bin 285566 -> 248791 bytes src/CausticsEngineering.jl | 28 ++++- src/create_mesh.jl | 245 ++++++++++++++++++++----------------- src/io.jl | 27 +++- src/parameters.jl | 2 +- src/scratchpad.jl | 44 ++++++- src/utilities.jl | 142 +++++++++++---------- 9 files changed, 300 insertions(+), 190 deletions(-) diff --git a/Project.toml b/Project.toml index 2628409..7596ad2 100644 --- a/Project.toml +++ b/Project.toml @@ -13,6 +13,8 @@ JuliaFormatter = "98e50ef6-434e-11e9-1051-2b60c6c9e899" MeshIO = "7269a6da-0436-5bbc-96c2-40638cbb6118" Meshes = "eacbb407-ea5a-433e-ab97-5258b1ca43fa" Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" +Revise = "295af30f-e4ad-537b-8983-00126c2a3abe" +StaticArrays = "90137ffa-7385-5640-81b9-e52037218182" [compat] julia = "1" diff --git a/examples/loss_it2.png b/examples/loss_it2.png index 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with coordinates (x, y) # The area of a triangle is 1/2 * [ Ax (By - Cy) + Bx (Cy - Ay) + Cx (Ay - By)] # where each point of the triangle is where it will be after time t # i.e. a point goes from P to P+tV where V is the velocity of that point. @@ -25,9 +26,9 @@ function find_maximum_t(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) # (Bx + t_vBx) (Cy + t_vCy )- (Cx + t_vCx) (By + t_vBy) = 0. # After expansion and reshuffling to have a quadratic equation where t # is the variable, the coefficients of that equation are: - a = t_vBy * t_vCx - t_vCy * t_vBx - b = By * t_vCx + Cx * t_vBy - (Bx * t_vCy + Cy * t_vBx) - c = Cx * By - Bx * Cy + a = t_vCy * t_vBx - t_vBy * t_vCx + b = -By * t_vCx - Cx * t_vBy + Bx * t_vCy + Cy * t_vBx + c = Bx * Cy - Cx * By # if a = 0, this is just a linear equation. if a == 0 @@ -87,14 +88,6 @@ function get_pixel_area(mesh::FaceMesh) pixelAreas = zeros(Float64, size(mesh)) for ci ∈ CartesianIndices(pixelAreas) - # - # *------* - # | TOP/ | - # | / | - # | / | - # | /BOT | - # *------* - # pixelAreas[ci] = area(top_triangle3D(mesh, ci)...) + area(bot_triangle3D(mesh, ci)...) end @@ -199,7 +192,7 @@ function march_mesh!(mesh::FaceMesh, ϕ::Matrix{Float64}) end # Basically infinity time to shrink a triangle to zip. - min_t = 10_000.0 + min_t = 1.0 for ci ∈ CartesianIndices(ϕ) top_tri = top_triangle3D(mesh, ci) @@ -246,8 +239,8 @@ $(SIGNATURES) """ function quantifyLoss!(D, suffix, img) println("Loss:") - println("\tMinimum: $(minimum(D))") - println("\tMaximum: $(maximum(D))") + println("\tMinimum loss: $(minimum(D))") + println("\tMaximum loss: $(maximum(D))") blue = zeros(size(D)) blue[D.>0] = D[D.>0] @@ -255,10 +248,6 @@ function quantifyLoss!(D, suffix, img) red[D.<0] = -D[D.<0] green = zeros(size(D)) - println(size(blue)) - println(size(red)) - println(size(green)) - rgbImg = RGB.(red, green, blue)' save("./examples/loss_$(suffix).png", map(clamp01nan, rgbImg)) @@ -281,8 +270,6 @@ function single_iteration!(mesh, image, suffix) D = Float64.(LJ - image) # Save the loss image as a png - println(minimum(D)) - println(maximum(D)) quantifyLoss!(D, suffix, image) width, height = size(image) @@ -298,7 +285,8 @@ function single_iteration!(mesh, image, suffix) old_max_update = max_update max_update = relax!(ϕ, D) - if max_update < 1e-6 || abs((max_update - old_max_update) / old_max_update) < 0.01 + if abs(max_update) < 1e-6 || + abs((max_update - old_max_update) / old_max_update) < 0.01 println( "Convergence stopped at step $(interaction_count) with max_update of $(max_update)", ) @@ -318,6 +306,8 @@ function single_iteration!(mesh, image, suffix) # Now we need to march the x,y locations in our mesh according to this gradient! march_mesh!(mesh, ϕ) save_stl!(mesh, "./examples/mesh_$(suffix).obj", flipxy = true) + + return max_update end @@ -502,7 +492,8 @@ function find_surface( old_max_update = max_update max_update = relax!(height_map, divergence) - if max_update < 1e-6 || abs((max_update - old_max_update) / old_max_update) < 0.01 + if abs(max_update) < 1e-6 || + abs((max_update - old_max_update) / old_max_update) < 0.01 println( "Convergence stopped improving at step $(iteration_count) with max_update of $(max_update)", ) @@ -534,18 +525,15 @@ function engineer_caustics(source_image) # We need to boost the brightness of the image so that its sum and the sum of the area are equal average_intensity = sum(imageBW) / (width * height) - # img3 is `grid_definition x grid_definition` and is normalised to the same (sort of) _energy_ as the + # imageBW is `grid_definition x grid_definition` and is normalised to the same (sort of) _energy_ as the # original image. imageBW = imageBW ./ average_intensity - single_iteration!(mesh, imageBW, "it1") - single_iteration!(mesh, imageBW, "it2") - single_iteration!(mesh, imageBW, "it3") - - # single_teration(meshy, imageBW, "it4") - # single_teration(meshy, imageBW, "it5") - # single_teration(meshy, imageBW, "it6") - + for i ∈ 1:5 + println("\nSTARTING ITERATION $(i) \t--------------------------------------- ") + max_update = single_iteration!(mesh, imageBW, "it$(i)") + println("---------- ITERATION $(i): $(max_update)") + end height_map = find_surface(mesh, imageBW; f = 1.0, picture_width = Caustics_Side) diff --git a/src/scratchpad.jl b/src/scratchpad.jl index 4317fce..23e6343 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -1,4 +1,4 @@ -using Revise +using Revise, Debugger using Images image = Images.load("./examples/cat_posing.jpg"); # Check current working directory with pwd() @@ -9,6 +9,31 @@ mesh, image_caustics = engineer_caustics(image); Gray.(image_caustics') +using Test + + + + + +t3 = ( + CausticsEngineering.Vertex3D(5.0, 5.0, 0.01, 0.1, -2.0), + CausticsEngineering.Vertex3D(6.0, 5.0, 0.01, 0.1, 2.0), + CausticsEngineering.Vertex3D(5.5, 5.5, 0.01, 0.5, -3.0), +) + +CausticsEngineering.find_maximum_t(t3) + + + + + + + + + + + + typeof(CartesianIndex(3, 5)[1]) t = Matrix{Tuple{CartesianIndex(2),CartesianIndex(2),CartesianIndex(2)}}(undef, 2, 2) @@ -16,12 +41,12 @@ t = Matrix{Tuple{CartesianIndex(2),CartesianIndex(2),CartesianIndex(2)}}(undef, t[1, 1] = (CartesianIndex(1, 1), CartesianIndex(2, 1), CartesianIndex(1, 2)) typeof((CartesianIndex(1, 1), CartesianIndex(2, 1), CartesianIndex(1, 2))) -f = FaceMesh(5, 5); f.toptriangles[CartesianIndex(5, 5)] -f.topleft - +f = FaceMesh(5, 5); +v3 = CausticsEngineering.top_triangle3D(f, CartesianIndex(5, 5)) +CausticsEngineering.find_maximum_t(v3) v3 = CausticsEngineering.top_triangle3D(f, CartesianIndex(5, 5)) CausticsEngineering.area(v3...) diff --git a/test/runtests.jl b/test/runtests.jl index 406e8cb..0c068d9 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -1,6 +1,4 @@ using CausticsEngineering using Test -@testset "CausticsEngineering.jl" begin - # Write your tests here. -end +include("triangles.jl") diff --git a/test/triangles.jl b/test/triangles.jl new file mode 100644 index 0000000..e7aebf8 --- /dev/null +++ b/test/triangles.jl @@ -0,0 +1,42 @@ + + +@testset "Find maximum time to nil triangle" begin + t3 = ( + CausticsEngineering.Vertex3D(5.0, 5.0, 0.0, 0.0, 0.0), + CausticsEngineering.Vertex3D(6.0, 5.0, 0.0, 0.0, 0.0), + CausticsEngineering.Vertex3D(5.5, 5.5, 0.0, 0.0, -3.0), + ) + @test CausticsEngineering.find_maximum_t(t3)[1] ≈ 0.5 / 3.0 atol = 0.01 + + + t3 = ( + CausticsEngineering.Vertex3D(5.0, 5.0, 0.0, 0.0, 0.0), + CausticsEngineering.Vertex3D(6.0, 5.0, 0.0, 0.0, 0.0), + CausticsEngineering.Vertex3D(5.5, 5.5, 0.0, 0.7, -3.0), + ) + @test CausticsEngineering.find_maximum_t(t3)[1] ≈ 0.5 / 3.0 atol = 0.01 + + + t3 = ( + CausticsEngineering.Vertex3D(5.0, 5.0, 0.0, 0.0, 0.0), + CausticsEngineering.Vertex3D(6.0, 5.0, 0.0, 0.0, 0.0), + CausticsEngineering.Vertex3D(5.5, 5.5, 0.0, -10.0, -3.0), + ) + @test CausticsEngineering.find_maximum_t(t3)[1] ≈ 0.5 / 3.0 atol = 0.01 + + + t3 = ( + CausticsEngineering.Vertex3D(5.0, 5.0, 0.01, 0.1, -2.0), + CausticsEngineering.Vertex3D(6.0, 5.0, 0.01, 0.1, 2.0), + CausticsEngineering.Vertex3D(5.5, 5.5, 0.01, 0.5, -3.0), + ) + @test CausticsEngineering.find_maximum_t(t3)[1] ≈ 0.1540 atol = 0.01 + + t3 = ( + CausticsEngineering.Vertex3D(5.0, 5.0, 0.01, 0.1, -2.0), + CausticsEngineering.Vertex3D(6.0, 5.0, 0.01, 0.1, 2.0), + CausticsEngineering.Vertex3D(5.5, 5.5, 0.01, 0.5, -3.0), + ) + @test CausticsEngineering.find_maximum_t(t3)[1] ≈ 0.1540 atol = 0.01 + +end From ce67002f49605ea3a2053dbea7be22871d12f08b Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Fri, 3 Sep 2021 18:09:34 +0200 Subject: [PATCH 09/58] Refactoring. Snapshot 7 --- src/create_mesh.jl | 20 +++++++++++++------- src/debug_script.jl | 7 +++++++ src/parameters.jl | 3 ++- 3 files changed, 22 insertions(+), 8 deletions(-) create mode 100644 src/debug_script.jl diff --git a/src/create_mesh.jl b/src/create_mesh.jl index c734458..2ab4e6e 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -52,9 +52,9 @@ function find_maximum_t(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) end end - find_maximum_t(p::Tuple{Vertex3D,Vertex3D,Vertex3D}) = find_maximum_t(p[1], p[2], p[3]) + """ $(SIGNATURES) """ @@ -121,10 +121,18 @@ function relax!(height_map::Matrix{Float64}, divergence::Matrix{Float64}) val_left = container[2:height+1, 1:width] val_right = container[2:height+1, 3:width+2] - delta = (val_up + val_down + val_left + val_right - divergence) ./ 4.0 - height_map = height_map + ω .* (delta - height_map) + # Target position. The target is the current height map smoothed by averaging to which the + # divergence is added. + target_map = (val_up + val_down + val_left + val_right) ./ 4.0 + target_map += divergence + + # Let the heightmap converge towards the target at a slow rate. + height_map = height_map + ω .* (target_map - height_map) - return maximum(abs.(delta)) + max_update = maximum(abs.(delta)) + println("\t\tMax update = $(target_map)") + + return max_update end @@ -272,10 +280,8 @@ function single_iteration!(mesh, image, suffix) # Save the loss image as a png quantifyLoss!(D, suffix, image) - width, height = size(image) - # ϕ is the heightmap - ϕ = zeros(Float64, width, height) + ϕ = zeros(Float64, size(image)) max_update = 100.0 interaction_count = 0 diff --git a/src/debug_script.jl b/src/debug_script.jl new file mode 100644 index 0000000..cf32b11 --- /dev/null +++ b/src/debug_script.jl @@ -0,0 +1,7 @@ +using Revise, Debugger + +using Images +image = Images.load("./examples/cat_posing.jpg"); # Check current working directory with pwd() + +using CausticsEngineering +mesh, image_caustics = engineer_caustics(image); diff --git a/src/parameters.jl b/src/parameters.jl index e72e7c9..bde9dda 100644 --- a/src/parameters.jl +++ b/src/parameters.jl @@ -32,5 +32,6 @@ global Meters_Per_Pixel = Caustics_Height / N_Pixel_Height # calculation -const ω = 2 / (1 + π / sqrt(N_Pixel_Height * N_Pixel_Width)) +const ω = 0.50 +# const ω = 2 / (1 + π / sqrt(N_Pixel_Height * N_Pixel_Width)) const N_Iterations_Convergence = 10_000 # CHECK: What is a reasonable number of iterations? From 24f47f5d803bbbce1e8cbf472bf9c22bd5d7fe95 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Sun, 5 Sep 2021 14:48:37 +0200 Subject: [PATCH 10/58] Refactoring. Snapshot 7 --- Project.toml | 1 + examples/loss_it1.png | Bin 248791 -> 183499 bytes examples/loss_it2.png | Bin 248791 -> 183499 bytes examples/loss_it3.png | Bin 248791 -> 183499 bytes examples/loss_it4.png | Bin 248791 -> 183499 bytes examples/loss_it5.png | Bin 248791 -> 183499 bytes src/CausticsEngineering.jl | 4 +- src/create_mesh.jl | 764 ++++++++++++++++++------------------- src/plots.jl | 27 ++ src/scratchpad.jl | 19 +- src/utilities.jl | 280 ++++++++++---- 11 files changed, 632 insertions(+), 463 deletions(-) diff --git a/Project.toml b/Project.toml index 3bcf539..0a6f84f 100644 --- a/Project.toml +++ b/Project.toml @@ -16,6 +16,7 @@ Meshes = "eacbb407-ea5a-433e-ab97-5258b1ca43fa" Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" Revise = "295af30f-e4ad-537b-8983-00126c2a3abe" StaticArrays = "90137ffa-7385-5640-81b9-e52037218182" +StructArrays = "09ab397b-f2b6-538f-b94a-2f83cf4a842a" [compat] julia = "1" diff --git a/examples/loss_it1.png b/examples/loss_it1.png index 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zglN)Eojdq3kMIe8zz!+|EV7F@RSI-)kP>z7=leX(ab_s9L7D=itkC2Y_Hzf5oZ}9L zIK?yc@i-&g&5yaAG*i6M&{4EDLW9dX3mjGpD6)$MmjkAr8lSHLj1uB)I=`@8e9X*jU5&4i< h*pLZUnV<>&_5)5ms7LO&A!z^r002ovPDHLkV1mws%Lf1e diff --git a/src/CausticsEngineering.jl b/src/CausticsEngineering.jl index 7a51c9f..5cbdad5 100644 --- a/src/CausticsEngineering.jl +++ b/src/CausticsEngineering.jl @@ -8,8 +8,8 @@ gr() include("parameters.jl") include("utilities.jl") -include("plots.jl") include("io.jl") +include("plots.jl") include("create_mesh.jl") @@ -32,6 +32,6 @@ $(SIGNATURES) main() -export FaceMesh, main, engineer_caustics +export Vertex3D, FieldVertex3D, FaceMesh, main, engineer_caustics end # End module diff --git a/src/create_mesh.jl b/src/create_mesh.jl index 2ab4e6e..802c96c 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -1,59 +1,3 @@ -""" -$(SIGNATURES) - -Given 3 points and their velocities, calculate the time `t` required to bring the area of that triangle to zero -""" -function find_maximum_t(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) - # Three points A, B and C, with coordinates (x, y) - # The area of a triangle is 1/2 * [ Ax (By - Cy) + Bx (Cy - Ay) + Cx (Ay - By)] - # where each point of the triangle is where it will be after time t - # i.e. a point goes from P to P+tV where V is the velocity of that point. - # Notation is here B -> B + t_vB - - # To make the calculation simpler, everything is translated so that A is at the - # origin of the plane and its velocity is nil. - Bx = p2.x - p1.x - By = p2.y - p1.y - Cx = p3.x - p1.x - Cy = p3.y - p1.y - - t_vBx = p2.vx - p1.vx - t_vBy = p2.vy - p1.vy - t_vCx = p3.vx - p1.vx - t_vCy = p3.vy - p1.vy - - # After this, given that Ax = Ay = t_vAx = t_vAy = 0, the area is nil iff - # (Bx + t_vBx) (Cy + t_vCy )- (Cx + t_vCx) (By + t_vBy) = 0. - # After expansion and reshuffling to have a quadratic equation where t - # is the variable, the coefficients of that equation are: - a = t_vCy * t_vBx - t_vBy * t_vCx - b = -By * t_vCx - Cx * t_vBy + Bx * t_vCy + Cy * t_vBx - c = Bx * Cy - Cx * By - - # if a = 0, this is just a linear equation. - if a == 0 - # Fingers crossed that b != 0 but extremely unlikely since B is a Float64. - return -c / b, -c / b - else - - discriminant = b^2 - 4a * c - - # If there is a solution - if discriminant >= 0 - d = sqrt(discriminant) - return (-b - d) / 2a, (-b + d) / 2a - else - - # There can be no solution if, after translation, B abd C move in parallel direction. - # C will never end up on the line AB.result_mesh.rectangles[row, col].z = height_map[row, col] - # Very unlikely with Float64. - return missing, missing - end - end -end - -find_maximum_t(p::Tuple{Vertex3D,Vertex3D,Vertex3D}) = find_maximum_t(p[1], p[2], p[3]) - """ $(SIGNATURES) @@ -79,63 +23,6 @@ function ∇(ϕ::Matrix{Float64}) end -""" -$(SIGNATURES) -""" -function get_pixel_area(mesh::FaceMesh) - # A Mesh is a grid of 3D points. The X and Y coordinates are not necessarily aligned or square - # The Z coordinate represents the value. brightness is just proportional to area. - pixelAreas = zeros(Float64, size(mesh)) - - for ci ∈ CartesianIndices(pixelAreas) - pixelAreas[ci] = - area(top_triangle3D(mesh, ci)...) + area(bot_triangle3D(mesh, ci)...) - end - - return pixelAreas -end - - -""" -$(SIGNATURES) - -This function implements successive over relaxation for a matrix and its associated error matrix -There is a hardcoded assumption of Neumann boundary conditions--that the derivative across the -boundary must be zero in all cases. See: -https://math.stackexchange.com/questions/3790299/how-to-iteratively-solve-poissons-equation-with-no-boundary-conditions - -""" -function relax!(height_map::Matrix{Float64}, divergence::Matrix{Float64}) - height, width = size(height_map) - n_pixels = height * width - val_average = sum(height_map) / n_pixels - - # Embed matrix within a larger matrix for better vectorization and avoid duplicated code - container = zeros(Float64, height + 2, width + 2) - - container .= val_average - container[2:height+1, 2:height+1] .= height_map[:, :] - - val_up = container[1:height, 2:width+1] - val_down = container[3:height+2, 2:width+1] - val_left = container[2:height+1, 1:width] - val_right = container[2:height+1, 3:width+2] - - # Target position. The target is the current height map smoothed by averaging to which the - # divergence is added. - target_map = (val_up + val_down + val_left + val_right) ./ 4.0 - target_map += divergence - - # Let the heightmap converge towards the target at a slow rate. - height_map = height_map + ω .* (target_map - height_map) - - max_update = maximum(abs.(delta)) - println("\t\tMax update = $(target_map)") - - return max_update -end - - """ $(SIGNATURES) @@ -148,125 +35,61 @@ function matrix_to_mesh(height_map::Matrix{Float64}) mesh = FaceMesh(height, width) - for ci ∈ CartesianIndices(height_map) - mesh.topleft[ci].z = height_map[ci] - end + # 1 more topleft than pixels! Therefore compiler needs to specify exact indices. + mesh.topleft.z[1:height, 1:width] .= height_map[1:height, 1:width] # The borders' height is forced at 0. - for row ∈ 1:height - mesh.topleft[row, 1].z = 0.0 - mesh.topleft[row, end].z = 0.0 - end - - for col ∈ 1:width - mesh.topleft[1, col].z = 0.0 - mesh.topleft[end, col].z = 0.0 - end + fill_borders!(mesh.topleft.z, 0.0) return mesh end + + """ $(SIGNATURES) """ -function march_mesh!(mesh::FaceMesh, ϕ::Matrix{Float64}) - ∇ϕᵤ, ∇ϕᵥ = ∇(ϕ) - - height, width = size(mesh) - - # For each point in the mesh we need to figure out its velocity - # However all the nodes located at a border will never move - # I.e. velocity (Vx, Vy) = (0, 0) and the square of acrylate will remain - # of the same size. - for ci ∈ CartesianIndices(ϕ) - mesh.topleft[ci].vx = -∇ϕᵤ[ci] - mesh.topleft[ci].vy = -∇ϕᵥ[ci] - end - - # The velocity matrix was initialized with zeros everywhere. We nevertheless ovewrite them just in case... - for row ∈ 1:height - mesh.topleft[row, 1].vx = 0.0 - mesh.topleft[row, 1].vy = 0.0 - mesh.topleft[row, end].vx = 0.0 - mesh.topleft[row, end].vy = 0.0 - end - - for col ∈ 1:width - mesh.topleft[1, col].vx = 0.0 - mesh.topleft[1, col].vy = 0.0 - mesh.topleft[end, col].vx = 0.0 - mesh.topleft[end, col].vy = 0.0 - end - - # Basically infinity time to shrink a triangle to zip. - min_t = 1.0 - - for ci ∈ CartesianIndices(ϕ) - top_tri = top_triangle3D(mesh, ci) +function engineer_caustics(source_image) + imageBW = Float64.(Gray.(source_image)) + imageBW = permutedims(imageBW) - # Get the time, at that velocity, for the area of the triangle to be nil. - # We are only interested in positive times. - t1, t2 = find_maximum_t(top_tri) - for t ∈ [t1, t2] - if (!ismissing(t)) && (0 < t < min_t) - min_t = t - end - end + width, height = size(imageBW) + println("Image size: $((height, width))") + # meshy is the same size as the image with an extra row/column to have coordinates to + # cover each image pixel with a triangle. + mesh = FaceMesh(height, width) - bot_tri = bot_triangle3D(mesh, ci) + # We need to boost the brightness of the image so that its sum and the sum of the area are equal + average_intensity = sum(imageBW) / (width * height) - # Get the time, at that velocity, for the area of the triangle to be nil. - # We are only interested in positive times. - t1, t2 = find_maximum_t(bot_tri) - for t ∈ [t1, t2] - if (!ismissing(t)) && (0 < t < min_t) - min_t = t - end - end + # imageBW is `grid_definition x grid_definition` and is normalised to the same (sort of) _energy_ as the + # original image. + imageBW = imageBW ./ average_intensity + for i ∈ 1:2 + println("\nSTARTING ITERATION $(i) ---") + max_update = single_iteration!(mesh, imageBW, "it$(i)") + println("---------- ITERATION $(i): $(max_update)") end - println("Overall min_t:", min_t) + height_map = find_surface(mesh, imageBW; f = 1.0, picture_width = Caustics_Side) - # Modify the mesh triangles but ensuring that we are far from destroying any of them with a nil area. - δ = min_t / 2 + set_heights!(mesh, height_map) - for ci ∈ CartesianIndices(mesh.topleft) - mesh.topleft[ci].x += δ * mesh.topleft[ci].vx - mesh.topleft[ci].y += δ * mesh.topleft[ci].vy - end + # solidMesh = create_solid(mesh) + # save_stl!( + # solidMesh, + # "./examples/original_image.obj", + # scale = Float64(1 / Grid_Definition * Artifact_Size), + # scalez = Float64(1 / Grid_Definition * Artifact_Size), + # ) - # saveObj(mesh, "gateau.obj") + return mesh, imageBW end -""" -$(SIGNATURES) -""" -function quantifyLoss!(D, suffix, img) - println("Loss:") - println("\tMinimum loss: $(minimum(D))") - println("\tMaximum loss: $(maximum(D))") - - blue = zeros(size(D)) - blue[D.>0] = D[D.>0] - red = zeros(size(D)) - red[D.<0] = -D[D.<0] - green = zeros(size(D)) - - rgbImg = RGB.(red, green, blue)' - save("./examples/loss_$(suffix).png", map(clamp01nan, rgbImg)) - - # println("Saving output image:") - # println(typeof(img)) - # E = Gray.(D) - # println(typeof(E)) - # outputImg = img - E - # save("./examples/actual_$(suffix).png", outputImg) -end - """ $(SIGNATURES) @@ -274,11 +97,11 @@ $(SIGNATURES) function single_iteration!(mesh, image, suffix) # Remember meshy is (will be) `grid_definition x grid_definition` just like the image # `grid_definition x grid_definition`, so LJ is `grid_definition x grid_definition`. - LJ = get_pixel_area(mesh) + LJ = get_area_pixels(mesh) D = Float64.(LJ - image) # Save the loss image as a png - quantifyLoss!(D, suffix, image) + plot_loss!(D, suffix, image) # ϕ is the heightmap ϕ = zeros(Float64, size(image)) @@ -320,238 +143,411 @@ end """ $(SIGNATURES) """ -function set_heights!( - mesh, - height_map, - height_scale = 1.0, - height_offset = Top_Offset / Meters_Per_Pixel, +function find_surface( + mesh::FaceMesh, + image; + f = Focal_Length, + picture_width = Caustics_Side, ) - width, height = size(height_map) - - for ci ∈ CartesianIndices(height_map) - mesh.topleft[ci].z = height_map[ci] * height_scale + height_offset - end - # Forces the borders at Height_Offset. They will never change because nil velocity. - for row ∈ 1:height - mesh.topleft[row, 1].z = Top_Offset - mesh.topleft[row, end].z = Top_Offset - end - - for col ∈ 1:width - mesh.topleft[1, col].z = Top_Offset - mesh.topleft[end, col].z = Top_Offset - end -end + # h(eight) indexes rows, w(idth) indexes columns + height, width = size(mesh) + # Coordinates difference + # C; Coordinates on the caustics. Simple rectangular values in pixels. + # Coordinates on the lens face coming from topleft field. + # x = rows; y = columns + dx = repeat(Float64.(1:height+1), 1, width + 1) - mesh.topleft.x + dy = repeat(Float64.(1:width+1)', height + 1, 1) - mesh.topleft.y -""" -$(SIGNATURES) -""" -function set_heights(height_map, height_scale = 1.0) - height, width = size(height_map) - mesh = RectangleMesh(height, width) + # true_H is the real distance beteen the surface of the lens and the projection + # H is the initial distance from the surface of the carved face to the projection screen. + # H is constant and does not account for the change in heights due to carving. + # The focal length is in meters. H is in Pixels. + H = f / Meters_Per_Pixel - return set_heights!(mesh, height_map, height_scale = 1.0) -end + true_H = similar(mesh.topleft.z) + @. true_H[:] = -mesh.topleft.z[:] + H + # Normals. + Nx = zeros(Float64, height + 1, width + 1) + Ny = zeros(Float64, height + 1, width + 1) + @. Nx[:] = tan(atan(dx[:] / true_H[:]) / (n₁ - n₂)) + @. Ny[:] = tan(atan(dy[:] / true_H[:]) / (n₁ - n₂)) -""" -$(SIGNATURES) -""" -function create_solid(mesh, bottom_offset = Bottom_Offset / Meters_Per_Pixel) - height, width = size(mesh) + # We need to find the divergence of the Vector field described by Nx and Ny + divergence = zeros(Float64, width, height) + δr = zeros(Float64, width, height) + δc = zeros(Float64, width, height) - ### - ### Top mesh - ### - # List top mesh top triangles - list_triangles_top_top = [top_triangles(mesh, r, c) for r ∈ 1:height, c ∈ 1:width] + @. δr[1:end, 1:end] = Nx[2:end, 1:end-1] - Nx[1:end-1, 1:end-1] + @. δc[1:end, 1:end] = Nx[1:end-1, 2:end] - Ny[1:end-1, 1:end-1] + divergence = δr + δc - # List top mesh bottom triangles - list_triangles_top_bottom = [bottom_triangle(mesh, r, c) for r ∈ 1:height, c ∈ 1:width] + println("Have all the divergences") + height_map = zeros(Float64, height, width) + max_update = 1000.0 + iteration_count = 0 + while true + iteration_count += 1 + iteration_count % 100 == 0 && println("Converging for divergence: $(max_update)") - ### - ### Botttom mesh - ### - # Build the bottom surface which is prepopulated by its constructor. However, its height is incorrect. - bottom_mesh = FaceMesh(height, width) - for ci ∈ CartesianIndices(bottom_mesh) - row = ci[1] - col = ci[2] - bottom_mesh.topleft[ci] = Vertex3D(row, col, -Bottom_Offset, 0.0, 0.0) + old_max_update = max_update + max_update = relax!(height_map, divergence) + if abs(max_update) < 1e-6 || + abs((max_update - old_max_update) / old_max_update) < 0.01 + println( + "Convergence stopped improving at step $(iteration_count) with max_update of $(max_update)", + ) + break + end end - ### - ### Side meshes - ### - # Build the triangles to close the mesh - x = 1 - for y = 1:(height-1) - count += 1 + # saveObj(matrix_to_mesh(h / 10), "./examples/heightmap.obj") + return height_map +end - ll = (y - 1) * width + x - ul = ll + totalNodes / 2 - lr = y * width + x - ur = lr + totalNodes / 2 - triangles[2*count-1] = Triangle(ll, ul, ur) - triangles[2*count] = Triangle(ur, lr, ll) - end - x = width - for y = 1:(height-1) - count += 1 +""" +$(SIGNATURES) - ll = (y - 1) * width + x - ul = ll + totalNodes / 2 - lr = y * width + x - ur = lr + totalNodes / 2 - triangles[2*count-1] = Triangle(ll, ur, ul) - triangles[2*count] = Triangle(ur, ll, lr) - end +TODO: Think about the optimal offset for convergence. +""" +function set_heights!( + mesh, + height_map, + height_scale = 1.0, + height_offset = 0.0 * Top_Offset / Meters_Per_Pixel, +) + width, height = size(height_map) - y = 1 - for x = 2:width - count += 1 + @. mesh.topleft.z[1:height, 1:width] = + height_map[1:height, 1:width] * height_scale + height_offset - ll = (y - 1) * width + x - ul = ll + totalNodes / 2 - lr = (y - 1) * width + (x - 1) - ur = lr + totalNodes / 2 - triangles[2*count-1] = Triangle(ll, ul, ur) - triangles[2*count] = Triangle(ur, lr, ll) - end + # Forces the borders at Height_Offset. They will never change because nil velocity. + fill_borders!(mesh.topleft.z, height_offset) +end - y = height - for x = 2:width - count += 1 - ll = (y - 1) * width + x - ul = ll + totalNodes / 2 - lr = (y - 1) * width + (x - 1) - ur = lr + totalNodes / 2 - triangles[2*count-1] = Triangle(ll, ur, ul) - triangles[2*count] = Triangle(ur, ll, lr) +""" +$(SIGNATURES) +""" +function set_heights(height_map, height_scale = 1.0) + height, width = size(height_map) + mesh = FaceMesh(height, width) + + return set_heights!(mesh, height_map, height_scale = 1.0) +end + + + +""" +$(SIGNATURES) +""" +function get_area_pixels(mesh::FaceMesh) + height, width = size(mesh) + + # A Mesh is a grid of 3D points. The X and Y coordinates are not necessarily aligned or square + # The Z coordinate represents the value. brightness is just proportional to area. + pixel_areas = zeros(Float64, size(mesh)) + + for ci ∈ CartesianIndices(pixel_areas) + pixel_areas[ci] = + area(top_triangle3D(mesh, ci)...) + area(bot_triangle3D(mesh, ci)...) end - return RectangleMesh(nodeList, nodeArrayBottom, triangles, width, height) + return pixel_areas end """ $(SIGNATURES) """ -function find_surface( - mesh::FaceMesh, - image; - f = Focal_Length, - picture_width = Caustics_Side, -) +function quantifyLoss!(D, suffix, img) + println("Loss:") + println("Minimum: $(minimum(D))") + println("Maximum: $(maximum(D))") - # H is the initial distance from the surface of the carved face to the projection screen. - # H is constant and does not account for the change in heights due to carving. - # The focal length is in meters. H is in Pixels. - H = f / Meters_Per_Pixel + blue = zeros(size(D)) + blue[D.>0] = D[D.>0] + red = zeros(size(D)) + red[D.<0] = -D[D.<0] + green = zeros(size(D)) - # h(eight) indexes rows, w(idth) indexes columns - height, width = size(mesh) - Nx = zeros(Float64, height + 1, width + 1) - Ny = zeros(Float64, height + 1, width + 1) + # println(size(blue)) + # println(size(red)) + # println(size(green)) + + rgbImg = RGB.(red, green, blue)' + save("./examples/loss_$(suffix).png", map(clamp01nan, rgbImg)) + + # println("Saving output image:") + # println(typeof(img)) + # E = Gray.(D) + # println(typeof(E)) + # outputImg = img - E + # save("./examples/actual_$(suffix).png", outputImg) +end + + + + +""" +$(SIGNATURES) + +This function implements successive over relaxation for a matrix and its associated error matrix +There is a hardcoded assumption of Neumann boundary conditions--that the derivative across the +boundary must be zero in all cases. See: +https://math.stackexchange.com/questions/3790299/how-to-iteratively-solve-poissons-equation-with-no-boundary-conditions + +""" +function relax!(height_map::Matrix{Float64}, divergence::Matrix{Float64}) + height, width = size(height_map) + n_pixels = height * width + val_average = sum(height_map) / n_pixels + + # Embed matrix within a larger matrix for better vectorization and avoid duplicated code + container = zeros(Float64, height + 2, width + 2) + + container .= val_average + container[2:height+1, 2:height+1] .= height_map[:, :] + + val_up = container[1:height, 2:width+1] + val_down = container[3:height+2, 2:width+1] + val_left = container[2:height+1, 1:width] + val_right = container[2:height+1, 3:width+2] + + # Target position. The target is the current height map smoothed by averaging to which the + # divergence is added. + target_map = (val_up + val_down + val_left + val_right) ./ 4.0 + target_map += divergence + + # Let the heightmap converge towards the target at a slow rate. + height_map = height_map + ω .* (target_map - height_map) + + max_update = maximum(abs.(height_map)) + # println("\t\tMax update = $(target_map)") + + return max_update +end + + +""" +$(SIGNATURES) + +Given 3 points and their velocities, calculate the time `t` required to bring the area of that triangle to zero +""" +function find_maximum_t(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) + # Three points A, B and C, with coordinates (x, y) + # The area of a triangle is 1/2 * [ Ax (By - Cy) + Bx (Cy - Ay) + Cx (Ay - By)] + # where each point of the triangle is where it will be after time t + # i.e. a point goes from P to P+tV where V is the velocity of that point. + # Notation is here B -> B + t_vB + + # To make the calculation simpler, everything is translated so that A is at the + # origin of the plane and its velocity is nil. + Bx = p2.x - p1.x + By = p2.y - p1.y + Cx = p3.x - p1.x + Cy = p3.y - p1.y + + t_vBx = p2.vx - p1.vx + t_vBy = p2.vy - p1.vy + t_vCx = p3.vx - p1.vx + t_vCy = p3.vy - p1.vy - for row ∈ 1:height+1, col ∈ 1:width+1 - # Coordinates on the caustics - cx = row - cy = col + # After this, given that Ax = Ay = t_vAx = t_vAy = 0, the area is nil iff + # (Bx + t_vBx) (Cy + t_vCy )- (Cx + t_vCx) (By + t_vBy) = 0. + # After expansion and reshuffling to have a quadratic equation where t + # is the variable, the coefficients of that equation are: + a = t_vCy * t_vBx - t_vBy * t_vCx + b = -By * t_vCx - Cx * t_vBy + Bx * t_vCy + Cy * t_vBx + c = Bx * Cy - Cx * By - # Coordinates on the lens face - lx = mesh.topleft[row, col].x - ly = mesh.topleft[row, col].y + # if a = 0, this is just a linear equation. + if a == 0 + # Fingers crossed that b != 0 but extremely unlikely since B is a Float64. + return -c / b, -c / b + else - # Coordinates difference - dx = cx - lx - dy = cy - ly + discriminant = b^2 - 4a * c - true_H = H - mesh.topleft[row, col].z + # If there is a solution + if discriminant >= 0 + d = sqrt(discriminant) + return (-b - d) / 2a, (-b + d) / 2a + else - Nx[row, col] = tan(atan(dx / true_H) / (n₁ - n₂)) - Ny[row, col] = tan(atan(dy / true_H) / (n₁ - n₂)) + # There can be no solution if, after translation, B abd C move in parallel direction. + # C will never end up on the line AB.result_mesh.rectangles[row, col].z = height_map[row, col] + # Very unlikely with Float64. + return missing, missing + end end +end - # We need to find the divergence of the Vector field described by Nx and Ny - divergence = zeros(Float64, width, height) - δr = zeros(Float64, width, height) - δc = zeros(Float64, width, height) +find_maximum_t(p::Tuple{Vertex3D,Vertex3D,Vertex3D}) = find_maximum_t(p[1], p[2], p[3]) - δr[1:end, 1:end] .= Nx[2:end, 1:end-1] .- Nx[1:end-1, 1:end-1] - δc[1:end, 1:end] .= Nx[1:end-1, 2:end] .- Ny[1:end-1, 1:end-1] - divergence = δr + δc - println("Have all the divergences") +""" +$(SIGNATURES) +""" +function march_mesh!(mesh::FaceMesh, ϕ::Matrix{Float64}) + ∇ϕᵤ, ∇ϕᵥ = ∇(ϕ) - height_map = zeros(Float64, height, width) - max_update = 1000.0 - iteration_count = 0 - while true - iteration_count += 1 - iteration_count % 100 == 0 && println("Converging for divergence: $(max_update)") + height, width = size(ϕ) - old_max_update = max_update - max_update = relax!(height_map, divergence) - if abs(max_update) < 1e-6 || - abs((max_update - old_max_update) / old_max_update) < 0.01 - println( - "Convergence stopped improving at step $(iteration_count) with max_update of $(max_update)", - ) - break + # For each point in the mesh we need to figure out its velocity + # However all the nodes located at a border will never move + # I.e. velocity (Vx, Vy) = (0, 0) and the square of acrylate will remain + # of the same size. + mesh.topleft.vx[1:height, 1:width] .= -∇ϕᵤ[1:height, 1:width] + mesh.topleft.vy[1:height, 1:width] .= -∇ϕᵥ[1:height, 1:width] + + # The velocity matrix was initialized with zeros everywhere. We nevertheless ovewrite them just in case... + fill_borders!(mesh.topleft.vx, 0.0) + fill_borders!(mesh.topleft.vy, 0.0) + + # Basically infinity time to shrink a triangle to zip. + min_t = 1.0 + + for row ∈ 1:height-1, col ∈ 1:width-1 + top_tri = top_triangle3D(mesh, row, col) + + # Get the time, at that velocity, for the area of the triangle to be nil. + # We are only interested in positive times. + t1, t2 = find_maximum_t(top_tri) + for t ∈ [t1, t2] + if (!ismissing(t)) && (0 < t < min_t) + min_t = t + end end + + + bot_tri = bot_triangle3D(mesh, row, col) + + # Get the time, at that velocity, for the area of the triangle to be nil. + # We are only interested in positive times. + t1, t2 = find_maximum_t(bot_tri) + for t ∈ [t1, t2] + if (!ismissing(t)) && (0 < t < min_t) + min_t = t + end + end + end - # saveObj(matrix_to_mesh(h / 10), "./examples/heightmap.obj") - return height_map -end + println("Overall min_t:", min_t) + # Modify the mesh triangles but ensuring that we are far from destroying any of them with a nil area. + δ = min_t / 2 + mesh.topleft.x[:] .+= δ * mesh.topleft.vx[:] + mesh.topleft.y[:] .+= δ * mesh.topleft.vy[:] + + # saveObj(mesh, "gateau.obj") +end """ $(SIGNATURES) + +TO REFACTOR. """ -function engineer_caustics(source_image) - imageBW = Float64.(Gray.(source_image)) - imageBW = permutedims(imageBW) +function create_solid( + mesh::FaceMesh; + bottom_offset = Bottom_Offset / Meters_Per_Pixel, + top_offset = Top_Offset / Meters_Per_Pixel, +) + height, width = size(mesh) - width, height = size(imageBW) - println("Image size: $((height, width))") - # meshy is the same size as the image with an extra row/column to have coordinates to - # cover each image pixel with a triangle. - mesh = FaceMesh(height, width) + ### + ### Top mesh + ### + # List top mesh top triangles + list_triangles_top_top = [top_triangles(mesh, r, c) for r ∈ 1:height, c ∈ 1:width] - # We need to boost the brightness of the image so that its sum and the sum of the area are equal - average_intensity = sum(imageBW) / (width * height) + # List top mesh bottom triangles + list_triangles_top_bottom = [bottom_triangle(mesh, r, c) for r ∈ 1:height, c ∈ 1:width] - # imageBW is `grid_definition x grid_definition` and is normalised to the same (sort of) _energy_ as the - # original image. - imageBW = imageBW ./ average_intensity - for i ∈ 1:5 - println("\nSTARTING ITERATION $(i) \t--------------------------------------- ") - max_update = single_iteration!(mesh, imageBW, "it$(i)") - println("---------- ITERATION $(i): $(max_update)") + ### + ### Botttom mesh + ### + # Build the bottom surface which is prepopulated by its constructor. However, its height is incorrect. + + # Coordinates on the caustics + rows = repeat(Float64.(1:height), 1, width) + cols = repeat(Float64.(1:width)', height, 1) + + bottom_mesh = FaceMesh(height, width) + bottom_mesh.topleft.x[:] .= rows[:] + bottom_mesh.topleft.y[:] .= cols[:] + bottom_mesh.topleft.z[:] .= -Bottom_Offset + bottom_mesh.topleft.vx[:] .= 0.0 + bottom_mesh.topleft.vx[:] .= 0.0 + + + ### + ### Side meshes + ### + # Build triangles to create side meshes and close the mesh + # The mesh is made of a single top/bottom triangles joining the bottom face + # and the top face. + + # (Looking from above), left side. + + list_triangles = [] + col = 1 + for row = 1:height + count += 1 + + ll = (row - 1) * width + col + ul = ll + totalNodes / 2 + lr = row * width + col + ur = lr + totalNodes / 2 + triangles[2*count-1] = Triangle(ll, ul, ur) + triangles[2*count] = Triangle(ur, lr, ll) end - height_map = find_surface(mesh, imageBW; f = 1.0, picture_width = Caustics_Side) + mesh_right = FaceMesh(height, 1) + for row = 1:(height-1) + count += 1 - set_heights!(mesh, height_map) - # solidMesh = create_solid(mesh) + ll = (row - 1) * width + col + ul = ll + totalNodes / 2 + lr = row * width + col + ur = lr + totalNodes / 2 + triangles[2*count-1] = Triangle(ll, ur, ul) + triangles[2*count] = Triangle(ur, ll, lr) + end - # save_stl!( - # solidMesh, - # "./examples/original_image.obj", - # scale = Float64(1 / Grid_Definition * Artifact_Size), - # scalez = Float64(1 / Grid_Definition * Artifact_Size), - # ) + mesh_up = FaceMesh(1, width) + row = 1 + for col = 2:width + count += 1 - return mesh, imageBW + ll = (row - 1) * width + col + ul = ll + totalNodes / 2 + lr = (row - 1) * width + (col - 1) + ur = lr + totalNodes / 2 + triangles[2*count-1] = Triangle(ll, ul, ur) + triangles[2*count] = Triangle(ur, lr, ll) + end + + mesh_down = FaceMesh(1, width) + for col = 2:width + count += 1 + + ll = (row - 1) * width + col + ul = ll + totalNodes / 2 + lr = (row - 1) * width + (col - 1) + ur = lr + totalNodes / 2 + triangles[2*count-1] = Triangle(ll, ur, ul) + triangles[2*count] = Triangle(ur, ll, lr) + end + + return RectangleMesh(nodeList, nodeArrarowBottom, triangles, width, height) end diff --git a/src/plots.jl b/src/plots.jl index aa5fa06..4ee0716 100644 --- a/src/plots.jl +++ b/src/plots.jl @@ -72,3 +72,30 @@ function plot_velocities_as_quiver(vx, vy; stride = 4, scale = 300, max_length = display(q) readline() end + + + +""" +$(SIGNATURES) +""" +function plot_loss!(D, suffix, img) + println("Loss:") + println("\tMinimum loss: $(minimum(D))") + println("\tMaximum loss: $(maximum(D))") + + blue = zeros(size(D)) + blue[D.>0] = D[D.>0] + red = zeros(size(D)) + red[D.<0] = -D[D.<0] + green = zeros(size(D)) + + rgbImg = RGB.(red, green, blue)' + save("./examples/loss_$(suffix).png", map(clamp01nan, rgbImg)) + + # println("Saving output image:") + # println(typeof(img)) + # E = Gray.(D) + # println(typeof(E)) + # outputImg = img - E + # save("./examples/actual_$(suffix).png", outputImg) +end diff --git a/src/scratchpad.jl b/src/scratchpad.jl index 23e6343..cdf9320 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -9,6 +9,7 @@ mesh, image_caustics = engineer_caustics(image); Gray.(image_caustics') + using Test @@ -21,7 +22,8 @@ t3 = ( CausticsEngineering.Vertex3D(5.5, 5.5, 0.01, 0.5, -3.0), ) -CausticsEngineering.find_maximum_t(t3) +C +austicsEngineering.find_maximum_t(t3) @@ -67,3 +69,18 @@ c = t[1] f.topleft(c) t = CausticsEngineering.top_triangle3D(f, CartesianIndex(1, 1)) + + + +# Indexing structs +struct TT + a::Int + b::Int +end + +using StructArrays + + +aa = StructArrays() + +aa[:].a = 0 diff --git a/src/utilities.jl b/src/utilities.jl index d4e960d..6fe9621 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -1,19 +1,10 @@ -using StaticArrays - """ $(TYPEDEF) ## Coordinates -Origin is top left, going right and down .`x` goes horizontal and follows columns. x is within 1 and width -`y` goes vertical and follows rows. y is within 1 and height. - -# Velocity - -Velocity vector along `x` and `y` (velocity along z not necessary). - """ -mutable struct Vertex3D +struct Vertex3D x::Float64 y::Float64 z::Float64 @@ -22,9 +13,18 @@ mutable struct Vertex3D vy::Float64 Vertex3D(x, y, z, vx, vy) = new(x, y, z, vx, vy) - Vertex3D() = new(0.0, 0.0, Height_Offset, 0.0, 0.0) + Vertex3D() = new(0.0, 0.0, 0.0, 0.0, 0.0) end +""" +$(SIGNATURES) +""" +function dist(p1::Tuple{Float64,Float64,Float64}, p2::Tuple{Float64,Float64,Float64}) + dx = p2[1] - p1[1] + dy = p2[2] - p1[2] + dz = p2[3] - p1[3] + return sqrt(dx^2 + dy^2 + dz^2) +end """ $(SIGNATURES) @@ -36,6 +36,23 @@ function dist(p1::Vertex3D, p2::Vertex3D) return sqrt(dx^2 + dy^2 + dz^2) end + +""" +$(SIGNATURES) +""" +function area( + p1::Tuple{Float64,Float64,Float64}, + p2::Tuple{Float64,Float64,Float64}, + p3::Tuple{Float64,Float64,Float64}, +) + a = dist(p1, p2) + b = dist(p2, p3) + c = dist(p3, p1) + s = (a + b + c) / 2.0 + + return sqrt(s * (s - a) * (s - b) * (s - c)) +end + """ $(SIGNATURES) """ @@ -61,7 +78,7 @@ midpoint(p1::Vertex3D, p2::Vertex3D) = """ $(SIGNATURES) -Barycentre of three points. +Centroid of three points. """ centroid(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) = Vertex3D( (p1.x + p2.x + p3.x) / 3.0, @@ -72,6 +89,66 @@ centroid(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) = Vertex3D( ) +""" +$(TYPEDEF) + +## Coordinates + +Origin is top left, going right and down .`x` goes horizontal and follows columns. x is within 1 and width +`y` goes vertical and follows rows. y is within 1 and height. + +# Velocity + +Velocity vector along `x` and `y` (velocity along z not necessary). + +Implementation is a struc of arrays. Easier to vectorise. + +""" +struct FieldVertex3D + size::Tuple{Int,Int} + + x::AbstractMatrix{Float64} + y::AbstractMatrix{Float64} + z::AbstractMatrix{Float64} + + vx::AbstractMatrix{Float64} + vy::AbstractMatrix{Float64} + + function FieldVertex3D(height, width) + mx = zeros(Float64, height + 1, width + 1) + my = zeros(Float64, height + 1, width + 1) + mz = zeros(Float64, height + 1, width + 1) + + mvx = zeros(Float64, height + 1, width + 1) + mvy = zeros(Float64, height + 1, width + 1) + + new((height, width), mx, my, mz, mvx, mvy) + end +end + +Base.size(fv::FieldVertex3D) = FieldVertex3D.size + + +""" +$(SIGNATURES) +""" +function Vertex3D(fv::FieldVertex3D, row, col) + height, width = size(fv) + + if (1 <= row <= height + 1) && (1 <= col <= width + 1) + Vertex3D( + fv.x[row, col], + fv.y[row, col], + fv.z[row, col], + fv.vx[row, col], + fv.vy[row, col], + ) + else + missing + end +end + + """ $(TYPEDEF) @@ -92,17 +169,12 @@ Each rectangle is split into 2 trangles: one upper-left, the other bottom-right Although the corners of each triangle match corners of the rectangles, it is sometimes easier to think in terms of triangles rather than corners coming from different rectangles. """ -Rectangle = Nothing - - -""" -$(TYPEDEF) -""" struct FaceMesh size::Tuple{Int,Int} - topleft::AbstractMatrix{Vertex3D} - toptriangles::AbstractMatrix{Tuple{CartesianIndex,CartesianIndex,CartesianIndex}} - bottriangles::AbstractMatrix{Tuple{CartesianIndex,CartesianIndex,CartesianIndex}} + topleft::FieldVertex3D + + toptriangles::AbstractMatrix{Tuple{Tuple{Int,Int},Tuple{Int,Int},Tuple{Int,Int}}} + bottriangles::AbstractMatrix{Tuple{Tuple{Int,Int},Tuple{Int,Int},Tuple{Int,Int}}} as_index::Function @@ -121,45 +193,29 @@ function FaceMesh(height::Int, width::Int) end as_index(ci::CartesianIndex) = as_index(ci[1], ci[2]) - m_topleft = Matrix{Vertex3D}(undef, height + 1, width + 1) - t_triangles = Matrix{Tuple{CartesianIndex{2},CartesianIndex{2},CartesianIndex{2}}}( - undef, - height, - width, - ) - b_triangles = Matrix{Tuple{CartesianIndex{2},CartesianIndex{2},CartesianIndex{2}}}( - undef, - height, - width, - ) - - - for ci ∈ CartesianIndices(m_topleft) - row = ci[1] - col = ci[2] - m_topleft[ci] = Vertex3D(row, col, Top_Offset, 0.0, 0.0) - end - - for ci ∈ CartesianIndices(t_triangles) - row = ci[1] - col = ci[2] + m_topleft = FieldVertex3D(height, width) + t_triangles = + Matrix{Tuple{Tuple{Int,Int},Tuple{Int,Int},Tuple{Int,Int}}}(undef, height, width) + b_triangles = + Matrix{Tuple{Tuple{Int,Int},Tuple{Int,Int},Tuple{Int,Int}}}(undef, height, width) - t_triangles[ci] = ( - CartesianIndex(row, col), - CartesianIndex(row + 1, col), - CartesianIndex(row, col + 1), - ) - b_triangles[ci] = ( - CartesianIndex(row, col + 1), - CartesianIndex(row + 1, col), - CartesianIndex(row + 1, col + 1), - ) + for row ∈ 1:height, col ∈ 1:width + t_triangles[row, col] = ((row, col), (row + 1, col), (row, col + 1)) + b_triangles[row, col] = ((row, col + 1), (row + 1, col), (row + 1, col + 1)) end return FaceMesh((height, width), m_topleft, t_triangles, b_triangles) end +""" +$(SIGNATURES) + +Return the dimension of the mesh as the number of rectangles. It does not return the number of corner points. +""" +Base.size(mesh::FaceMesh) = mesh.size + + """ $(TYPEDEF) """ @@ -176,13 +232,13 @@ struct Triangle end +function fill_borders!(mat::AbstractMatrix{T}, val::T) where {T} + mat[begin:end, begin] .= val + mat[begin:end, end] .= val + mat[begin, begin:end] .= val + mat[end, begin:end] .= val +end -""" -$(SIGNATURES) - -Return the dimension of the mesh as the number of rectangles. It does not return the number of corner points. -""" -Base.size(mesh::FaceMesh) = mesh.size """ @@ -190,35 +246,78 @@ $(SIGNATURES) Converts a triangle as a triplet of references to mesh vertices to a triplet of 3D coordinates. """ -function top_triangle3D(mesh::FaceMesh, ci::CartesianIndex) - if ci ∈ CartesianIndices(mesh.toptriangles) - t = mesh.toptriangles[ci] - p1 = mesh.topleft[t[1]] - p2 = mesh.topleft[t[2]] - p3 = mesh.topleft[t[3]] +function top_triangle3D(mesh::FaceMesh, row::Int, col::Int) + height, width = size(mesh) + if 1 <= row <= height + 1 && 1 <= col <= width + 1 + t = mesh.toptriangles[row, col] + t1 = CartesianIndex(t[1][1], t[1][2]) + t2 = CartesianIndex(t[2][1], t[2][2]) + t3 = CartesianIndex(t[3][1], t[3][2]) + p1 = Vertex3D( + mesh.topleft.x[t1], + mesh.topleft.y[t1], + mesh.topleft.z[t1], + mesh.topleft.vx[t1], + mesh.topleft.vy[t1], + ) + p2 = Vertex3D( + mesh.topleft.x[t2], + mesh.topleft.y[t2], + mesh.topleft.z[t2], + mesh.topleft.vx[t2], + mesh.topleft.vy[t2], + ) + p3 = Vertex3D( + mesh.topleft.x[t3], + mesh.topleft.y[t3], + mesh.topleft.z[t3], + mesh.topleft.vx[t3], + mesh.topleft.vy[t3], + ) return (p1, p2, p3) else return missing end end -top_triangle3D(mesh::FaceMesh, row::Int, width::Int) = - top_triangle3D(mesh, CartesianIndex(row, col)) - -function bot_triangle3D(mesh::FaceMesh, ci::CartesianIndex) - if ci ∈ CartesianIndices(mesh.bottriangles) - t = mesh.bottriangles[ci] - p1 = mesh.topleft[t[1]] - p2 = mesh.topleft[t[2]] - p3 = mesh.topleft[t[3]] +top_triangle3D(mesh::FaceMesh, ci::CartesianIndex{2}) = top_triangle3D(mesh, ci[1], ci[2]) + + +function bot_triangle3D(mesh::FaceMesh, row::Int, col::Int) + height, width = size(mesh) + if 1 <= row <= height + 1 && 1 <= col <= width + 1 + t = mesh.bottriangles[row, col] + t1 = CartesianIndex(t[1][1], t[1][2]) + t2 = CartesianIndex(t[2][1], t[2][2]) + t3 = CartesianIndex(t[3][1], t[3][2]) + p1 = Vertex3D( + mesh.topleft.x[t1], + mesh.topleft.y[t1], + mesh.topleft.z[t1], + mesh.topleft.vx[t1], + mesh.topleft.vy[t1], + ) + p2 = Vertex3D( + mesh.topleft.x[t2], + mesh.topleft.y[t2], + mesh.topleft.z[t2], + mesh.topleft.vx[t2], + mesh.topleft.vy[t2], + ) + p3 = Vertex3D( + mesh.topleft.x[t3], + mesh.topleft.y[t3], + mesh.topleft.z[t3], + mesh.topleft.vx[t3], + mesh.topleft.vy[t3], + ) return (p1, p2, p3) else return missing end end -bot_triangle3D(mesh::FaceMesh, row::Int, width::Int) = - bot_triangle3D(mesh, CartesianIndex(row, col)) +bot_triangle3D(mesh::FaceMesh, ci::CartesianIndex{2}) = bot_triangle3D(mesh, ci[1], ci[2]) function triangle3D(mesh::FaceMesh, ci::CartesianIndex; side = Union{:top,:bottom}) @@ -237,6 +336,8 @@ triangle3D(mesh::FaceMesh, row::Int, col::Int; side = Union{:top,:bottom}) = """ $(SIGNATURES) + +Centroid of a specific mesh triangle. """ function centroid(mesh::FaceMesh, ci::CartesianIndex; side = Union{:top,:bottom}) if side == :top @@ -248,6 +349,20 @@ function centroid(mesh::FaceMesh, ci::CartesianIndex; side = Union{:top,:bottom} end end +""" +$(SIGNATURES) + +Centroid of a specific mesh triangle. +""" +function centroid(mesh::FaceMesh, row::Int, col::Int; side = Union{:top,:bottom}) + if side == :top + return centroid(top_triangle3D(mesh, row, col)...) + elseif side == :bottom + return centroid(bot_triangle3D(mesh, row, col)...) + else + return missing + end +end """ $(SIGNATURES) @@ -261,3 +376,16 @@ function area(mesh::FaceMesh, ci::CartesianIndex; side = Union{:top,:bottom}) return missing end end + +""" +$(SIGNATURES) +""" +function area(mesh::FaceMesh, row::Int, col::Int; side = Union{:top,:bottom}) + if side == :top + return area(top_triangle3D(mesh, row, col)...) + elseif side == :bottom + return area(top_triangle3D(mesh, row, col)...) + else + return missing + end +end From c566148995ab667843a1b333e076db200bf6ac35 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Sun, 5 Sep 2021 21:40:58 +0200 Subject: [PATCH 11/58] Refactoring. 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zuiQdEUJ#o6urTs5vq%-+%|dZd3nTf=PyjgY6B%$qF`U+eZ$J@XRULA^xKM0] = D[D.>0] @@ -327,7 +290,9 @@ function relax!(height_map::Matrix{Float64}, divergence::Matrix{Float64}) height_map = height_map + ω .* (target_map - height_map) max_update = maximum(abs.(height_map)) - # println("\t\tMax update = $(target_map)") + println("Minimum / Maximum of the height map after relaxation.") + println("\tMax update = $( maximum(height_map) )") + println("\tMin update = $( minimum(height_map) )") return max_update end @@ -392,9 +357,17 @@ find_maximum_t(p::Tuple{Vertex3D,Vertex3D,Vertex3D}) = find_maximum_t(p[1], p[2] """ $(SIGNATURES) + +ϕ is the height map. + +`march_mesh!` flexes the mesh """ function march_mesh!(mesh::FaceMesh, ϕ::Matrix{Float64}) + ∇ϕᵤ, ∇ϕᵥ = ∇(ϕ) + println("Min/Max of values of ϕ: $(minimum(ϕ)) / $(maximum(ϕ))") + println("Sum of values of ∇ϕᵤ: $( sum(∇ϕᵤ) )") + println("Sum of values of ∇ϕᵥ: $( sum(∇ϕᵥ) )") height, width = size(ϕ) @@ -402,6 +375,7 @@ function march_mesh!(mesh::FaceMesh, ϕ::Matrix{Float64}) # However all the nodes located at a border will never move # I.e. velocity (Vx, Vy) = (0, 0) and the square of acrylate will remain # of the same size. + # Warning: The indices are necessary because topleft and ∇ϕ are of different sizes mesh.topleft.vx[1:height, 1:width] .= -∇ϕᵤ[1:height, 1:width] mesh.topleft.vy[1:height, 1:width] .= -∇ϕᵥ[1:height, 1:width] @@ -410,7 +384,8 @@ function march_mesh!(mesh::FaceMesh, ϕ::Matrix{Float64}) fill_borders!(mesh.topleft.vy, 0.0) # Basically infinity time to shrink a triangle to zip. - min_t = 1.0 + min_positive_t = Inf + max_negative_t = -Inf for row ∈ 1:height-1, col ∈ 1:width-1 top_tri = top_triangle3D(mesh, row, col) @@ -419,32 +394,40 @@ function march_mesh!(mesh::FaceMesh, ϕ::Matrix{Float64}) # We are only interested in positive times. t1, t2 = find_maximum_t(top_tri) for t ∈ [t1, t2] - if (!ismissing(t)) && (0 < t < min_t) - min_t = t + if (!ismissing(t)) && (0 < t < min_positive_t) + min_positive_t = t + end + if (!ismissing(t)) && (max_negative_t < t < 0) + max_negative_t = t end end - bot_tri = bot_triangle3D(mesh, row, col) # Get the time, at that velocity, for the area of the triangle to be nil. # We are only interested in positive times. t1, t2 = find_maximum_t(bot_tri) for t ∈ [t1, t2] - if (!ismissing(t)) && (0 < t < min_t) - min_t = t + if (!ismissing(t)) && (0 < t < min_positive_t) + min_positive_t = t + end + if (!ismissing(t)) && (max_negative_t < t < 0) + max_negative_t = t end end - end - println("Overall min_t:", min_t) - # Modify the mesh triangles but ensuring that we are far from destroying any of them with a nil area. - δ = min_t / 2 + # Use the maximum change possible (negative or positive) + δ = (abs(max_negative_t) < min_positive_t) ? min_positive_t / 2.0 : max_negative_t / 2.0 + + println("Overall maximum variations:") + println("\tOverall min_positive_t: $(min_positive_t)") + println("\tOverall max_negative_t: $(max_negative_t)") + println("\tUsing δ: $(δ)") - mesh.topleft.x[:] .+= δ * mesh.topleft.vx[:] - mesh.topleft.y[:] .+= δ * mesh.topleft.vy[:] + mesh.topleft.x[1:height, 1:width] .-= δ .* ∇ϕᵤ[1:height, 1:width] + mesh.topleft.y[1:height, 1:width] .-= δ .* ∇ϕᵥ[1:height, 1:width] # saveObj(mesh, "gateau.obj") end @@ -551,3 +534,51 @@ function create_solid( return RectangleMesh(nodeList, nodeArrarowBottom, triangles, width, height) end + + + + +""" +$(SIGNATURES) +""" +function ∇(ϕ::Matrix{Float64}) + height, width = size(ϕ) + + ∇ϕᵤ = zeros(Float64, height, width) # the right edge will be filled with zeros + ∇ϕᵥ = zeros(Float64, height, width) # the bottom edge will be filled with zeros + + for row ∈ 1:height-1, col ∈ 1:width-1 + ∇ϕᵤ[row, col] = ϕ[row+1, col] - ϕ[row, col] + ∇ϕᵥ[row, col] = ϕ[row, col+1] - ϕ[row, col] + end + + ∇ϕᵤ[1:end, end] .= 0.0 + ∇ϕᵤ[end, 1:end] .= 0.0 + + ∇ϕᵥ[1:end, end] .= 0.0 + ∇ϕᵥ[end, 1:end] .= 0.0 + + return ∇ϕᵤ, ∇ϕᵥ +end + + +""" +$(SIGNATURES) + +This function will take a `grid_definition x grid_definition` matrix and returns a +`grid_definition x grid_definition` mesh. + +""" +function matrix_to_mesh(height_map::Matrix{Float64}) + height, width = size(height_map) + + mesh = FaceMesh(height, width) + + # 1 more topleft than pixels! Therefore compiler needs to specify exact indices. + mesh.topleft.z[1:height, 1:width] .= height_map[1:height, 1:width] + + # The borders' height is forced at 0. + fill_borders!(mesh.topleft.z, 0.0) + + return mesh +end diff --git a/src/io.jl b/src/io.jl index 2fc86b7..522e7fb 100644 --- a/src/io.jl +++ b/src/io.jl @@ -26,6 +26,8 @@ $(SIGNATURES) This function saves the mesh object in stl format. The format difinition is sourced from [https://en.wikipedia.org/wiki/STL_(file_format)](). + +TO REFACTOR. """ function save_stl!( mesh::FaceMesh, diff --git a/src/scratchpad.jl b/src/scratchpad.jl index cdf9320..bba6fea 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -6,34 +6,18 @@ image = Images.load("./examples/cat_posing.jpg"); # Check current working direct using CausticsEngineering mesh, image_caustics = engineer_caustics(image); -Gray.(image_caustics') - - +Gray.(image_caustics) +Gray.(Float64.(Gray.(image)) - image_caustics) using Test - - - - t3 = ( CausticsEngineering.Vertex3D(5.0, 5.0, 0.01, 0.1, -2.0), CausticsEngineering.Vertex3D(6.0, 5.0, 0.01, 0.1, 2.0), CausticsEngineering.Vertex3D(5.5, 5.5, 0.01, 0.5, -3.0), ) -C -austicsEngineering.find_maximum_t(t3) - - - - - - - - - - +CausticsEngineering.find_maximum_t(t3) typeof(CartesianIndex(3, 5)[1]) diff --git a/src/utilities.jl b/src/utilities.jl index 6fe9621..7535ee6 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -89,6 +89,17 @@ centroid(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) = Vertex3D( ) +""" +$(SIGNATURES) +""" +function fill_borders!(mat::AbstractMatrix{T}, val::T) where {T} + mat[begin:end, begin] .= val + mat[begin:end, end] .= val + mat[begin, begin:end] .= val + mat[end, begin:end] .= val +end + + """ $(TYPEDEF) @@ -104,7 +115,7 @@ Velocity vector along `x` and `y` (velocity along z not necessary). Implementation is a struc of arrays. Easier to vectorise. """ -struct FieldVertex3D +mutable struct FieldVertex3D size::Tuple{Int,Int} x::AbstractMatrix{Float64} @@ -115,12 +126,19 @@ struct FieldVertex3D vy::AbstractMatrix{Float64} function FieldVertex3D(height, width) - mx = zeros(Float64, height + 1, width + 1) - my = zeros(Float64, height + 1, width + 1) - mz = zeros(Float64, height + 1, width + 1) + # mx = zeros(Float64, height + 1, width + 1) + # my = zeros(Float64, height + 1, width + 1) + # mz = zeros(Float64, height + 1, width + 1) - mvx = zeros(Float64, height + 1, width + 1) - mvy = zeros(Float64, height + 1, width + 1) + # mvx = zeros(Float64, height + 1, width + 1) + # mvy = zeros(Float64, height + 1, width + 1) + + mx = rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 + my = rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 + mz = rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 + + mvx = rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 + mvy = rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 new((height, width), mx, my, mz, mvx, mvy) end @@ -232,14 +250,6 @@ struct Triangle end -function fill_borders!(mat::AbstractMatrix{T}, val::T) where {T} - mat[begin:end, begin] .= val - mat[begin:end, end] .= val - mat[begin, begin:end] .= val - mat[end, begin:end] .= val -end - - """ $(SIGNATURES) From f3d0e840c101c761403e5be0d892b7468a4dbfbd Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Mon, 6 Sep 2021 09:50:15 +0200 Subject: [PATCH 12/58] Refactoring. Snapshot 9 --- src/create_mesh.jl | 17 ++++++++++++----- 1 file changed, 12 insertions(+), 5 deletions(-) diff --git a/src/create_mesh.jl b/src/create_mesh.jl index 2009d07..0078c17 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -7,7 +7,7 @@ function engineer_caustics(source_image) width, height = size(imageBW) println("Image size: $((height, width))") - # meshy is the same size as the image with an extra row/column to have coordinates to + # mesh is the same size as the image with an extra row/column to have coordinates to # cover each image pixel with a triangle. mesh = FaceMesh(height, width) print("Mesh creation: ") @@ -55,9 +55,13 @@ end $(SIGNATURES) """ function single_iteration!(mesh, image, suffix) - # Remember meshy is (will be) `grid_definition x grid_definition` just like the image + # Remember mesh is (will be) `grid_definition x grid_definition` just like the image # `grid_definition x grid_definition`, so LJ is `grid_definition x grid_definition`. + # The idea is that: + # - any pixel on the caustic projection receives light from a given 'rectangle' on the lens. + # - That rectangle is made of 2 triangles. + # DOES NOT WORK. D IS ALWAYS IDENTICAL LJ = get_area_pixels(mesh) D = Float64.(LJ - image) @@ -204,15 +208,18 @@ function set_heights(height_map, height_scale = 1.0) end - """ $(SIGNATURES) + +A Mesh is a collection of triangles. The brightness flowing through a given triangle is just proportional to its +area in the x, y plane. z is ignored. + +The function returns a matrix with the quantity of light coming from each 'rectangle' around a pixel. That 'rectangle' +has been shifted and flexed around. """ function get_area_pixels(mesh::FaceMesh) height, width = size(mesh) - # A Mesh is a grid of 3D points. The X and Y coordinates are not necessarily aligned or square - # The Z coordinate represents the value. brightness is just proportional to area. pixel_areas = zeros(Float64, size(mesh)) for ci ∈ CartesianIndices(pixel_areas) From 00e9612cb162999c9978808a612701fddb71e80b Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Mon, 6 Sep 2021 11:51:38 +0200 Subject: [PATCH 13/58] Minor --- src/create_mesh.jl | 11 ++++++++--- src/parameters.jl | 3 ++- 2 files changed, 10 insertions(+), 4 deletions(-) diff --git a/src/create_mesh.jl b/src/create_mesh.jl index c734458..2fa17c2 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -52,9 +52,9 @@ function find_maximum_t(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) end end - find_maximum_t(p::Tuple{Vertex3D,Vertex3D,Vertex3D}) = find_maximum_t(p[1], p[2], p[3]) + """ $(SIGNATURES) """ @@ -121,8 +121,13 @@ function relax!(height_map::Matrix{Float64}, divergence::Matrix{Float64}) val_left = container[2:height+1, 1:width] val_right = container[2:height+1, 3:width+2] - delta = (val_up + val_down + val_left + val_right - divergence) ./ 4.0 - height_map = height_map + ω .* (delta - height_map) + # Target position. The target is the current height map smoothed by averaging to which the + # divergence is added. + target_map = (val_up + val_down + val_left + val_right) ./ 4.0 + target_map += divergence + + # Let the heightmap converge towards the target at a slow rate. + height_map = height_map + ω .* (target_map - height_map) return maximum(abs.(delta)) end diff --git a/src/parameters.jl b/src/parameters.jl index e72e7c9..bde9dda 100644 --- a/src/parameters.jl +++ b/src/parameters.jl @@ -32,5 +32,6 @@ global Meters_Per_Pixel = Caustics_Height / N_Pixel_Height # calculation -const ω = 2 / (1 + π / sqrt(N_Pixel_Height * N_Pixel_Width)) +const ω = 0.50 +# const ω = 2 / (1 + π / sqrt(N_Pixel_Height * N_Pixel_Width)) const N_Iterations_Convergence = 10_000 # CHECK: What is a reasonable number of iterations? From 78848108e5a1a7bf2d955b58a4e2f5a704f6fdf6 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Mon, 6 Sep 2021 17:51:41 +0200 Subject: [PATCH 14/58] Refactoring ongoing. Snapshot 10 --- Project.toml | 1 + examples/loss_it1.png | Bin 186765 -> 260739 bytes examples/loss_it10.png | Bin 248791 -> 188017 bytes examples/loss_it11.png | Bin 0 -> 188017 bytes examples/loss_it2.png | Bin 186765 -> 241645 bytes examples/loss_it3.png | Bin 183499 -> 216340 bytes examples/loss_it4.png | Bin 183499 -> 204447 bytes examples/loss_it5.png | Bin 183499 -> 173745 bytes examples/loss_it6.png | Bin 248791 -> 188018 bytes examples/loss_it7.png | Bin 248791 -> 188018 bytes examples/loss_it8.png | Bin 248791 -> 188018 bytes examples/loss_it9.png | Bin 248791 -> 188018 bytes src/CausticsEngineering.jl | 2 +- src/create_mesh.jl | 419 +++++++++++++++++++------------------ src/scratchpad.jl | 10 +- src/utilities.jl | 177 ++++++++-------- 16 files changed, 314 insertions(+), 295 deletions(-) create mode 100644 examples/loss_it11.png diff --git a/Project.toml b/Project.toml index 0a6f84f..1919c58 100644 --- a/Project.toml +++ b/Project.toml @@ -14,6 +14,7 @@ JuliaFormatter = 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zglN)Eojdq3kMIe8zz!+|EV7F@RSI-)kP>z7=leX(ab_s9L7D=itkC2Y_Hzf5oZ}9L zIK?yc@i-&g&5yaAG*i6M&{4EDLW9dX3mjGpD6)$MmjkAr8lSHLj1uB)I=`@8e9X*jU5&4i< h*pLZUnV<>&_5)5ms7LO&A!z^r002ovPDHLkV1mws%Lf1e diff --git a/src/CausticsEngineering.jl b/src/CausticsEngineering.jl index 5cbdad5..d017991 100644 --- a/src/CausticsEngineering.jl +++ b/src/CausticsEngineering.jl @@ -1,7 +1,7 @@ module CausticsEngineering using DocStringExtensions -using Meshes, Images +using Random, Meshes, Images using Plots gr() diff --git a/src/create_mesh.jl b/src/create_mesh.jl index d7d7d5b..5a95ede 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -11,7 +11,7 @@ function engineer_caustics(source_image) # cover each image pixel with a triangle. mesh = FaceMesh(height, width) print("Mesh creation: ") - println("$(mesh.topleft.vx[15, 5]) , $(mesh.topleft.vy[15, 5])") + println("$(mesh.topleft.vr[256, 256]) , $(mesh.topleft.vc[256, 256])") # We need to boost the brightness of the image so that its sum and the sum of the area are equal average_intensity = sum(imageBW) / (width * height) @@ -20,22 +20,27 @@ function engineer_caustics(source_image) # original image. imageBW = imageBW ./ average_intensity - for i ∈ 1:2 - println("\nSTARTING ITERATION $(i) ---") - max_update = single_iteration!(mesh, imageBW, "it$(i)") - print("Single iteration: ") - println("$(mesh.topleft.vx[15, 5]) , $(mesh.topleft.vy[15, 5])") + for i ∈ 1:5 + println("\nSTARTING HORIZONTAL ITERATION $(i) ---") - println("---------- ITERATION $(i): $(max_update)") + print("Horizontal move: ") + max_update = move_vertically!(mesh, imageBW, "it$(i)") + println(" max update = $(max_update)") + + # println("$(mesh.topleft.vr[256, 256]) , $(mesh.topleft.vc[256, 256])") + # println(" (Speed at 256, 256 = $(mesh.topleft.vr[256, 256]) , $(mesh.topleft.vc[256, 256])") + + println("---------- ITERATION $(i): $(max_update)/n") end - height_map = find_surface(mesh, imageBW; f = 1.0, picture_width = Caustics_Side) - print("Find surface: ") - println("$(mesh.topleft.vx[15, 5]) , $(mesh.topleft.vy[15, 5])") + print("Vertical move: ") + mesh.topleft.z, max_update = + move_horizontally(mesh, imageBW; f = 1.0, picture_width = Caustics_Side) + println(" max update = $(max_update)") + - set_heights!(mesh, height_map) - print("Set heights!: ") - println("$(mesh.topleft.vx[15, 5]) , $(mesh.topleft.vy[15, 5])") + + println("$(mesh.topleft.vr[256, 256]) , $(mesh.topleft.vc[256, 256])") # solidMesh = create_solid(mesh) @@ -54,24 +59,33 @@ end """ $(SIGNATURES) """ -function single_iteration!(mesh, image, suffix) +function move_vertically!(mesh, image, suffix) # Remember mesh is (will be) `grid_definition x grid_definition` just like the image # `grid_definition x grid_definition`, so LJ is `grid_definition x grid_definition`. # The idea is that: # - any pixel on the caustic projection receives light from a given 'rectangle' on the lens. # - That rectangle is made of 2 triangles. + area_distorted_pixels = get_area_pixels(mesh) + intensity_error = Float64.(area_distorted_pixels - image) + + # The divergence matrix moves all the topleft corners. illumination_error is therefore not large enough. + height, width = size(mesh) + divergence_intensity = zeros(Float64, height + 1, width + 1) + divergence_intensity[1:height, 1:width] .= intensity_error[1:height, 1:width] - # DOES NOT WORK. D IS ALWAYS IDENTICAL - LJ = get_area_pixels(mesh) - D = Float64.(LJ - image) + divergence_intensity[:, 1] .= 0.0 + divergence_intensity[:, end] .= 0.0 + divergence_intensity[1, :] .= 0.0 + divergence_intensity[end, :] .= 0.0 # Save the loss image as a png - plot_loss!(D, suffix, image) + plot_loss!(divergence_intensity, suffix, image) - # ϕ is the _heightmap_ + # ϕ is the _heightmap_ therefore size of topleft # ϕ = zeros(Float64, size(image)) - height_map = rand(Float64, size(image)) ./ 1_000 .- 0.5 / 1_000 + # ϕ = rand(Float64, height+1, width+1) ./ 1_000 .- 0.5 / 1_000 + ϕ = mesh.topleft.z max_update = 100.0 interaction_count = 0 @@ -80,7 +94,7 @@ function single_iteration!(mesh, image, suffix) interaction_count % 500 == 0 && println("Converging for intensity: $(max_update)") old_max_update = max_update - max_update = relax!(height_map, D) + ϕ, max_update = relax_vertically(ϕ, divergence_intensity) if abs(max_update) < 1e-6 || abs((max_update - old_max_update) / old_max_update) < 0.01 println( @@ -90,8 +104,10 @@ function single_iteration!(mesh, image, suffix) end end + mesh.topleft.z[1:height+1, 1:width+1] .= ϕ[1:height+1, 1:width+1] + save_stl!( - matrix_to_mesh(height_map * 0.02), + matrix_to_mesh(ϕ * 0.02), "./examples/phi_$(suffix).obj", reverse = false, flipxy = true, @@ -100,17 +116,19 @@ function single_iteration!(mesh, image, suffix) # saveObj(matrix_to_mesh(D * 10), "D_$(suffix).obj") # Now we need to march the x,y locations in our mesh according to this gradient! - march_mesh!(mesh, height_map) + march_mesh!(mesh, ϕ) save_stl!(mesh, "./examples/mesh_$(suffix).obj", flipxy = true) return max_update end + + """ $(SIGNATURES) """ -function find_surface( +function move_horizontally( mesh::FaceMesh, image; f = Focal_Length, @@ -121,48 +139,51 @@ function find_surface( height, width = size(mesh) # Coordinates difference - # C; Coordinates on the caustics. Simple rectangular values in pixels. - # Coordinates on the lens face coming from topleft field. - # x = rows; y = columns - dx = repeat(Float64.(1:height+1), 1, width + 1) - mesh.topleft.x - dy = repeat(Float64.(1:width+1)', height + 1, 1) - mesh.topleft.y - height_map = height_map + ω .* (target_map - height_map) + # Coordinates on the caustics = simple rectangular values in pixels. + # Coordinates on the lens face comes from topleft field. + d_row = repeat(Float64.(1:height+1), 1, width + 1) - mesh.topleft.r + d_col = repeat(Float64.(1:width+1)', height + 1, 1) - mesh.topleft.c # true_H is the real distance beteen the surface of the lens and the projection # H is the initial distance from the surface of the carved face to the projection screen. # H is constant and does not account for the change in heights due to carving. # The focal length is in meters. H is in Pixels. + # Note: Higher location means closer to the caustics => negative sign H = f / Meters_Per_Pixel true_H = similar(mesh.topleft.z) @. true_H[:] = -mesh.topleft.z[:] + H # Normals. - Nx = zeros(Float64, height + 1, width + 1) - Ny = zeros(Float64, height + 1, width + 1) - @. Nx[:] = tan(atan(dx[:] / true_H[:]) / (n₁ - n₂)) - @. Ny[:] = tan(atan(dy[:] / true_H[:]) / (n₁ - n₂)) + N_row = zeros(Float64, height + 1, width + 1) + N_col = zeros(Float64, height + 1, width + 1) + @. N_row[:] = tan(atan(d_row[:] / true_H[:]) / (n₁ - n₂)) + @. N_col[:] = tan(atan(d_col[:] / true_H[:]) / (n₁ - n₂)) # We need to find the divergence of the Vector field described by Nx and Ny - divergence = zeros(Float64, width, height) - δr = zeros(Float64, width, height) - δc = zeros(Float64, width, height) - - @. δr[1:end, 1:end] = Nx[2:end, 1:end-1] - Nx[1:end-1, 1:end-1] - @. δc[1:end, 1:end] = Nx[1:end-1, 2:end] - Ny[1:end-1, 1:end-1] - divergence = δr + δc + div_row = zeros(Float64, width, height) + div_col = zeros(Float64, width, height) + @. div_row[1:end, 1:end] = N_row[2:end, 1:end-1] - N_row[1:end-1, 1:end-1] + @. div_col[1:end, 1:end] = N_col[1:end-1, 2:end] - N_col[1:end-1, 1:end-1] + + divergence_direction = zeros(Float64, width + 1, height + 1) + divergence_direction[1:height, 1:width] = div_row + div_col + divergence_direction[:, 1] .= 0.0 + divergence_direction[:, end] .= 0.0 + divergence_direction[1, :] .= 0.0 + divergence_direction[end, :] .= 0.0 println("Have all the divergences") - height_map = zeros(Float64, height, width) - max_update = 1000.0 + ϕ = zeros(Float64, height + 1, width + 1) + max_update = 1_000.0 iteration_count = 0 while true iteration_count += 1 iteration_count % 100 == 0 && println("Converging for divergence: $(max_update)") old_max_update = max_update - max_update = relax!(height_map, divergence) + ϕ, max_update = relax_vertically(ϕ, divergence_direction) if abs(max_update) < 1e-6 || abs((max_update - old_max_update) / old_max_update) < 0.01 println( @@ -173,39 +194,68 @@ function find_surface( end # saveObj(matrix_to_mesh(h / 10), "./examples/heightmap.obj") - return height_map + return ϕ, max_update end """ $(SIGNATURES) -TODO: Think about the optimal offset for convergence. +This function implements successive over relaxation for a matrix and its associated error matrix +There is a hardcoded assumption of Neumann boundary conditions--that the derivative across the +boundary must be zero in all cases. See: +https://math.stackexchange.com/questions/3790299/how-to-iteratively-solve-poissons-equation-with-no-boundary-conditions + """ -function set_heights!( - mesh, - height_map, - height_scale = 1.0, - height_offset = 0.0 * Top_Offset / Meters_Per_Pixel, -) - width, height = size(height_map) +function relax_vertically(ϕ::Matrix{Float64}, divergence::Matrix{Float64}) - @. mesh.topleft.z[1:height, 1:width] = - height_map[1:height, 1:width] * height_scale + height_offset + # ϕ is the size of topleft + height, width = size(ϕ) + n_pixels = height * width + height_average = sum(ϕ) / n_pixels - # Forces the borders at Height_Offset. They will never change because nil velocity. - fill_borders!(mesh.topleft.z, height_offset) -end + # Embed matrix within a larger matrix for better vectorization and avoid duplicated code + # Size of ϕ/topleft is h+1, w+1. container adds 1 row/col before and 1 row/col after + container_height = 1 + height + 1 + container_width = 1 + width + 1 + container = zeros(Float64, container_height, container_width) + + container[2:container_height-1, 2:container_width-1] .= ϕ[:, :] + container[:, begin] .= height_average + container[:, end] .= height_average + container[begin, :] .= height_average + container[end, :] .= height_average + + # Those values are height x width + height_up = container[2-1:container_height-1-1, 2:container_width-1] + height_down = container[2+1:container_height-1+1, 2:container_width-1] + height_left = container[2:container_height-1, 2-1:container_width-1-1] + height_right = container[2:container_height-1, 2+1:container_width-1+1] + # Target position. The target is the current height map smoothed by averaging to which the + # divergence is added. + # target_map is the same size mesh.topleft. + target_map = zeros(Float64, height, width) + target_map = (height_up + height_down + height_left + height_right) ./ 4.0 + target_map += divergence -""" -$(SIGNATURES) -""" -function set_heights(height_map, height_scale = 1.0) - height, width = size(height_map) - mesh = FaceMesh(height, width) + target_map[:, begin] .= height_average + target_map[:, end] .= height_average + target_map[begin, :] .= height_average + target_map[end, :] .= height_average + + # Let the heightmap converge towards the target at a slow rate. + new_ϕ = ϕ + ω .* (target_map - ϕ) + + max_update = maximum(abs.(new_ϕ)) + # println("Minimum / Maximum of the height map after relaxation.") + # println("\tMax update = $( maximum(ϕ) )") + # println("\tMin update = $( minimum(ϕ) )") + @assert !isnan(max_update) """ MAX UPDATE IS NOT A NaN!!! \n + Max height = $( maximum(ϕ) ) -- Min height = $( minimum(ϕ) ) -- Height average = $(height_average) \n + Max divergence = $( maximum(divergence) ) -- Min divergence = $( minimum(divergence) )""" - return set_heights!(mesh, height_map, height_scale = 1.0) + return new_ϕ, max_update end @@ -224,8 +274,15 @@ function get_area_pixels(mesh::FaceMesh) pixel_areas = zeros(Float64, size(mesh)) for ci ∈ CartesianIndices(pixel_areas) - pixel_areas[ci] = - area(top_triangle3D(mesh, ci)...) + area(bot_triangle3D(mesh, ci)...) + top_tri_area = area(top_triangle3D(mesh, ci)...) + bot_tri_area = area(bot_triangle3D(mesh, ci)...) + + isnan(top_tri_area) && + println("NaN area at $(ci) for top triangle $(top_triangle3D(mesh, ci)).") + isnan(bot_tri_area) && + println("NaN area at $(ci) for bottom triangle $(bot_triangle3D(mesh, ci)).") + + pixel_areas[ci] = top_tri_area + bot_tri_area end return pixel_areas @@ -264,48 +321,6 @@ end -""" -$(SIGNATURES) - -This function implements successive over relaxation for a matrix and its associated error matrix -There is a hardcoded assumption of Neumann boundary conditions--that the derivative across the -boundary must be zero in all cases. See: -https://math.stackexchange.com/questions/3790299/how-to-iteratively-solve-poissons-equation-with-no-boundary-conditions - -""" -function relax!(height_map::Matrix{Float64}, divergence::Matrix{Float64}) - height, width = size(height_map) - n_pixels = height * width - val_average = sum(height_map) / n_pixels - - # Embed matrix within a larger matrix for better vectorization and avoid duplicated code - container = zeros(Float64, height + 2, width + 2) - - container .= val_average - container[2:height+1, 2:height+1] .= height_map[:, :] - - val_up = container[1:height, 2:width+1] - val_down = container[3:height+2, 2:width+1] - val_left = container[2:height+1, 1:width] - val_right = container[2:height+1, 3:width+2] - - # Target position. The target is the current height map smoothed by averaging to which the - # divergence is added. - target_map = (val_up + val_down + val_left + val_right) ./ 4.0 - target_map += divergence - - # Let the heightmap converge towards the target at a slow rate. - height_map = height_map + ω .* (target_map - height_map) - - max_update = maximum(abs.(height_map)) - println("Minimum / Maximum of the height map after relaxation.") - println("\tMax update = $( maximum(height_map) )") - println("\tMin update = $( minimum(height_map) )") - - return max_update -end - - """ $(SIGNATURES) @@ -353,9 +368,10 @@ function find_maximum_t(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) else # There can be no solution if, after translation, B abd C move in parallel direction. - # C will never end up on the line AB.result_mesh.rectangles[row, col].z = height_map[row, col] + # C will never end up on the line AB. # Very unlikely with Float64. - return missing, missing + # Negative numbers are filtered out when calculating the minimum jiggle ratio + return -1.0, -1.0 end end end @@ -373,9 +389,9 @@ $(SIGNATURES) function march_mesh!(mesh::FaceMesh, ϕ::Matrix{Float64}) ∇ϕᵤ, ∇ϕᵥ = ∇(ϕ) - println("Min/Max of values of ϕ: $(minimum(ϕ)) / $(maximum(ϕ))") - println("Sum of values of ∇ϕᵤ: $( sum(∇ϕᵤ) )") - println("Sum of values of ∇ϕᵥ: $( sum(∇ϕᵥ) )") + # println("Min/Max of values of ϕ: $(minimum(ϕ)) / $(maximum(ϕ))") + # println("Sum of values of ∇ϕᵤ: $( sum(∇ϕᵤ) )") + # println("Sum of values of ∇ϕᵥ: $( sum(∇ϕᵥ) )") height, width = size(ϕ) @@ -384,63 +400,110 @@ function march_mesh!(mesh::FaceMesh, ϕ::Matrix{Float64}) # I.e. velocity (Vx, Vy) = (0, 0) and the square of acrylate will remain # of the same size. # Warning: The indices are necessary because topleft and ∇ϕ are of different sizes - mesh.topleft.vx[1:height, 1:width] .= -∇ϕᵤ[1:height, 1:width] - mesh.topleft.vy[1:height, 1:width] .= -∇ϕᵥ[1:height, 1:width] + # CHECK SIGNS! + mesh.topleft.vr[1:height, 1:width] .= ∇ϕᵤ[1:height, 1:width] + mesh.topleft.vc[1:height, 1:width] .= ∇ϕᵥ[1:height, 1:width] # The velocity matrix was initialized with zeros everywhere. We nevertheless ovewrite them just in case... - fill_borders!(mesh.topleft.vx, 0.0) - fill_borders!(mesh.topleft.vy, 0.0) + fill_borders!(mesh.topleft.vr, 0.0) + fill_borders!(mesh.topleft.vc, 0.0) - # Basically infinity time to shrink a triangle to zip. + # Basically infinity time to shrink a triangle to nothing. min_positive_t = Inf - max_negative_t = -Inf + list_min_pos_t = zeros(Float64, (height - 2) * (width - 2)) + mesh_x = copy(mesh.topleft.r) for row ∈ 1:height-1, col ∈ 1:width-1 - top_tri = top_triangle3D(mesh, row, col) + # # Jiggle each point in a random order. + # for (row, col) ∈ shuffle([(r, c) for r ∈ 2:height-1, c ∈ 2:width-1]) # Get the time, at that velocity, for the area of the triangle to be nil. - # We are only interested in positive times. - t1, t2 = find_maximum_t(top_tri) - for t ∈ [t1, t2] - if (!ismissing(t)) && (0 < t < min_positive_t) - min_positive_t = t + # We are only interested by positive values to only move in the direction of the gradient + for triangle ∈ [top_triangle3D(mesh, row, col), bot_triangle3D(mesh, row, col)] + t1, t2 = find_maximum_t(triangle) + for t ∈ [t1, t2] + if (!ismissing(t)) && (0 < t < min_positive_t) + min_positive_t = t + end end - if (!ismissing(t)) && (max_negative_t < t < 0) - max_negative_t = t - end - end - bot_tri = bot_triangle3D(mesh, row, col) - - # Get the time, at that velocity, for the area of the triangle to be nil. - # We are only interested in positive times. - t1, t2 = find_maximum_t(bot_tri) - for t ∈ [t1, t2] - if (!ismissing(t)) && (0 < t < min_positive_t) - min_positive_t = t - end - if (!ismissing(t)) && (max_negative_t < t < 0) - max_negative_t = t - end + δ = min_positive_t / 2.0 + mesh.topleft.r[row, col] -= δ * ∇ϕᵤ[row, col] + mesh.topleft.c[row, col] -= δ * ∇ϕᵥ[row, col] end + # list_min_pos_t[(row-1)+(col-2)*(width-2)] + # println("March mesh δ: $(δ)") end + mesh.topleft.r[1:height, 1] .= 1:height + mesh.topleft.r[1:height, width] .= 1:height + mesh.topleft.c[1, 1:width] .= 1:width + mesh.topleft.c[height, 1:width] .= 1:width + + print("Average mesh changes on x = $(sum(abs.(mesh.topleft.r - mesh_x)))") + # Modify the mesh triangles but ensuring that we are far from destroying any of them with a nil area. # Use the maximum change possible (negative or positive) - δ = (abs(max_negative_t) < min_positive_t) ? min_positive_t / 2.0 : max_negative_t / 2.0 - - println("Overall maximum variations:") - println("\tOverall min_positive_t: $(min_positive_t)") - println("\tOverall max_negative_t: $(max_negative_t)") - println("\tUsing δ: $(δ)") + # δ = min_positive_t / 2.0 + # println( + # "\tMarch mesh with average factor $(sum(list_min_pos_t) / length(list_min_pos_t))\n", + # ) - mesh.topleft.x[1:height, 1:width] .-= δ .* ∇ϕᵤ[1:height, 1:width] - mesh.topleft.y[1:height, 1:width] .-= δ .* ∇ϕᵥ[1:height, 1:width] + # println("Overall maximum variations:") + # println("\tOverall min_positive_t: $(min_positive_t)") + # println("\tOverall max_negative_t: $(max_negative_t)") + # println("\tUsing δ: $(δ)") # saveObj(mesh, "gateau.obj") end +""" +$(SIGNATURES) +""" +function ∇(ϕ::Matrix{Float64}) + height, width = size(ϕ) + + ∇ϕᵤ = zeros(Float64, height, width) # the right edge will be filled with zeros + ∇ϕᵥ = zeros(Float64, height, width) # the bottom edge will be filled with zeros + + for row ∈ 1:height-1, col ∈ 1:width-1 + ∇ϕᵤ[row, col] = ϕ[row+1, col] - ϕ[row, col] + ∇ϕᵥ[row, col] = ϕ[row, col+1] - ϕ[row, col] + end + + ∇ϕᵤ[1:end, end] .= 0.0 + ∇ϕᵤ[end, 1:end] .= 0.0 + + ∇ϕᵥ[1:end, end] .= 0.0 + ∇ϕᵥ[end, 1:end] .= 0.0 + + return ∇ϕᵤ, ∇ϕᵥ +end + + +""" +$(SIGNATURES) + +This function will take a `grid_definition x grid_definition` matrix and returns a +`grid_definition x grid_definition` mesh. + +""" +function matrix_to_mesh(ϕ::Matrix{Float64}) + height, width = size(ϕ) + + mesh = FaceMesh(height, width) + + # 1 more topleft than pixels! Therefore compiler needs to specify exact indices. + mesh.topleft.z[1:height, 1:width] .= ϕ[1:height, 1:width] + + # The borders' height is forced at 0. + fill_borders!(mesh.topleft.z, 0.0) + + return mesh +end + + """ $(SIGNATURES) @@ -474,11 +537,11 @@ function create_solid( cols = repeat(Float64.(1:width)', height, 1) bottom_mesh = FaceMesh(height, width) - bottom_mesh.topleft.x[:] .= rows[:] - bottom_mesh.topleft.y[:] .= cols[:] + bottom_mesh.topleft.r[:] .= rows[:] + bottom_mesh.topleft.c[:] .= cols[:] bottom_mesh.topleft.z[:] .= -Bottom_Offset - bottom_mesh.topleft.vx[:] .= 0.0 - bottom_mesh.topleft.vx[:] .= 0.0 + bottom_mesh.topleft.vr[:] .= 0.0 + bottom_mesh.topleft.vr[:] .= 0.0 ### @@ -542,51 +605,3 @@ function create_solid( return RectangleMesh(nodeList, nodeArrarowBottom, triangles, width, height) end - - - - -""" -$(SIGNATURES) -""" -function ∇(ϕ::Matrix{Float64}) - height, width = size(ϕ) - - ∇ϕᵤ = zeros(Float64, height, width) # the right edge will be filled with zeros - ∇ϕᵥ = zeros(Float64, height, width) # the bottom edge will be filled with zeros - - for row ∈ 1:height-1, col ∈ 1:width-1 - ∇ϕᵤ[row, col] = ϕ[row+1, col] - ϕ[row, col] - ∇ϕᵥ[row, col] = ϕ[row, col+1] - ϕ[row, col] - end - - ∇ϕᵤ[1:end, end] .= 0.0 - ∇ϕᵤ[end, 1:end] .= 0.0 - - ∇ϕᵥ[1:end, end] .= 0.0 - ∇ϕᵥ[end, 1:end] .= 0.0 - - return ∇ϕᵤ, ∇ϕᵥ -end - - -""" -$(SIGNATURES) - -This function will take a `grid_definition x grid_definition` matrix and returns a -`grid_definition x grid_definition` mesh. - -""" -function matrix_to_mesh(height_map::Matrix{Float64}) - height, width = size(height_map) - - mesh = FaceMesh(height, width) - - # 1 more topleft than pixels! Therefore compiler needs to specify exact indices. - mesh.topleft.z[1:height, 1:width] .= height_map[1:height, 1:width] - - # The borders' height is forced at 0. - fill_borders!(mesh.topleft.z, 0.0) - - return mesh -end diff --git a/src/scratchpad.jl b/src/scratchpad.jl index bba6fea..05c6b24 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -4,10 +4,14 @@ using Images image = Images.load("./examples/cat_posing.jpg"); # Check current working directory with pwd() using CausticsEngineering -mesh, image_caustics = engineer_caustics(image); +mesh, imageBW = engineer_caustics(image); + +Gray.(imageBW) + +mesh.topleft.r[250:260, 250:260] +mesh.topleft.c[250:260, 250:260] +mesh.topleft.z[250:260, 250:260] -Gray.(image_caustics) -Gray.(Float64.(Gray.(image)) - image_caustics) using Test diff --git a/src/utilities.jl b/src/utilities.jl index 7535ee6..40d2c13 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -5,14 +5,14 @@ $(TYPEDEF) """ struct Vertex3D - x::Float64 - y::Float64 + r::Float64 + c::Float64 z::Float64 - vx::Float64 - vy::Float64 + vr::Float64 + vc::Float64 - Vertex3D(x, y, z, vx, vy) = new(x, y, z, vx, vy) + Vertex3D(r, c, z, vr, vc) = new(r, c, z, vr, vc) Vertex3D() = new(0.0, 0.0, 0.0, 0.0, 0.0) end @@ -20,20 +20,20 @@ end $(SIGNATURES) """ function dist(p1::Tuple{Float64,Float64,Float64}, p2::Tuple{Float64,Float64,Float64}) - dx = p2[1] - p1[1] - dy = p2[2] - p1[2] + dr = p2[1] - p1[1] + dc = p2[2] - p1[2] dz = p2[3] - p1[3] - return sqrt(dx^2 + dy^2 + dz^2) + return sqrt(dr^2 + dc^2 + dz^2) end """ $(SIGNATURES) """ function dist(p1::Vertex3D, p2::Vertex3D) - dx = p2.x - p1.x - dy = p2.y - p1.y + dr = p2.r - p1.r + dc = p2.c - p1.c dz = p2.z - p1.z - return sqrt(dx^2 + dy^2 + dz^2) + return sqrt(dr^2 + dc^2 + dz^2) end @@ -72,7 +72,7 @@ $(SIGNATURES) A midpoint is the average between two points """ midpoint(p1::Vertex3D, p2::Vertex3D) = - Vertex3D((p1.x + p2.x) / 2.0, (p1.y + p2.y) / 2.0, (p1.z + p2.z) / 2.0, 0.0, 0.0) + Vertex3D((p1.r + p2.r) / 2.0, (p1.c + p2.c) / 2.0, (p1.z + p2.z) / 2.0, 0.0, 0.0) """ @@ -81,8 +81,8 @@ $(SIGNATURES) Centroid of three points. """ centroid(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) = Vertex3D( - (p1.x + p2.x + p3.x) / 3.0, - (p1.y + p2.y + p3.y) / 3.0, + (p1.r + p2.r + p3.r) / 3.0, + (p1.c + p2.c + p3.c) / 3.0, (p1.z + p2.z + p3.z) / 3.0, 0, 0, @@ -118,29 +118,32 @@ Implementation is a struc of arrays. Easier to vectorise. mutable struct FieldVertex3D size::Tuple{Int,Int} - x::AbstractMatrix{Float64} + r::AbstractMatrix{Float64} y::AbstractMatrix{Float64} z::AbstractMatrix{Float64} - vx::AbstractMatrix{Float64} - vy::AbstractMatrix{Float64} + vr::AbstractMatrix{Float64} + vc::AbstractMatrix{Float64} function FieldVertex3D(height, width) - # mx = zeros(Float64, height + 1, width + 1) + # mr = zeros(Float64, height + 1, width + 1) # my = zeros(Float64, height + 1, width + 1) # mz = zeros(Float64, height + 1, width + 1) - # mvx = zeros(Float64, height + 1, width + 1) - # mvy = zeros(Float64, height + 1, width + 1) + # mvr = zeros(Float64, height + 1, width + 1) + # mvc = zeros(Float64, height + 1, width + 1) - mx = rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 - my = rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 + rows = repeat(Float64.(1:height+1), 1, width + 1) + cols = repeat(Float64.(1:width+1)', height + 1, 1) + + mr = rows + rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 + my = cols + rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 mz = rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 - mvx = rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 - mvy = rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 + mvr = rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 + mvc = rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 - new((height, width), mx, my, mz, mvx, mvy) + new((height, width), mr, my, mz, mvr, mvc) end end @@ -155,11 +158,11 @@ function Vertex3D(fv::FieldVertex3D, row, col) if (1 <= row <= height + 1) && (1 <= col <= width + 1) Vertex3D( - fv.x[row, col], + fv.r[row, col], fv.y[row, col], fv.z[row, col], - fv.vx[row, col], - fv.vy[row, col], + fv.vr[row, col], + fv.vc[row, col], ) else missing @@ -194,38 +197,32 @@ struct FaceMesh toptriangles::AbstractMatrix{Tuple{Tuple{Int,Int},Tuple{Int,Int},Tuple{Int,Int}}} bottriangles::AbstractMatrix{Tuple{Tuple{Int,Int},Tuple{Int,Int},Tuple{Int,Int}}} - as_index::Function - FaceMesh(s, tl, tt, bt) = new(s, tl, tt, bt) -end -function FaceMesh(height::Int, width::Int) + function FaceMesh(height::Int, width::Int) + m_topleft = FieldVertex3D(height, width) + t_triangles = Matrix{Tuple{Tuple{Int,Int},Tuple{Int,Int},Tuple{Int,Int}}}( + undef, + height, + width, + ) + b_triangles = Matrix{Tuple{Tuple{Int,Int},Tuple{Int,Int},Tuple{Int,Int}}}( + undef, + height, + width, + ) - function as_index(r, c) - # Adding "+ 1" since it is the size of the `topleft` matrix - if 1 <= r <= height + 1 && 1 <= c <= width + 1 - return r + (c - 1) * (width + 1) - else - return nothing + for row ∈ 1:height, col ∈ 1:width + t_triangles[row, col] = ((row, col), (row + 1, col), (row, col + 1)) + b_triangles[row, col] = ((row, col + 1), (row + 1, col), (row + 1, col + 1)) end - end - as_index(ci::CartesianIndex) = as_index(ci[1], ci[2]) - m_topleft = FieldVertex3D(height, width) - t_triangles = - Matrix{Tuple{Tuple{Int,Int},Tuple{Int,Int},Tuple{Int,Int}}}(undef, height, width) - b_triangles = - Matrix{Tuple{Tuple{Int,Int},Tuple{Int,Int},Tuple{Int,Int}}}(undef, height, width) - - for row ∈ 1:height, col ∈ 1:width - t_triangles[row, col] = ((row, col), (row + 1, col), (row, col + 1)) - b_triangles[row, col] = ((row, col + 1), (row + 1, col), (row + 1, col + 1)) + return FaceMesh((height, width), m_topleft, t_triangles, b_triangles) end - - return FaceMesh((height, width), m_topleft, t_triangles, b_triangles) end + """ $(SIGNATURES) @@ -258,31 +255,32 @@ Converts a triangle as a triplet of references to mesh vertices to a triplet of """ function top_triangle3D(mesh::FaceMesh, row::Int, col::Int) height, width = size(mesh) - if 1 <= row <= height + 1 && 1 <= col <= width + 1 + if 1 <= row <= height && 1 <= col <= width t = mesh.toptriangles[row, col] - t1 = CartesianIndex(t[1][1], t[1][2]) - t2 = CartesianIndex(t[2][1], t[2][2]) - t3 = CartesianIndex(t[3][1], t[3][2]) + t1_row, t1_col = t[1] + t2_row, t2_col = t[2] + t3_row, t3_col = t[3] + p1 = Vertex3D( - mesh.topleft.x[t1], - mesh.topleft.y[t1], - mesh.topleft.z[t1], - mesh.topleft.vx[t1], - mesh.topleft.vy[t1], + mesh.topleft.r[t1_row, t1_col], + mesh.topleft.c[t1_row, t1_col], + mesh.topleft.z[t1_row, t1_col], + mesh.topleft.vr[t1_row, t1_col], + mesh.topleft.vc[t1_row, t1_col], ) p2 = Vertex3D( - mesh.topleft.x[t2], - mesh.topleft.y[t2], - mesh.topleft.z[t2], - mesh.topleft.vx[t2], - mesh.topleft.vy[t2], + mesh.topleft.r[t2_row, t2_col], + mesh.topleft.c[t2_row, t2_col], + mesh.topleft.z[t2_row, t2_col], + mesh.topleft.vr[t2_row, t2_col], + mesh.topleft.vc[t2_row, t2_col], ) p3 = Vertex3D( - mesh.topleft.x[t3], - mesh.topleft.y[t3], - mesh.topleft.z[t3], - mesh.topleft.vx[t3], - mesh.topleft.vy[t3], + mesh.topleft.r[t3_row, t3_col], + mesh.topleft.c[t3_row, t3_col], + mesh.topleft.z[t3_row, t3_col], + mesh.topleft.vr[t3_row, t3_col], + mesh.topleft.vc[t3_row, t3_col], ) return (p1, p2, p3) else @@ -295,31 +293,32 @@ top_triangle3D(mesh::FaceMesh, ci::CartesianIndex{2}) = top_triangle3D(mesh, ci[ function bot_triangle3D(mesh::FaceMesh, row::Int, col::Int) height, width = size(mesh) - if 1 <= row <= height + 1 && 1 <= col <= width + 1 + if 1 <= row <= height && 1 <= col <= width t = mesh.bottriangles[row, col] - t1 = CartesianIndex(t[1][1], t[1][2]) - t2 = CartesianIndex(t[2][1], t[2][2]) - t3 = CartesianIndex(t[3][1], t[3][2]) + t1_row, t1_col = t[1] + t2_row, t2_col = t[2] + t3_row, t3_col = t[3] + p1 = Vertex3D( - mesh.topleft.x[t1], - mesh.topleft.y[t1], - mesh.topleft.z[t1], - mesh.topleft.vx[t1], - mesh.topleft.vy[t1], + mesh.topleft.r[t1_row, t1_col], + mesh.topleft.c[t1_row, t1_col], + mesh.topleft.z[t1_row, t1_col], + mesh.topleft.vr[t1_row, t1_col], + mesh.topleft.vc[t1_row, t1_col], ) p2 = Vertex3D( - mesh.topleft.x[t2], - mesh.topleft.y[t2], - mesh.topleft.z[t2], - mesh.topleft.vx[t2], - mesh.topleft.vy[t2], + mesh.topleft.r[t2_row, t2_col], + mesh.topleft.c[t2_row, t2_col], + mesh.topleft.z[t2_row, t2_col], + mesh.topleft.vr[t2_row, t2_col], + mesh.topleft.vc[t2_row, t2_col], ) p3 = Vertex3D( - mesh.topleft.x[t3], - mesh.topleft.y[t3], - mesh.topleft.z[t3], - mesh.topleft.vx[t3], - mesh.topleft.vy[t3], + mesh.topleft.r[t3_row, t3_col], + mesh.topleft.c[t3_row, t3_col], + mesh.topleft.z[t3_row, t3_col], + mesh.topleft.vr[t3_row, t3_col], + mesh.topleft.vc[t3_row, t3_col], ) return (p1, p2, p3) else From c97a3173adae5ce9bf2450f217b6df31c43ab9d2 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Tue, 7 Sep 2021 09:10:34 +0200 Subject: [PATCH 15/58] gitignore --- .gitignore | 6 ++++++ 1 file changed, 6 insertions(+) diff --git a/.gitignore b/.gitignore index 049a072..70e3c74 100644 --- a/.gitignore +++ b/.gitignore @@ -1,3 +1,4 @@ +# Editors .vscode # Files generated by invoking Julia with --code-coverage @@ -27,3 +28,8 @@ docs/site/ # committed for packages, but should be committed for applications that require a static # environment. Manifest.toml + +# Misc. +*.tmp +*.temp + From ddb9137fb37d75cce2d7ec57121785f16d169774 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Tue, 7 Sep 2021 17:57:34 +0200 Subject: [PATCH 16/58] Refactoring ongoing. Snapshot 11 --- .gitignore | 1 + examples/loss_it1.png | Bin 260739 -> 0 bytes examples/loss_it10.png | Bin 188017 -> 0 bytes examples/loss_it11.png | Bin 188017 -> 0 bytes examples/loss_it2.png | Bin 241645 -> 0 bytes examples/loss_it3.png | Bin 216340 -> 0 bytes examples/loss_it4.png | Bin 204447 -> 0 bytes examples/loss_it5.png | Bin 173745 -> 0 bytes examples/loss_it6.png | Bin 188018 -> 0 bytes examples/loss_it7.png | Bin 188018 -> 0 bytes examples/loss_it8.png | Bin 188018 -> 0 bytes examples/loss_it9.png | Bin 188018 -> 0 bytes src/CausticsEngineering.jl | 7 - src/create_mesh.jl | 280 +++++++++++++++++++++++-------------- src/io.jl | 26 +--- src/parameters.jl | 7 +- src/plots.jl | 54 ++++++- src/scratchpad.jl | 11 +- src/utilities.jl | 237 ++++++++++++++++--------------- 19 files changed, 366 insertions(+), 257 deletions(-) delete mode 100644 examples/loss_it1.png delete mode 100644 examples/loss_it10.png delete mode 100644 examples/loss_it11.png delete mode 100644 examples/loss_it2.png delete mode 100644 examples/loss_it3.png delete mode 100644 examples/loss_it4.png delete mode 100644 examples/loss_it5.png delete mode 100644 examples/loss_it6.png delete mode 100644 examples/loss_it7.png delete mode 100644 examples/loss_it8.png delete mode 100644 examples/loss_it9.png diff --git a/.gitignore b/.gitignore index 70e3c74..5376b6d 100644 --- a/.gitignore +++ b/.gitignore @@ -6,6 +6,7 @@ *.jl.*.cov *.obj +loss*.png # Files generated by invoking Julia with --track-allocation diff --git a/examples/loss_it1.png b/examples/loss_it1.png deleted file mode 100644 index c95fd1f2b83d3eb9121b7a3fcba82100a85878dd..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 260739 zcmXtf3p`W*|9|CD5^|3a+f43k$X)JRbIU#CHup;|Qz0sgFv47ix#n8rek=F;W#*dr zP`S>O+!LkzkMIBSdl-8-J7*7G@8|3JdOn}$y;u_?eWuI2m(QI$$Am=an4UX#;r!Y6 zr3=6jhsZw)z!R;zrlID!b2W*KCr)(0@8>b5`da7Sk@+@&Uj)$zQ^RxTLZRo*J&!zh 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--- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -4,43 +4,55 @@ $(SIGNATURES) function engineer_caustics(source_image) imageBW = Float64.(Gray.(source_image)) - width, height = size(imageBW) + height, width = size(imageBW) println("Image size: $((height, width))") # mesh is the same size as the image with an extra row/column to have coordinates to # cover each image pixel with a triangle. mesh = FaceMesh(height, width) - print("Mesh creation: ") - println("$(mesh.topleft.vr[256, 256]) , $(mesh.topleft.vc[256, 256])") + println("Mesh creation: ") + r_check = 1 + c_check = 1 + println( + "\tCoordinates: $(mesh.topleft.r[r_check, c_check]) , $(mesh.topleft.c[r_check, c_check]) , $(mesh.topleft.h[r_check, c_check])", + ) + println( + "\tVelocities: $(mesh.topleft.vr[r_check, c_check]) , $(mesh.topleft.vc[r_check, c_check])", + ) - # We need to boost the brightness of the image so that its sum and the sum of the area are equal - average_intensity = sum(imageBW) / (width * height) + # The energy going through the lens is equal to the amount of energy on the caustics + total_energy_lens = height * width + total_energy_caustics = sum(imageBW) + correction_ratio = (width * height) / sum(imageBW) # imageBW is `grid_definition x grid_definition` and is normalised to the same (sort of) _energy_ as the # original image. - imageBW = imageBW ./ average_intensity + imageBW = imageBW .* correction_ratio - for i ∈ 1:5 - println("\nSTARTING HORIZONTAL ITERATION $(i) ---") + for i ∈ 1:256 + println("\nSTARTING VERTICAL ITERATION $(i) ---") - print("Horizontal move: ") max_update = move_vertically!(mesh, imageBW, "it$(i)") - println(" max update = $(max_update)") + print("Vertical move max update = $(max_update)") - # println("$(mesh.topleft.vr[256, 256]) , $(mesh.topleft.vc[256, 256])") - # println(" (Speed at 256, 256 = $(mesh.topleft.vr[256, 256]) , $(mesh.topleft.vc[256, 256])") + println( + "\tCoordinates: $(mesh.topleft.r[r_check, c_check]) , $(mesh.topleft.c[r_check, c_check]) , $(mesh.topleft.h[r_check, c_check])", + ) + println( + "\tVelocities: $(mesh.topleft.vr[r_check, c_check]) , $(mesh.topleft.vc[r_check, c_check])", + ) println("---------- ITERATION $(i): $(max_update)/n") end - print("Vertical move: ") - mesh.topleft.z, max_update = + println("\nSTARTING HORIZONTAL ITERATION ---") + mesh.topleft.h, max_update = move_horizontally(mesh, imageBW; f = 1.0, picture_width = Caustics_Side) println(" max update = $(max_update)") - println("$(mesh.topleft.vr[256, 256]) , $(mesh.topleft.vc[256, 256])") + println("$(mesh.topleft.vr[r_check, c_check]) , $(mesh.topleft.vc[r_check, c_check])") # solidMesh = create_solid(mesh) @@ -48,7 +60,7 @@ function engineer_caustics(source_image) # solidMesh, # "./examples/original_image.obj", # scale = Float64(1 / Grid_Definition * Artifact_Size), - # scalez = Float64(1 / Grid_Definition * Artifact_Size), + # scaleh = Float64(1 / Grid_Definition * Artifact_Size), # ) return mesh, imageBW @@ -67,25 +79,25 @@ function move_vertically!(mesh, image, suffix) # - any pixel on the caustic projection receives light from a given 'rectangle' on the lens. # - That rectangle is made of 2 triangles. area_distorted_pixels = get_area_pixels(mesh) + @assert max_sum_abs(area_distorted_pixels) "ALERT: vert. Δ area_distorted_pixels is too large - max/min = $(maximum(area_distorted_pixels)) / $(minimum(area_distorted_pixels))" + intensity_error = Float64.(area_distorted_pixels - image) + @assert max_sum_abs(intensity_error) "ALERT: vert. Δ intensity_error is too large - max/min = $(maximum(intensity_error)) / $(minimum(intensity_error))" # The divergence matrix moves all the topleft corners. illumination_error is therefore not large enough. height, width = size(mesh) divergence_intensity = zeros(Float64, height + 1, width + 1) divergence_intensity[1:height, 1:width] .= intensity_error[1:height, 1:width] + fill_borders!(divergence_intensity, 0.0) + + @assert max_sum_abs(divergence_intensity) "ALERT: vert. Δ divergence_intensity is too large - max/min = $(maximum(divergence_intensity)) / $(minimum(divergence_intensity))" - divergence_intensity[:, 1] .= 0.0 - divergence_intensity[:, end] .= 0.0 - divergence_intensity[1, :] .= 0.0 - divergence_intensity[end, :] .= 0.0 # Save the loss image as a png plot_loss!(divergence_intensity, suffix, image) # ϕ is the _heightmap_ therefore size of topleft - # ϕ = zeros(Float64, size(image)) - # ϕ = rand(Float64, height+1, width+1) ./ 1_000 .- 0.5 / 1_000 - ϕ = mesh.topleft.z + ϕ = mesh.topleft.h max_update = 100.0 interaction_count = 0 @@ -98,13 +110,16 @@ function move_vertically!(mesh, image, suffix) if abs(max_update) < 1e-6 || abs((max_update - old_max_update) / old_max_update) < 0.01 println( - "Convergence stopped at step $(interaction_count) with max_update of $(max_update)", + "Convergence stopped at step $(interaction_count) with ", + "max_update = $(max_update) -- ", + "max/min area_distorted_pixels = $(maximum(area_distorted_pixels)) / $(minimum(area_distorted_pixels)) -- ", + "max divergence = $(maximum(abs.(divergence_intensity)))", ) break end end - mesh.topleft.z[1:height+1, 1:width+1] .= ϕ[1:height+1, 1:width+1] + mesh.topleft.h[1:height+1, 1:width+1] .= ϕ[1:height+1, 1:width+1] save_stl!( matrix_to_mesh(ϕ * 0.02), @@ -112,10 +127,24 @@ function move_vertically!(mesh, image, suffix) reverse = false, flipxy = true, ) - # plotAsQuiver(ϕ * -1.0, stride=30, scale=1.0, max_length=200, flipxy=true, reversex=false, reversey=false) + + # plot_as_quiver(ϕ * -1.0, stride=30, scale=1.0, max_length=200, flipxy=true, reverser=false, reversec=false) + plot_as_quiver( + mesh, + stride = 30, + scale = 1.0, + max_length = 200, + flipxy = true, + reverser = false, + reversec = false, + ) + + # plot_as_quiver(ϕ * -1.0, stride=30, scale=1.0, max_length=200, flipxy=true, reversex=false, reversey=false) # saveObj(matrix_to_mesh(D * 10), "D_$(suffix).obj") # Now we need to march the x,y locations in our mesh according to this gradient! + # Tasks are a control flow feature that allows computations to be suspended and resumed in a flexible manner. + # We mention them here only for completeness; for a full discussion see Asynchronous Programming. march_mesh!(mesh, ϕ) save_stl!(mesh, "./examples/mesh_$(suffix).obj", flipxy = true) @@ -141,8 +170,8 @@ function move_horizontally( # Coordinates difference # Coordinates on the caustics = simple rectangular values in pixels. # Coordinates on the lens face comes from topleft field. - d_row = repeat(Float64.(1:height+1), 1, width + 1) - mesh.topleft.r - d_col = repeat(Float64.(1:width+1)', height + 1, 1) - mesh.topleft.c + d_row = mesh.topleft.rows_numbers - mesh.topleft.r + d_col = mesh.topleft.cols_numbers - mesh.topleft.c # true_H is the real distance beteen the surface of the lens and the projection # H is the initial distance from the surface of the carved face to the projection screen. @@ -151,8 +180,8 @@ function move_horizontally( # Note: Higher location means closer to the caustics => negative sign H = f / Meters_Per_Pixel - true_H = similar(mesh.topleft.z) - @. true_H[:] = -mesh.topleft.z[:] + H + true_H = similar(mesh.topleft.h) + @. true_H[:] = -mesh.topleft.h[:] + H # Normals. N_row = zeros(Float64, height + 1, width + 1) @@ -168,10 +197,10 @@ function move_horizontally( divergence_direction = zeros(Float64, width + 1, height + 1) divergence_direction[1:height, 1:width] = div_row + div_col - divergence_direction[:, 1] .= 0.0 - divergence_direction[:, end] .= 0.0 - divergence_direction[1, :] .= 0.0 - divergence_direction[end, :] .= 0.0 + fill_borders!(divergence_direction, 0.0) + + @assert max_sum_abs(divergence_direction) "ALERT: horiz. Δ divergence_direction is too large - max/min = $(maximum(divergence_direction)) / $(minimum(divergence_direction))" + println("Have all the divergences") @@ -183,11 +212,15 @@ function move_horizontally( iteration_count % 100 == 0 && println("Converging for divergence: $(max_update)") old_max_update = max_update - ϕ, max_update = relax_vertically(ϕ, divergence_direction) + ϕ, max_update = relax_vertically(ϕ, -divergence_direction) + @assert max_sum_abs(ϕ) "ALERT: horiz. Δ ϕ is too large - max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ))" + + if abs(max_update) < 1e-6 || abs((max_update - old_max_update) / old_max_update) < 0.01 println( - "Convergence stopped improving at step $(iteration_count) with max_update of $(max_update)", + "Convergence stopped improving at step $(iteration_count) ", + "with max_update of $(max_update)", ) break end @@ -209,51 +242,64 @@ https://math.stackexchange.com/questions/3790299/how-to-iteratively-solve-poisso """ function relax_vertically(ϕ::Matrix{Float64}, divergence::Matrix{Float64}) - # ϕ is the size of topleft + @assert max_sum_abs(ϕ) "ALERT: relaxation ϕ is too large - max/min = $(maximum(ϕ)) / $(minimum(ϕ))" + @assert max_sum_abs(divergence) "ALERT: relaxation divergence is too large - max/min = $(maximum(divergence)) / $(minimum(divergence))" + + @assert any(isnan.(ϕ)) == false "Calling relaxation with a ϕ that contains NaN!!" + @assert any(isnan.(divergence)) == false "Calling relaxation with a divergence that contains NaN!!" + + + # ϕ is of the same size of topleft height, width = size(ϕ) n_pixels = height * width height_average = sum(ϕ) / n_pixels + # Laplacian + # Embed matrix within a larger matrix for better vectorization and avoid duplicated code # Size of ϕ/topleft is h+1, w+1. container adds 1 row/col before and 1 row/col after container_height = 1 + height + 1 container_width = 1 + width + 1 container = zeros(Float64, container_height, container_width) + container[2:container_height-1, 2:container_width-1] .= ϕ + @assert max_sum_abs(container) "ALERT: relaxation container is too large - max/min = $(maximum(container)) / $(minimum(container))" - container[2:container_height-1, 2:container_width-1] .= ϕ[:, :] - container[:, begin] .= height_average - container[:, end] .= height_average - container[begin, :] .= height_average - container[end, :] .= height_average - - # Those values are height x width - height_up = container[2-1:container_height-1-1, 2:container_width-1] - height_down = container[2+1:container_height-1+1, 2:container_width-1] - height_left = container[2:container_height-1, 2-1:container_width-1-1] - height_right = container[2:container_height-1, 2+1:container_width-1+1] + # Those values are all of ϕ's size but shifted in 4 directions + height_above = container[2-1:container_height-1-1, 2+0:container_width-1] + height_below = container[2+1:container_height-1+1, 2+0:container_width-1] + height_left = container[2+0:container_height-1, 2-1:container_width-1-1] + height_right = container[2+0:container_height-1, 2+1:container_width-1+1] # Target position. The target is the current height map smoothed by averaging to which the # divergence is added. - # target_map is the same size mesh.topleft. - target_map = zeros(Float64, height, width) - target_map = (height_up + height_down + height_left + height_right) ./ 4.0 - target_map += divergence + # δ_map is the same size as divergence. + δ_map = zeros(Float64, size(divergence)) + + # δ_map is the Laplacian of the height + δ_map = (height_above + height_below + height_left + height_right) / 4.0 - ϕ + @assert max_sum_abs(δ_map) "ALERT: relaxation δ_map as (average - ϕ) is too large - max/min = $(maximum(δ_map)) / $(minimum(δ_map))" - target_map[:, begin] .= height_average - target_map[:, end] .= height_average - target_map[begin, :] .= height_average - target_map[end, :] .= height_average + # This has to converge towards the divergence. Difference to calculate speed of the descent. + δ_map -= divergence + @assert max_sum_abs(δ_map) "ALERT: relaxation δ_map as including divergence is too large - max/min = $(maximum(δ_map)) / $(minimum(δ_map))" + + # height_div, width_div = size(divergence) + # @. target_map[height_div, width_div] += divergence / 4.0 + fill_borders!(δ_map, 0.0) # Let the heightmap converge towards the target at a slow rate. - new_ϕ = ϕ + ω .* (target_map - ϕ) + # new_ϕ = ϕ + ω .* δ_map + new_ϕ = zeros(Float64, size(divergence)) + + # new_ϕ = ϕ + 1.94 * δ_map + new_ϕ = ϕ + 0.2 * δ_map + @assert any(isnan.(new_ϕ)) == false "new_ϕ contains NaN!!" max_update = maximum(abs.(new_ϕ)) - # println("Minimum / Maximum of the height map after relaxation.") - # println("\tMax update = $( maximum(ϕ) )") - # println("\tMin update = $( minimum(ϕ) )") - @assert !isnan(max_update) """ MAX UPDATE IS NOT A NaN!!! \n - Max height = $( maximum(ϕ) ) -- Min height = $( minimum(ϕ) ) -- Height average = $(height_average) \n - Max divergence = $( maximum(divergence) ) -- Min divergence = $( minimum(divergence) )""" + @assert !isnan(max_update) """ MAX UPDATE IS NOT A NaN!!! + Max height = $( maximum(ϕ) ) -- Min height = $( minimum(ϕ) ) -- Height average = $(height_average) + Max divergence = $( maximum(divergence) ) -- Min divergence = $( minimum(divergence) ) + """ return new_ϕ, max_update end @@ -263,7 +309,7 @@ end $(SIGNATURES) A Mesh is a collection of triangles. The brightness flowing through a given triangle is just proportional to its -area in the x, y plane. z is ignored. +area in the x, y plane. h is ignored. The function returns a matrix with the quantity of light coming from each 'rectangle' around a pixel. That 'rectangle' has been shifted and flexed around. @@ -274,8 +320,8 @@ function get_area_pixels(mesh::FaceMesh) pixel_areas = zeros(Float64, size(mesh)) for ci ∈ CartesianIndices(pixel_areas) - top_tri_area = area(top_triangle3D(mesh, ci)...) - bot_tri_area = area(bot_triangle3D(mesh, ci)...) + top_tri_area = area(triangle3D(mesh, ci, :top)...) + bot_tri_area = area(triangle3D(mesh, ci, :bottom)...) isnan(top_tri_area) && println("NaN area at $(ci) for top triangle $(top_triangle3D(mesh, ci)).") @@ -297,10 +343,13 @@ function quantifyLoss!(D, suffix, img) println("\tMinimum loss: $(minimum(D))") println("\tMaximum loss: $(maximum(D))") + normalised_D_max = D ./ maximum(D) + normalised_D_min = D ./ minimum(D) + blue = zeros(size(D)) - blue[D.>0] = D[D.>0] + blue[D.>0] = normalised_D_max[D.>0] red = zeros(size(D)) - red[D.<0] = -D[D.<0] + red[D.<0] = -normalised_D_min[D.<0] green = zeros(size(D)) # println(size(blue)) @@ -335,23 +384,23 @@ function find_maximum_t(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) # To make the calculation simpler, everything is translated so that A is at the # origin of the plane and its velocity is nil. - Bx = p2.x - p1.x - By = p2.y - p1.y - Cx = p3.x - p1.x - Cy = p3.y - p1.y - - t_vBx = p2.vx - p1.vx - t_vBy = p2.vy - p1.vy - t_vCx = p3.vx - p1.vx - t_vCy = p3.vy - p1.vy - - # After this, given that Ax = Ay = t_vAx = t_vAy = 0, the area is nil iff - # (Bx + t_vBx) (Cy + t_vCy )- (Cx + t_vCx) (By + t_vBy) = 0. + Br = p2.r - p1.r + Bc = p2.c - p1.c + Cr = p3.r - p1.r + Cc = p3.c - p1.c + + t_vBr = p2.vr - p1.vr + t_vBc = p2.vc - p1.vc + t_vCr = p3.vr - p1.vr + t_vCc = p3.vc - p1.vc + + # After this, given that Ar = Ac = t_vAr = t_vAc = 0, the area is nil iff + # (Br + t_vBr) (Cc + t_vCc ) - (Cr + t_vCr) (Bc + t_vBc) = 0. # After expansion and reshuffling to have a quadratic equation where t # is the variable, the coefficients of that equation are: - a = t_vCy * t_vBx - t_vBy * t_vCx - b = -By * t_vCx - Cx * t_vBy + Bx * t_vCy + Cy * t_vBx - c = Bx * Cy - Cx * By + a = t_vCc * t_vBr - t_vBc * t_vCr + b = -Bc * t_vCr - Cr * t_vBc + Br * t_vCc + Cc * t_vBr + c = Br * Cc - Cr * Bc # if a = 0, this is just a linear equation. if a == 0 @@ -401,46 +450,63 @@ function march_mesh!(mesh::FaceMesh, ϕ::Matrix{Float64}) # of the same size. # Warning: The indices are necessary because topleft and ∇ϕ are of different sizes # CHECK SIGNS! - mesh.topleft.vr[1:height, 1:width] .= ∇ϕᵤ[1:height, 1:width] - mesh.topleft.vc[1:height, 1:width] .= ∇ϕᵥ[1:height, 1:width] + mesh.topleft.vr[1:height, 1:width] .= -∇ϕᵤ[1:height, 1:width] + mesh.topleft.vc[1:height, 1:width] .= -∇ϕᵥ[1:height, 1:width] - # The velocity matrix was initialized with zeros everywhere. We nevertheless ovewrite them just in case... - fill_borders!(mesh.topleft.vr, 0.0) - fill_borders!(mesh.topleft.vc, 0.0) + # Just in case... + reset_border_values!(mesh.topleft) # Basically infinity time to shrink a triangle to nothing. min_positive_t = Inf list_min_pos_t = zeros(Float64, (height - 2) * (width - 2)) - mesh_x = copy(mesh.topleft.r) + t1 = zeros(Float64, height, width) + t2 = zeros(Float64, height, width) + + mesh_r = copy(mesh.topleft.r) + mesh_c = copy(mesh.topleft.c) + mesh_h = copy(mesh.topleft.h) for row ∈ 1:height-1, col ∈ 1:width-1 # # Jiggle each point in a random order. # for (row, col) ∈ shuffle([(r, c) for r ∈ 2:height-1, c ∈ 2:width-1]) # Get the time, at that velocity, for the area of the triangle to be nil. # We are only interested by positive values to only move in the direction of the gradient - for triangle ∈ [top_triangle3D(mesh, row, col), bot_triangle3D(mesh, row, col)] + for triangle ∈ + [triangle3D(mesh, row, col, :top), triangle3D(mesh, row, col, :bottom)] t1, t2 = find_maximum_t(triangle) - for t ∈ [t1, t2] - if (!ismissing(t)) && (0 < t < min_positive_t) - min_positive_t = t - end - end - - δ = min_positive_t / 2.0 - mesh.topleft.r[row, col] -= δ * ∇ϕᵤ[row, col] - mesh.topleft.c[row, col] -= δ * ∇ϕᵥ[row, col] + @assert typeof(t1) == Float64 && typeof(t2) == Float64 "Maximum times are not numerical at $(row), $(col)" end + # list_min_pos_t[(row-1)+(col-2)*(width-2)] # println("March mesh δ: $(δ)") end - mesh.topleft.r[1:height, 1] .= 1:height - mesh.topleft.r[1:height, width] .= 1:height - mesh.topleft.c[1, 1:width] .= 1:width - mesh.topleft.c[height, 1:width] .= 1:width + t1 = max.(t1, 0.0) + t2 = max.(t2, 0.0) + + min_positive_t = min(minimum(t1), minimum(t2)) - print("Average mesh changes on x = $(sum(abs.(mesh.topleft.r - mesh_x)))") + δ = min_positive_t / 2.0 + mesh.topleft.r -= δ .* ∇ϕᵤ + mesh.topleft.c -= δ .* ∇ϕᵥ + + # reset_border_values!(mesh.topleft) + + # Reset the border at the fixed values fixed coordinates. + reset_border_values!(mesh.topleft) + + println( + "Average mesh changes on row = $(sum(abs.(mesh.topleft.r - mesh_r)) / (height * width))", + ) + + println( + "Average mesh changes on col = $(sum(abs.(mesh.topleft.c - mesh_c)) / (height * width))", + ) + + println( + "Average mesh changes on height = $(sum(abs.(mesh.topleft.h - mesh_h)) / (height * width))", + ) # Modify the mesh triangles but ensuring that we are far from destroying any of them with a nil area. # Use the maximum change possible (negative or positive) @@ -495,10 +561,10 @@ function matrix_to_mesh(ϕ::Matrix{Float64}) mesh = FaceMesh(height, width) # 1 more topleft than pixels! Therefore compiler needs to specify exact indices. - mesh.topleft.z[1:height, 1:width] .= ϕ[1:height, 1:width] + mesh.topleft.h[1:height, 1:width] .= ϕ[1:height, 1:width] # The borders' height is forced at 0. - fill_borders!(mesh.topleft.z, 0.0) + reset_border_values!(mesh.topleft) return mesh end @@ -539,7 +605,7 @@ function create_solid( bottom_mesh = FaceMesh(height, width) bottom_mesh.topleft.r[:] .= rows[:] bottom_mesh.topleft.c[:] .= cols[:] - bottom_mesh.topleft.z[:] .= -Bottom_Offset + bottom_mesh.topleft.h[:] .= -Bottom_Offset bottom_mesh.topleft.vr[:] .= 0.0 bottom_mesh.topleft.vr[:] .= 0.0 diff --git a/src/io.jl b/src/io.jl index 522e7fb..f0d6529 100644 --- a/src/io.jl +++ b/src/io.jl @@ -33,7 +33,7 @@ function save_stl!( mesh::FaceMesh, filename::String; scale = 1.0, - scalez = 1.0, + scaleh = 1.0, reverse = false, flipxy = false, ) @@ -51,15 +51,9 @@ function save_stl!( n = centroid(top_triangle) if flipxy - println(io, "v $(n.y * scale) $(n.x * scale) $(n.z * scalez)") - else - println(io, "v $(n.x * scale) $(n.y * scale) $(n.z * scalez)") - end - - if flipxy - println(io, "v $(n.y * scale) $(n.x * scale) $(n.z * scalez)") + println(io, "v $(n.c * scale) $(n.r * scale) $(n.h * scaleh)") else - println(io, "v $(n.x * scale) $(n.y * scale) $(n.z * scalez)") + println(io, "v $(n.r * scale) $(n.c * scale) $(n.h * scaleh)") end # Bottom triangle @@ -71,12 +65,6 @@ function save_stl!( else println(io, "v $(n.x * scale) $(n.y * scale) $(n.z * scalez)") end - - if flipxy - println(io, "v $(n.y * scale) $(n.x * scale) $(n.z * scalez)") - else - println(io, "v $(n.x * scale) $(n.y * scale) $(n.z * scalez)") - end end # CHECK what dims exactly represents. Number of triangles? @@ -102,10 +90,10 @@ function stl_2_mesh(filename) for line in vertexLines count += 1 elements = split(line, " ") - x = parse(Float64, elements[2]) - y = parse(Float64, elements[3]) - z = parse(Float64, elements[4]) * 10 - pt = Vertex3D(x, y, z, 0, 0) + r = parse(Float64, elements[2]) + c = parse(Float64, elements[3]) + h = parse(Float64, elements[4]) * 10 + pt = Vertex3D(r, c, h, 0, 0) nodeList[count] = pt end diff --git a/src/parameters.jl b/src/parameters.jl index bde9dda..afbd201 100644 --- a/src/parameters.jl +++ b/src/parameters.jl @@ -32,6 +32,11 @@ global Meters_Per_Pixel = Caustics_Height / N_Pixel_Height # calculation -const ω = 0.50 +const ω = 1.94 # const ω = 2 / (1 + π / sqrt(N_Pixel_Height * N_Pixel_Width)) const N_Iterations_Convergence = 10_000 # CHECK: What is a reasonable number of iterations? + +# # Global allocations to avoid excessive re-allocations. USEFUL ??? +# global container = zeros(Float64, 1_024, 1_024) +# global divergence_intensity = zeros(Float64, 1_024, 1_024) +# global target_map = zeros(Float64, 1_024, 1_024) diff --git a/src/plots.jl b/src/plots.jl index 4ee0716..0b9c4b6 100644 --- a/src/plots.jl +++ b/src/plots.jl @@ -2,7 +2,50 @@ $(SIGNATURES) """ function plot_as_quiver( - g; + mesh::FaceMesh; + stride = 4, + scale = 300, + max_length = 2, + flipxy = false, + reverser = false, + reversec = false, +) + + height, width = size(mesh) + rs = Float64[] + cs = Float64[] + vrs = Float64[] + vcs = Float64[] + + ϕ = -mesh.topleft.h + + vrm = reverser ? mesh.topleft.vr .* scale : -mesh.topleft.vr .* scale + vcm = reversec ? -mesh.topleft.vc .* scale : mesh.topleft.vc .* scale + + vrm = clamp.(vrm, -max_length, max_length) + vcm = clamp.(vcm, -max_length, max_length) + + for row = 1:stride:height, col = 1:stride:width + reverser ? push!(rs, row) : push!(rs, -row) + reversec ? push!(cs, -col) : push!(cs, col) + + push!(vrs, vrm[row, col]) + push!(vcs, vcm[row, col]) + end + + q = + flipxy ? quiver(cs, rs, quiver = (vcs, vrs), aspect_ratio = :equal) : + quiver(rs, cs, quiver = (vrs, vcs), aspect_ratio = :equal) + + display(q) +end + + +""" +$(SIGNATURES) +""" +function plot_as_quiver( + ϕ; stride = 4, scale = 300, max_length = 2, @@ -11,7 +54,7 @@ function plot_as_quiver( reversex = false, ) - h, w = size(g) + h, w = size(ϕ) xs = Float64[] ys = Float64[] us = Float64[] @@ -21,9 +64,9 @@ function plot_as_quiver( reversex ? push!(xs, x) : push!(xs, -x) reversey ? push!(ys, -y) : push!(ys, y) - p1 = g[y, x] - u = (g[y, x+1] - g[y, x]) * scale - v = (g[y+1, x] - g[y, x]) * scale + p1 = ϕ[y, x] + u = (ϕ[y, x+1] - ϕ[y, x]) * scale + v = (ϕ[y+1, x] - ϕ[y, x]) * scale u = -u @@ -40,7 +83,6 @@ function plot_as_quiver( quiver(xs, ys, quiver = (us, vs), aspect_ratio = :equal) display(q) - readline() end diff --git a/src/scratchpad.jl b/src/scratchpad.jl index 05c6b24..3e91a0a 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -8,9 +8,18 @@ mesh, imageBW = engineer_caustics(image); Gray.(imageBW) +mesh.topleft.r[1:10, 1:10] +mesh.topleft.c[1:10, 1:10] +mesh.topleft.h[1:10, 1:10] +mesh.topleft.vr[1:10, 1:10] +mesh.topleft.vc[1:10, 1:10] + +mesh.toptriangles[1:10] +mesh.bottriangles[1:10] + mesh.topleft.r[250:260, 250:260] mesh.topleft.c[250:260, 250:260] -mesh.topleft.z[250:260, 250:260] +mesh.topleft.h[250:260, 250:260] using Test diff --git a/src/utilities.jl b/src/utilities.jl index 40d2c13..93ce1a0 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -7,12 +7,12 @@ $(TYPEDEF) struct Vertex3D r::Float64 c::Float64 - z::Float64 + h::Float64 vr::Float64 vc::Float64 - Vertex3D(r, c, z, vr, vc) = new(r, c, z, vr, vc) + Vertex3D(r, c, h, vr, vc) = new(r, c, h, vr, vc) Vertex3D() = new(0.0, 0.0, 0.0, 0.0, 0.0) end @@ -22,8 +22,8 @@ $(SIGNATURES) function dist(p1::Tuple{Float64,Float64,Float64}, p2::Tuple{Float64,Float64,Float64}) dr = p2[1] - p1[1] dc = p2[2] - p1[2] - dz = p2[3] - p1[3] - return sqrt(dr^2 + dc^2 + dz^2) + dh = p2[3] - p1[3] + return sqrt(dr^2 + dc^2 + dh^2) end """ @@ -31,27 +31,33 @@ $(SIGNATURES) """ function dist(p1::Vertex3D, p2::Vertex3D) dr = p2.r - p1.r + @assert 0.0 <= abs(dr) <= 1e6 "Distance (row coordinate = $(dr)) between $(p1) and $(p2) makes no sense " + dc = p2.c - p1.c - dz = p2.z - p1.z - return sqrt(dr^2 + dc^2 + dz^2) + @assert 0.0 <= abs(dc) <= 1e6 "Distance (col coordinate = $(dc)) between $(p1) and $(p2) makes no sense " + + dh = p2.h - p1.h + @assert 0.0 <= abs(dh) <= 1e6 "Distance (height coordinate = $(dh)) between $(p1) and $(p2) makes no sense " + + return sqrt(dr^2 + dc^2 + dh^2) end -""" -$(SIGNATURES) -""" -function area( - p1::Tuple{Float64,Float64,Float64}, - p2::Tuple{Float64,Float64,Float64}, - p3::Tuple{Float64,Float64,Float64}, -) - a = dist(p1, p2) - b = dist(p2, p3) - c = dist(p3, p1) - s = (a + b + c) / 2.0 +# """ +# $(SIGNATURES) +# """ +# function area( +# p1::Tuple{Float64,Float64,Float64}, +# p2::Tuple{Float64,Float64,Float64}, +# p3::Tuple{Float64,Float64,Float64}, +# ) +# a = dist(p1, p2) +# b = dist(p2, p3) +# c = dist(p3, p1) +# s = (a + b + c) / 2.0 - return sqrt(s * (s - a) * (s - b) * (s - c)) -end +# return sqrt(s * (s - a) * (s - b) * (s - c)) +# end """ $(SIGNATURES) @@ -62,6 +68,9 @@ function area(v1::Vertex3D, v2::Vertex3D, v3::Vertex3D) c = dist(v3, v1) s = (a + b + c) / 2.0 + surface = s * (s - a) * (s - b) * (s - c) + @assert surface >= 0.0 "Negative surface for $(v1), $(v2), $(v3)" + return sqrt(s * (s - a) * (s - b) * (s - c)) end @@ -72,7 +81,7 @@ $(SIGNATURES) A midpoint is the average between two points """ midpoint(p1::Vertex3D, p2::Vertex3D) = - Vertex3D((p1.r + p2.r) / 2.0, (p1.c + p2.c) / 2.0, (p1.z + p2.z) / 2.0, 0.0, 0.0) + Vertex3D((p1.r + p2.r) / 2.0, (p1.c + p2.c) / 2.0, (p1.h + p2.h) / 2.0, 0.0, 0.0) """ @@ -83,7 +92,7 @@ Centroid of three points. centroid(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) = Vertex3D( (p1.r + p2.r + p3.r) / 3.0, (p1.c + p2.c + p3.c) / 3.0, - (p1.z + p2.z + p3.z) / 3.0, + (p1.h + p2.h + p3.h) / 3.0, 0, 0, ) @@ -110,7 +119,7 @@ Origin is top left, going right and down .`x` goes horizontal and follows column # Velocity -Velocity vector along `x` and `y` (velocity along z not necessary). +Velocity vector along `x` and `y` (velocity along h not necessary). Implementation is a struc of arrays. Easier to vectorise. @@ -119,34 +128,66 @@ mutable struct FieldVertex3D size::Tuple{Int,Int} r::AbstractMatrix{Float64} - y::AbstractMatrix{Float64} - z::AbstractMatrix{Float64} + c::AbstractMatrix{Float64} + h::AbstractMatrix{Float64} vr::AbstractMatrix{Float64} vc::AbstractMatrix{Float64} - function FieldVertex3D(height, width) - # mr = zeros(Float64, height + 1, width + 1) - # my = zeros(Float64, height + 1, width + 1) - # mz = zeros(Float64, height + 1, width + 1) + rows_numbers::AbstractMatrix{Float64} + cols_numbers::AbstractMatrix{Float64} - # mvr = zeros(Float64, height + 1, width + 1) - # mvc = zeros(Float64, height + 1, width + 1) + # FieldVertex3D(size, mr, mc, mh, mvr, mvc, rows_numbers, cols_numbers) = new(size, mr, mc, mh, mvr, mvc, rows_numbers, cols_numbers) - rows = repeat(Float64.(1:height+1), 1, width + 1) - cols = repeat(Float64.(1:width+1)', height + 1, 1) +end - mr = rows + rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 - my = cols + rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 - mz = rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 - mvr = rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 - mvc = rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 +function FieldVertex3D(height, width) + # mr = zeros(Float64, height + 1, width + 1) + # my = zeros(Float64, height + 1, width + 1) + # mh = zeros(Float64, height + 1, width + 1) - new((height, width), mr, my, mz, mvr, mvc) - end + # mvr = zeros(Float64, height + 1, width + 1) + # mvc = zeros(Float64, height + 1, width + 1) + + rows_numbers = repeat(Float64.(1:height+1), 1, width + 1) + cols_numbers = repeat(Float64.(1:width+1)', height + 1, 1) + + mr = rows_numbers + rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 + mc = cols_numbers + rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 + mh = rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 + mvr = rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 + mvc = rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 + + fv = FieldVertex3D((height, width), mr, mc, mh, mvr, mvc, rows_numbers, cols_numbers) + reset_border_values!(fv) + return fv +end + + +""" +$(SIGNATURES) + +Return the dimension of the mesh as the number of rectangles. It does not return the number of corner points. +""" +function reset_border_values!(topleft::FieldVertex3D) + # Reset the border at the fixed values fixed coordinates. + topleft.r[1, :] .= topleft.rows_numbers[1, :] + topleft.r[end, :] .= topleft.rows_numbers[end, :] + topleft.r[:, 1] .= topleft.rows_numbers[:, 1] + topleft.r[:, end] .= topleft.rows_numbers[:, end] + + topleft.c[1, :] .= topleft.cols_numbers[1, :] + topleft.c[end, :] .= topleft.cols_numbers[end, :] + topleft.c[:, 1] .= topleft.cols_numbers[:, 1] + topleft.c[:, end] .= topleft.cols_numbers[:, end] + + fill_borders!(topleft.h, 0.0) + fill_borders!(topleft.vr, 0.0) + fill_borders!(topleft.vc, 0.0) end + Base.size(fv::FieldVertex3D) = FieldVertex3D.size @@ -160,7 +201,7 @@ function Vertex3D(fv::FieldVertex3D, row, col) Vertex3D( fv.r[row, col], fv.y[row, col], - fv.z[row, col], + fv.h[row, col], fv.vr[row, col], fv.vc[row, col], ) @@ -223,6 +264,8 @@ end + + """ $(SIGNATURES) @@ -253,94 +296,53 @@ $(SIGNATURES) Converts a triangle as a triplet of references to mesh vertices to a triplet of 3D coordinates. """ -function top_triangle3D(mesh::FaceMesh, row::Int, col::Int) +function triangle3D(mesh::FaceMesh, row::Int, col::Int, side = Union{:top,:bottom}) height, width = size(mesh) if 1 <= row <= height && 1 <= col <= width - t = mesh.toptriangles[row, col] - t1_row, t1_col = t[1] - t2_row, t2_col = t[2] - t3_row, t3_col = t[3] - - p1 = Vertex3D( - mesh.topleft.r[t1_row, t1_col], - mesh.topleft.c[t1_row, t1_col], - mesh.topleft.z[t1_row, t1_col], - mesh.topleft.vr[t1_row, t1_col], - mesh.topleft.vc[t1_row, t1_col], - ) - p2 = Vertex3D( - mesh.topleft.r[t2_row, t2_col], - mesh.topleft.c[t2_row, t2_col], - mesh.topleft.z[t2_row, t2_col], - mesh.topleft.vr[t2_row, t2_col], - mesh.topleft.vc[t2_row, t2_col], - ) - p3 = Vertex3D( - mesh.topleft.r[t3_row, t3_col], - mesh.topleft.c[t3_row, t3_col], - mesh.topleft.z[t3_row, t3_col], - mesh.topleft.vr[t3_row, t3_col], - mesh.topleft.vc[t3_row, t3_col], - ) - return (p1, p2, p3) - else - return missing - end -end - -top_triangle3D(mesh::FaceMesh, ci::CartesianIndex{2}) = top_triangle3D(mesh, ci[1], ci[2]) - + if side == :top + t = mesh.toptriangles[row, col] + elseif side == :bottom + t = mesh.bottriangles[row, col] + end -function bot_triangle3D(mesh::FaceMesh, row::Int, col::Int) - height, width = size(mesh) - if 1 <= row <= height && 1 <= col <= width - t = mesh.bottriangles[row, col] t1_row, t1_col = t[1] t2_row, t2_col = t[2] t3_row, t3_col = t[3] - p1 = Vertex3D( - mesh.topleft.r[t1_row, t1_col], - mesh.topleft.c[t1_row, t1_col], - mesh.topleft.z[t1_row, t1_col], - mesh.topleft.vr[t1_row, t1_col], - mesh.topleft.vc[t1_row, t1_col], - ) - p2 = Vertex3D( - mesh.topleft.r[t2_row, t2_col], - mesh.topleft.c[t2_row, t2_col], - mesh.topleft.z[t2_row, t2_col], - mesh.topleft.vr[t2_row, t2_col], - mesh.topleft.vc[t2_row, t2_col], - ) - p3 = Vertex3D( - mesh.topleft.r[t3_row, t3_col], - mesh.topleft.c[t3_row, t3_col], - mesh.topleft.z[t3_row, t3_col], - mesh.topleft.vr[t3_row, t3_col], - mesh.topleft.vc[t3_row, t3_col], - ) + r1 = mesh.topleft.r[t1_row, t1_col] + c1 = mesh.topleft.c[t1_row, t1_col] + h1 = mesh.topleft.h[t1_row, t1_col] + vr1 = mesh.topleft.vr[t1_row, t1_col] + vc1 = mesh.topleft.vc[t1_row, t1_col] + @assert r1^2 + c1^2 + h1^2 <= 1e12 "Coordinate $(r1), $(c1), $(h1) of point #1 at $(row), $(col) side = $(side) makes no sense " + + r2 = mesh.topleft.r[t2_row, t2_col] + c2 = mesh.topleft.c[t2_row, t2_col] + h2 = mesh.topleft.h[t2_row, t2_col] + vr2 = mesh.topleft.vr[t2_row, t2_col] + vc2 = mesh.topleft.vc[t2_row, t2_col] + @assert r2^2 + c2^2 + h2^2 <= 1e12 "Coordinate $(r2), $(c2), $(h2) of point #2 at $(row), $(col) side = $(side) makes no sense " + + r3 = mesh.topleft.r[t3_row, t3_col] + c3 = mesh.topleft.c[t3_row, t3_col] + h3 = mesh.topleft.h[t3_row, t3_col] + vr3 = mesh.topleft.vr[t3_row, t3_col] + vc3 = mesh.topleft.vc[t3_row, t3_col] + @assert r3^2 + c3^2 + h3^2 <= 1e12 "Coordinate $(r3), $(c3), $(h3) of point #3 at $(row), $(col) side = $(side) makes no sense " + + p1 = Vertex3D(r1, c1, h1, vr1, vc1) + p2 = Vertex3D(r2, c2, h2, vr2, vc2) + p3 = Vertex3D(r3, c3, h3, vr3, vc3) return (p1, p2, p3) else - return missing + # return (missing, missing, missing) + @assert false "Coordinates out of bounds at $(row), $(col)" end end -bot_triangle3D(mesh::FaceMesh, ci::CartesianIndex{2}) = bot_triangle3D(mesh, ci[1], ci[2]) - - -function triangle3D(mesh::FaceMesh, ci::CartesianIndex; side = Union{:top,:bottom}) - if side == :top - return top_triangle3D(mesh, ci) - elseif side == :bottom - return bot_triangle3D(mesh, ci) - else - return missing - end -end +triangle3D(mesh::FaceMesh, ci::CartesianIndex{2}, side = Union{:top,:bottom}) = + triangle3D(mesh, ci[1], ci[2], side) -triangle3D(mesh::FaceMesh, row::Int, col::Int; side = Union{:top,:bottom}) = - triangle3D(mesh, CartesianIndex(row, col); side) """ @@ -398,3 +400,6 @@ function area(mesh::FaceMesh, row::Int, col::Int; side = Union{:top,:bottom}) return missing end end + + +max_sum_abs(m::AbstractMatrix) = (sum(abs.(m)) / length(m)) < 1_024 From 34a17e2150cade0ae5c087ed1aa129ddca5fdcf7 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Wed, 8 Sep 2021 18:31:24 +0200 Subject: [PATCH 17/58] Refactoring ongoing. Snapshot 12 --- src/create_mesh.jl | 463 ++++++++++++++++++++++++--------------------- src/io.jl | 6 +- src/plots.jl | 6 +- src/scratchpad.jl | 19 +- src/utilities.jl | 174 +++++++---------- 5 files changed, 333 insertions(+), 335 deletions(-) diff --git a/src/create_mesh.jl b/src/create_mesh.jl index 85e781a..eaaea2d 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -8,20 +8,20 @@ function engineer_caustics(source_image) println("Image size: $((height, width))") # mesh is the same size as the image with an extra row/column to have coordinates to - # cover each image pixel with a triangle. + # cover each image corner with a triangle. mesh = FaceMesh(height, width) - println("Mesh creation: ") - r_check = 1 - c_check = 1 - println( - "\tCoordinates: $(mesh.topleft.r[r_check, c_check]) , $(mesh.topleft.c[r_check, c_check]) , $(mesh.topleft.h[r_check, c_check])", - ) - println( - "\tVelocities: $(mesh.topleft.vr[r_check, c_check]) , $(mesh.topleft.vc[r_check, c_check])", - ) + # println("Mesh creation: ") + # r_check = 1 + # c_check = 1 + # println( + # "\tCoordinates: $(mesh.corners.r[r_check, c_check]) , $(mesh.corners.c[r_check, c_check]) , $(mesh.corners.ϕ[r_check, c_check])", + # ) + # println( + # "\tVelocities: $(mesh.corners.vr[r_check, c_check]) , $(mesh.corners.vc[r_check, c_check])", + # ) # The energy going through the lens is equal to the amount of energy on the caustics - total_energy_lens = height * width + total_energy_lens = height * width * 1 # 1 unit of energy per corner total_energy_caustics = sum(imageBW) correction_ratio = (width * height) / sum(imageBW) @@ -29,30 +29,30 @@ function engineer_caustics(source_image) # original image. imageBW = imageBW .* correction_ratio - for i ∈ 1:256 + for i ∈ 1:5 println("\nSTARTING VERTICAL ITERATION $(i) ---") - max_update = move_vertically!(mesh, imageBW, "it$(i)") + max_update = solve_velocity_potential!(mesh, imageBW, "it$(i)") print("Vertical move max update = $(max_update)") - println( - "\tCoordinates: $(mesh.topleft.r[r_check, c_check]) , $(mesh.topleft.c[r_check, c_check]) , $(mesh.topleft.h[r_check, c_check])", - ) - println( - "\tVelocities: $(mesh.topleft.vr[r_check, c_check]) , $(mesh.topleft.vc[r_check, c_check])", - ) + # println( + # "\tCoordinates: $(mesh.corners.r[r_check, c_check]) , $(mesh.corners.c[r_check, c_check]) , $(mesh.corners.ϕ[r_check, c_check])", + # ) + # println( + # "\tVelocities: $(mesh.corners.vr[r_check, c_check]) , $(mesh.corners.vc[r_check, c_check])", + # ) println("---------- ITERATION $(i): $(max_update)/n") end println("\nSTARTING HORIZONTAL ITERATION ---") - mesh.topleft.h, max_update = + mesh.corners.ϕ, max_update = move_horizontally(mesh, imageBW; f = 1.0, picture_width = Caustics_Side) println(" max update = $(max_update)") - println("$(mesh.topleft.vr[r_check, c_check]) , $(mesh.topleft.vc[r_check, c_check])") + println("$(mesh.corners.vr[r_check, c_check]) , $(mesh.corners.vc[r_check, c_check])") # solidMesh = create_solid(mesh) @@ -71,55 +71,89 @@ end """ $(SIGNATURES) """ -function move_vertically!(mesh, image, suffix) +function solve_velocity_potential!(mesh, image, suffix) # Remember mesh is (will be) `grid_definition x grid_definition` just like the image # `grid_definition x grid_definition`, so LJ is `grid_definition x grid_definition`. # The idea is that: - # - any pixel on the caustic projection receives light from a given 'rectangle' on the lens. + # - any corner on the caustic projection receives light from a given 'rectangle' on the lens. # - That rectangle is made of 2 triangles. - area_distorted_pixels = get_area_pixels(mesh) - @assert max_sum_abs(area_distorted_pixels) "ALERT: vert. Δ area_distorted_pixels is too large - max/min = $(maximum(area_distorted_pixels)) / $(minimum(area_distorted_pixels))" + area_distorted_corners = get_area_corners(mesh) + @assert average_absolute(area_distorted_corners) """ - intensity_error = Float64.(area_distorted_pixels - image) - @assert max_sum_abs(intensity_error) "ALERT: vert. Δ intensity_error is too large - max/min = $(maximum(intensity_error)) / $(minimum(intensity_error))" + solve_velocity_potential: area_distorted_corners values seem too large + $(maximum(area_distorted_corners)) / $(minimum(area_distorted_corners)) + + """ - # The divergence matrix moves all the topleft corners. illumination_error is therefore not large enough. - height, width = size(mesh) - divergence_intensity = zeros(Float64, height + 1, width + 1) - divergence_intensity[1:height, 1:width] .= intensity_error[1:height, 1:width] - fill_borders!(divergence_intensity, 0.0) - @assert max_sum_abs(divergence_intensity) "ALERT: vert. Δ divergence_intensity is too large - max/min = $(maximum(divergence_intensity)) / $(minimum(divergence_intensity))" + error_luminosity = Float64.(area_distorted_corners - image) + @assert average_absolute(error_luminosity) """ + solve_velocity_potential: error_luminosity values seem too large + max/min error_luminosity = $(maximum(error_luminosity)) / $(minimum(error_luminosity)) + max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) + + """ # Save the loss image as a png - plot_loss!(divergence_intensity, suffix, image) + plot_loss!(error_luminosity, suffix, image) - # ϕ is the _heightmap_ therefore size of topleft - ϕ = mesh.topleft.h + # ϕ is the _velocity potential_ + # ϕ is defined per corner + ϕ = zeros(Float64, size(mesh.corners.ϕ)) - max_update = 100.0 - interaction_count = 0 - while true - interaction_count += 1 - interaction_count % 500 == 0 && println("Converging for intensity: $(max_update)") + # For the purpose of Poisson, we need to divergence to increase towards the inside: negative divergence for high luminosity + error_luminosity = -error_luminosity + + max_update = Inf + iteration_count = 0 + for _ ∈ 1:5 + iteration_count += 1 + iteration_count % 100 == 0 && println("Converging for intensity: $(max_update)") old_max_update = max_update - ϕ, max_update = relax_vertically(ϕ, divergence_intensity) + println( + "solve_velocity_potential: iteration count = $(iteration_count) -- ", + "max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) -- ", + "max/min mesh.corners.ϕ = $(maximum(mesh.corners.ϕ)) / $(minimum(mesh.corners.ϕ)) -- ", + "max_update = $(max_update)", + ) + + # Solve the Poisson equation where the divergence of the gradient of ϕ is equal to the luminosity loss. + ϕ, max_update = gradient_descent(ϕ, error_luminosity) + @assert average_absolute(ϕ) """ + + solve_velocity_potential: ϕ values seem too large + iteration count = $(iteration_count) + max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) + max/min mesh.corners.ϕ = $(maximum(mesh.corners.ϕ)) / $(minimum(mesh.corners.ϕ)) + + max/min error_luminosity = $(maximum(error_luminosity)) / $(minimum(error_luminosity)) + max_update = $(max_update) + + """ + + + if abs(max_update) < 1e-6 || abs((max_update - old_max_update) / old_max_update) < 0.01 println( - "Convergence stopped at step $(interaction_count) with ", + "Convergence stopped at step $(iteraction_count) with ", "max_update = $(max_update) -- ", - "max/min area_distorted_pixels = $(maximum(area_distorted_pixels)) / $(minimum(area_distorted_pixels)) -- ", - "max divergence = $(maximum(abs.(divergence_intensity)))", + "max/min area_distorted_corners = $(maximum(area_distorted_corners)) / $(minimum(area_distorted_corners)) -- ", + "max error_luminosity = $(maximum(abs.(error_luminosity)))", ) break end end - mesh.topleft.h[1:height+1, 1:width+1] .= ϕ[1:height+1, 1:width+1] + mesh.corners.ϕ .= ϕ + + # Now we need to march the x,y locations in our mesh according to this gradient! + # Tasks are a control flow feature that allows computations to be suspended and resumed in a flexible manner. + # We mention them here only for completeness; for a full discussion see Asynchronous Programming. + march_mesh!(mesh) save_stl!( matrix_to_mesh(ϕ * 0.02), @@ -141,11 +175,6 @@ function move_vertically!(mesh, image, suffix) # plot_as_quiver(ϕ * -1.0, stride=30, scale=1.0, max_length=200, flipxy=true, reversex=false, reversey=false) # saveObj(matrix_to_mesh(D * 10), "D_$(suffix).obj") - - # Now we need to march the x,y locations in our mesh according to this gradient! - # Tasks are a control flow feature that allows computations to be suspended and resumed in a flexible manner. - # We mention them here only for completeness; for a full discussion see Asynchronous Programming. - march_mesh!(mesh, ϕ) save_stl!(mesh, "./examples/mesh_$(suffix).obj", flipxy = true) return max_update @@ -168,24 +197,24 @@ function move_horizontally( height, width = size(mesh) # Coordinates difference - # Coordinates on the caustics = simple rectangular values in pixels. - # Coordinates on the lens face comes from topleft field. - d_row = mesh.topleft.rows_numbers - mesh.topleft.r - d_col = mesh.topleft.cols_numbers - mesh.topleft.c + # Coordinates on the caustics = simple rectangular values in corners. + # Coordinates on the lens face comes from corner field. + d_row = mesh.corners.rows_numbers - mesh.corners.r + d_col = mesh.corners.cols_numbers - mesh.corners.c # true_H is the real distance beteen the surface of the lens and the projection # H is the initial distance from the surface of the carved face to the projection screen. # H is constant and does not account for the change in heights due to carving. - # The focal length is in meters. H is in Pixels. + # The focal length is in meters. H is in corners. # Note: Higher location means closer to the caustics => negative sign - H = f / Meters_Per_Pixel + H = f / Meters_Per_corner - true_H = similar(mesh.topleft.h) - @. true_H[:] = -mesh.topleft.h[:] + H + true_H = similar(mesh.corners.ϕ) + @. true_H[:] = -mesh.corners.ϕ[:] + H # Normals. - N_row = zeros(Float64, height + 1, width + 1) - N_col = zeros(Float64, height + 1, width + 1) + N_row = zeros(Float64, size(true_H)) + N_col = zeros(Float64, size(true_H)) @. N_row[:] = tan(atan(d_row[:] / true_H[:]) / (n₁ - n₂)) @. N_col[:] = tan(atan(d_col[:] / true_H[:]) / (n₁ - n₂)) @@ -195,16 +224,13 @@ function move_horizontally( @. div_row[1:end, 1:end] = N_row[2:end, 1:end-1] - N_row[1:end-1, 1:end-1] @. div_col[1:end, 1:end] = N_col[1:end-1, 2:end] - N_col[1:end-1, 1:end-1] - divergence_direction = zeros(Float64, width + 1, height + 1) + divergence_direction = zeros(Float64, size(div_row)) divergence_direction[1:height, 1:width] = div_row + div_col - fill_borders!(divergence_direction, 0.0) - - @assert max_sum_abs(divergence_direction) "ALERT: horiz. Δ divergence_direction is too large - max/min = $(maximum(divergence_direction)) / $(minimum(divergence_direction))" - + @assert average_absolute(divergence_direction) "ALERT: horiz. Δ divergence_direction is too large - max/min = $(maximum(divergence_direction)) / $(minimum(divergence_direction))" println("Have all the divergences") - ϕ = zeros(Float64, height + 1, width + 1) + corner_heights = zeros(Float64, size(mesh.corners.ϕ)) max_update = 1_000.0 iteration_count = 0 while true @@ -212,8 +238,8 @@ function move_horizontally( iteration_count % 100 == 0 && println("Converging for divergence: $(max_update)") old_max_update = max_update - ϕ, max_update = relax_vertically(ϕ, -divergence_direction) - @assert max_sum_abs(ϕ) "ALERT: horiz. Δ ϕ is too large - max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ))" + corner_heights, max_update = gradient_descent(corner_heights, -divergence_direction) + @assert average_absolute(corner_heights) "ALERT: horiz. Δ corner_heights is too large - max/min corner_heights = $(maximum(corner_heights)) / $(minimum(corner_heights))" if abs(max_update) < 1e-6 || @@ -227,7 +253,7 @@ function move_horizontally( end # saveObj(matrix_to_mesh(h / 10), "./examples/heightmap.obj") - return ϕ, max_update + return corner_heights, max_update end @@ -239,69 +265,98 @@ There is a hardcoded assumption of Neumann boundary conditions--that the derivat boundary must be zero in all cases. See: https://math.stackexchange.com/questions/3790299/how-to-iteratively-solve-poissons-equation-with-no-boundary-conditions +- ϕ is the potential to solve subject to the Poisson equation and is the same size as the corners (posts) +- target is ∇²ϕ and is of the size of the pixels (fences) + """ -function relax_vertically(ϕ::Matrix{Float64}, divergence::Matrix{Float64}) +function gradient_descent(ϕ::Matrix{Float64}, ∇ϕ::Matrix{Float64}) - @assert max_sum_abs(ϕ) "ALERT: relaxation ϕ is too large - max/min = $(maximum(ϕ)) / $(minimum(ϕ))" - @assert max_sum_abs(divergence) "ALERT: relaxation divergence is too large - max/min = $(maximum(divergence)) / $(minimum(divergence))" + # Ensure that border conditions are as they should + fill_borders!(∇ϕ, 0.0) + fill_borders!(ϕ, 0.0) - @assert any(isnan.(ϕ)) == false "Calling relaxation with a ϕ that contains NaN!!" - @assert any(isnan.(divergence)) == false "Calling relaxation with a divergence that contains NaN!!" + @assert average_absolute(ϕ) """ + Relaxation: ϕ values seem too large + max/min ∇ϕ = $(maximum(∇ϕ)) / $(minimum(∇ϕ)) + max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) + + """ + + @assert average_absolute(∇ϕ) """ + + Relaxation: ∇²ϕ values seem too large + max/min ∇ϕ = $(maximum(∇ϕ)) / $(minimum(∇ϕ)) + max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) + + """ - # ϕ is of the same size of topleft - height, width = size(ϕ) - n_pixels = height * width - height_average = sum(ϕ) / n_pixels + + @assert any(isnan.(ϕ)) == false "Relaxation: calling with a ϕ that contains NaN!!" + @assert any(isnan.(∇ϕ)) == false "Relaxation: calling with a ∇ϕ that contains NaN!!" + + + # ϕ is of the same size as corners = number of corners + 1 + height_corners, width_corners = size(ϕ) + height_pixels, width_pixels = size(∇ϕ) # Laplacian # Embed matrix within a larger matrix for better vectorization and avoid duplicated code - # Size of ϕ/topleft is h+1, w+1. container adds 1 row/col before and 1 row/col after - container_height = 1 + height + 1 - container_width = 1 + width + 1 - container = zeros(Float64, container_height, container_width) - container[2:container_height-1, 2:container_width-1] .= ϕ - @assert max_sum_abs(container) "ALERT: relaxation container is too large - max/min = $(maximum(container)) / $(minimum(container))" - - # Those values are all of ϕ's size but shifted in 4 directions - height_above = container[2-1:container_height-1-1, 2+0:container_width-1] - height_below = container[2+1:container_height-1+1, 2+0:container_width-1] - height_left = container[2+0:container_height-1, 2-1:container_width-1-1] - height_right = container[2+0:container_height-1, 2+1:container_width-1+1] + # Size of ϕ/corner is h, w. Padded matrix adds 1 row/col after + # ϕ is inserted in padded matrix within 1:height_corners+1 x 1:width_corners+1. + # The rest of the padded matrix (the borders) are set at 0.0. + padded_ϕ = zeros(Float64, height_corners + 1, width_corners + 1) + padded_ϕ[1:height_corners, 1:width_corners] .= ϕ + + # Those values are all of ϕ's size and represent the _flow_ in each direction + flow_up = zeros(Float64, size(∇ϕ)) + flow_down = zeros(Float64, size(∇ϕ)) + flow_left = zeros(Float64, size(∇ϕ)) + flow_right = zeros(Float64, size(∇ϕ)) + + flow_up[1:end, 1:end] .= padded_ϕ[1:end-2, 2:end-1] - padded_ϕ[2:end-1, 2:end-1] + flow_down[1:end, 1:end] .= padded_ϕ[3:end, 2:end-1] - padded_ϕ[2:end-1, 2:end-1] + flow_left[1:end, 1:end] .= padded_ϕ[2:end-1, 1:end-2] - padded_ϕ[2:end-1, 2:end-1] + flow_right[1:end, 1:end] .= padded_ϕ[2:end-1, 3:end] - padded_ϕ[2:end-1, 2:end-1] + + fill_borders!(flow_up, 0.0) + fill_borders!(flow_down, 0.0) + fill_borders!(flow_left, 0.0) + fill_borders!(flow_right, 0.0) # Target position. The target is the current height map smoothed by averaging to which the - # divergence is added. - # δ_map is the same size as divergence. - δ_map = zeros(Float64, size(divergence)) + # flow is added. + # This has to converge towards the ∇ϕ. Difference to calculate speed of the descent. + δ = (flow_up + flow_down + flow_left + flow_right) + ∇ϕ - # δ_map is the Laplacian of the height - δ_map = (height_above + height_below + height_left + height_right) / 4.0 - ϕ - @assert max_sum_abs(δ_map) "ALERT: relaxation δ_map as (average - ϕ) is too large - max/min = $(maximum(δ_map)) / $(minimum(δ_map))" + @assert average_absolute(δ) """ - # This has to converge towards the divergence. Difference to calculate speed of the descent. - δ_map -= divergence - @assert max_sum_abs(δ_map) "ALERT: relaxation δ_map as including divergence is too large - max/min = $(maximum(δ_map)) / $(minimum(δ_map))" + Relaxation: ∇ϕ_error as (current - target) seem too large + max/min target ∇ϕ = $(maximum(∇ϕ)) / $(minimum(∇ϕ)) + max/min ∇ϕ_error = $(maximum(δ)) / $(minimum(δ)) - # height_div, width_div = size(divergence) - # @. target_map[height_div, width_div] += divergence / 4.0 - fill_borders!(δ_map, 0.0) + max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) + max/min padded_ϕ = $(maximum(padded_ϕ)) / $(minimum(padded_ϕ)) + max/min flow_up = $(maximum(flow_up)) / $(minimum(flow_up)) + max/min flow_down = $(maximum(flow_down)) / $(minimum(flow_down)) + max/min flow_left = $(maximum(flow_left)) / $(minimum(flow_left)) + max/min flow_right = $(maximum(flow_right)) / $(minimum(flow_right)) - # Let the heightmap converge towards the target at a slow rate. - # new_ϕ = ϕ + ω .* δ_map - new_ϕ = zeros(Float64, size(divergence)) + """ - # new_ϕ = ϕ + 1.94 * δ_map - new_ϕ = ϕ + 0.2 * δ_map - @assert any(isnan.(new_ϕ)) == false "new_ϕ contains NaN!!" + # @. target_map[height_div, width_div] += ∇ϕ / 4.0 + # fill_borders!(∇ϕ_error, 0.0) - max_update = maximum(abs.(new_ϕ)) - @assert !isnan(max_update) """ MAX UPDATE IS NOT A NaN!!! - Max height = $( maximum(ϕ) ) -- Min height = $( minimum(ϕ) ) -- Height average = $(height_average) - Max divergence = $( maximum(divergence) ) -- Min divergence = $( minimum(divergence) ) - """ + # Let the heightmap converge towards the target at a slow rate = gradient descent. + # @. ϕ += 0.2 * ∇ϕ_error + @. ϕ[1:height_pixels, 1:width_pixels] += + 1.94 / 40.0 * δ[1:height_pixels, 1:width_pixels] + @assert !any(isnan.(ϕ)) "Relaxation: Updated ϕ contains NaN!!" - return new_ϕ, max_update + max_update = maximum(abs.(1.94 / 40.0 * δ)) + + return ϕ, max_update end @@ -311,34 +366,28 @@ $(SIGNATURES) A Mesh is a collection of triangles. The brightness flowing through a given triangle is just proportional to its area in the x, y plane. h is ignored. -The function returns a matrix with the quantity of light coming from each 'rectangle' around a pixel. That 'rectangle' +The function returns a matrix with the quantity of light coming from each 'rectangle' around a corner. That 'rectangle' has been shifted and flexed around. """ -function get_area_pixels(mesh::FaceMesh) +function get_area_corners(mesh::FaceMesh) height, width = size(mesh) - pixel_areas = zeros(Float64, size(mesh)) + top_tri_area = + [area(triangle3D(mesh, row, col, :top)...) for row ∈ 1:height, col ∈ 1:width] + @assert !any(isnan.(top_tri_area)) "get_area_corners: NaN area in top triangles." - for ci ∈ CartesianIndices(pixel_areas) - top_tri_area = area(triangle3D(mesh, ci, :top)...) - bot_tri_area = area(triangle3D(mesh, ci, :bottom)...) + bot_tri_area = + [area(triangle3D(mesh, row, col, :bottom)...) for row ∈ 1:height, col ∈ 1:width] + @assert !any(isnan.(top_tri_area)) "get_area_corners: NaN area in bottom triangles." - isnan(top_tri_area) && - println("NaN area at $(ci) for top triangle $(top_triangle3D(mesh, ci)).") - isnan(bot_tri_area) && - println("NaN area at $(ci) for bottom triangle $(bot_triangle3D(mesh, ci)).") - - pixel_areas[ci] = top_tri_area + bot_tri_area - end - - return pixel_areas + return top_tri_area + bot_tri_area end """ $(SIGNATURES) """ -function quantifyLoss!(D, suffix, img) +function quantify_loss(D, suffix, img) println("Loss:") println("\tMinimum loss: $(minimum(D))") println("\tMaximum loss: $(maximum(D))") @@ -352,19 +401,15 @@ function quantifyLoss!(D, suffix, img) red[D.<0] = -normalised_D_min[D.<0] green = zeros(size(D)) - # println(size(blue)) - # println(size(red)) - # println(size(green)) - rgbImg = RGB.(red, green, blue)' save("./examples/loss_$(suffix).png", map(clamp01nan, rgbImg)) - # println("Saving output image:") - # println(typeof(img)) - # E = Gray.(D) - # println(typeof(E)) - # outputImg = img - E - # save("./examples/actual_$(suffix).png", outputImg) + println("Saving output image:") + println(typeof(img)) + E = Gray.(D) + println(typeof(E)) + outputImg = img - E + save("./examples/actual_$(suffix).png", outputImg) end @@ -403,28 +448,25 @@ function find_maximum_t(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) c = Br * Cc - Cr * Bc # if a = 0, this is just a linear equation. - if a == 0 - # Fingers crossed that b != 0 but extremely unlikely since B is a Float64. - return -c / b, -c / b + if a == 0 && b != 0 + return smallest_positive(-c / b, c / b) else - discriminant = b^2 - 4a * c # If there is a solution if discriminant >= 0 d = sqrt(discriminant) - return (-b - d) / 2a, (-b + d) / 2a - else - - # There can be no solution if, after translation, B abd C move in parallel direction. - # C will never end up on the line AB. - # Very unlikely with Float64. - # Negative numbers are filtered out when calculating the minimum jiggle ratio - return -1.0, -1.0 + return smallest_positive((-b - d) / 2a, (-b + d) / 2a) end end + # There can be no solution if, after translation, B abd C move in parallel direction. + # C will never end up on the line AB. + # Very unlikely with Float64. + # Negative numbers are filtered out when calculating the minimum jiggle ratio + return 1e-10 end + find_maximum_t(p::Tuple{Vertex3D,Vertex3D,Vertex3D}) = find_maximum_t(p[1], p[2], p[3]) @@ -435,77 +477,73 @@ $(SIGNATURES) `march_mesh!` flexes the mesh """ -function march_mesh!(mesh::FaceMesh, ϕ::Matrix{Float64}) +function march_mesh!(mesh::FaceMesh) + + ϕ = mesh.corners.ϕ + height, width = size(ϕ) ∇ϕᵤ, ∇ϕᵥ = ∇(ϕ) # println("Min/Max of values of ϕ: $(minimum(ϕ)) / $(maximum(ϕ))") # println("Sum of values of ∇ϕᵤ: $( sum(∇ϕᵤ) )") # println("Sum of values of ∇ϕᵥ: $( sum(∇ϕᵥ) )") - height, width = size(ϕ) # For each point in the mesh we need to figure out its velocity # However all the nodes located at a border will never move # I.e. velocity (Vx, Vy) = (0, 0) and the square of acrylate will remain # of the same size. - # Warning: The indices are necessary because topleft and ∇ϕ are of different sizes + # Warning: The indices are necessary because corner and ∇ϕ are of different sizes # CHECK SIGNS! - mesh.topleft.vr[1:height, 1:width] .= -∇ϕᵤ[1:height, 1:width] - mesh.topleft.vc[1:height, 1:width] .= -∇ϕᵥ[1:height, 1:width] + mesh.corners.vr .= -∇ϕᵤ + mesh.corners.vc .= -∇ϕᵥ # Just in case... - reset_border_values!(mesh.topleft) + reset_border_values!(mesh.corners) + reset_border_values!(mesh.corners) # Basically infinity time to shrink a triangle to nothing. min_positive_t = Inf list_min_pos_t = zeros(Float64, (height - 2) * (width - 2)) - t1 = zeros(Float64, height, width) - t2 = zeros(Float64, height, width) - - mesh_r = copy(mesh.topleft.r) - mesh_c = copy(mesh.topleft.c) - mesh_h = copy(mesh.topleft.h) - for row ∈ 1:height-1, col ∈ 1:width-1 - # # Jiggle each point in a random order. - # for (row, col) ∈ shuffle([(r, c) for r ∈ 2:height-1, c ∈ 2:width-1]) - - # Get the time, at that velocity, for the area of the triangle to be nil. - # We are only interested by positive values to only move in the direction of the gradient - for triangle ∈ - [triangle3D(mesh, row, col, :top), triangle3D(mesh, row, col, :bottom)] - t1, t2 = find_maximum_t(triangle) - @assert typeof(t1) == Float64 && typeof(t2) == Float64 "Maximum times are not numerical at $(row), $(col)" - end + t1 = zeros(Float64, size(mesh)) + t2 = zeros(Float64, size(mesh)) - # list_min_pos_t[(row-1)+(col-2)*(width-2)] - # println("March mesh δ: $(δ)") - end + mesh_r = copy(mesh.corners.r) + mesh_c = copy(mesh.corners.c) + mesh_h = copy(mesh.corners.ϕ) - t1 = max.(t1, 0.0) - t2 = max.(t2, 0.0) + # Get the time, at that velocity, for the area of the triangle to be nil. + # We are only interested by positive values to only move in the direction of the gradient + + list_triangles = vcat( + [triangle3D(mesh, row, col, :top) for row ∈ 1:height-1, col ∈ 1:width-1], + [triangle3D(mesh, row, col, :bottom) for row ∈ 1:height-1, col ∈ 1:width-1], + ) + list_maximum_t = find_maximum_t.(list_triangles) + min_positive_t = minimum(list_maximum_t) - min_positive_t = min(minimum(t1), minimum(t2)) + # @assert all(typeof.(t1) .== Float64) && all(typeof.(t2) .== Float64) "March mesh: Maximum times are not numerical at $(row), $(col)" δ = min_positive_t / 2.0 - mesh.topleft.r -= δ .* ∇ϕᵤ - mesh.topleft.c -= δ .* ∇ϕᵥ + mesh.corners.r -= δ .* ∇ϕᵤ + mesh.corners.c -= δ .* ∇ϕᵥ - # reset_border_values!(mesh.topleft) + # reset_border_values!(mesh.corner) # Reset the border at the fixed values fixed coordinates. - reset_border_values!(mesh.topleft) + reset_border_values!(mesh.corners) println( - "Average mesh changes on row = $(sum(abs.(mesh.topleft.r - mesh_r)) / (height * width))", - ) + """ - println( - "Average mesh changes on col = $(sum(abs.(mesh.topleft.c - mesh_c)) / (height * width))", - ) + March mash: + δ = $(δ) + first minimum ts: $(list_maximum_t[1:5]) + Average mesh changes on row = $(sum(abs.(mesh.corners.r - mesh_r)) / (height * width)) + Average mesh changes on col = $(sum(abs.(mesh.corners.c - mesh_c)) / (height * width)) + Average mesh changes on height = $(sum(abs.(mesh.corners.ϕ - mesh_h)) / (height * width)) - println( - "Average mesh changes on height = $(sum(abs.(mesh.topleft.h - mesh_h)) / (height * width))", + """, ) # Modify the mesh triangles but ensuring that we are far from destroying any of them with a nil area. @@ -528,21 +566,14 @@ end $(SIGNATURES) """ function ∇(ϕ::Matrix{Float64}) - height, width = size(ϕ) - - ∇ϕᵤ = zeros(Float64, height, width) # the right edge will be filled with zeros - ∇ϕᵥ = zeros(Float64, height, width) # the bottom edge will be filled with zeros - - for row ∈ 1:height-1, col ∈ 1:width-1 - ∇ϕᵤ[row, col] = ϕ[row+1, col] - ϕ[row, col] - ∇ϕᵥ[row, col] = ϕ[row, col+1] - ϕ[row, col] - end + ∇ϕᵤ = zeros(Float64, size(ϕ)) # divergence on the right edge will be filled with zeros + ∇ϕᵥ = zeros(Float64, size(ϕ)) # divergence on bottom edge will be filled with zeros - ∇ϕᵤ[1:end, end] .= 0.0 - ∇ϕᵤ[end, 1:end] .= 0.0 + @. ∇ϕᵤ[begin:end-1, :] = ϕ[begin+1:end, :] - ϕ[begin:end-1, :] + @. ∇ϕᵥ[:, begin:end-1] = ϕ[:, begin+1:end] - ϕ[:, begin:end-1] - ∇ϕᵥ[1:end, end] .= 0.0 - ∇ϕᵥ[end, 1:end] .= 0.0 + fill_borders!(∇ϕᵤ, 0.0) + fill_borders!(∇ϕᵥ, 0.0) return ∇ϕᵤ, ∇ϕᵥ end @@ -560,11 +591,11 @@ function matrix_to_mesh(ϕ::Matrix{Float64}) mesh = FaceMesh(height, width) - # 1 more topleft than pixels! Therefore compiler needs to specify exact indices. - mesh.topleft.h[1:height, 1:width] .= ϕ[1:height, 1:width] + # 1 more corner than corners! Therefore compiler needs to specify exact indices. + mesh.corners.ϕ[1:height, 1:width] .= ϕ[1:height, 1:width] # The borders' height is forced at 0. - reset_border_values!(mesh.topleft) + reset_border_values!(mesh.corners) return mesh end @@ -577,8 +608,8 @@ TO REFACTOR. """ function create_solid( mesh::FaceMesh; - bottom_offset = Bottom_Offset / Meters_Per_Pixel, - top_offset = Top_Offset / Meters_Per_Pixel, + bottom_offset = Bottom_Offset / Meters_Per_corner, + top_offset = Top_Offset / Meters_Per_corner, ) height, width = size(mesh) @@ -603,11 +634,11 @@ function create_solid( cols = repeat(Float64.(1:width)', height, 1) bottom_mesh = FaceMesh(height, width) - bottom_mesh.topleft.r[:] .= rows[:] - bottom_mesh.topleft.c[:] .= cols[:] - bottom_mesh.topleft.h[:] .= -Bottom_Offset - bottom_mesh.topleft.vr[:] .= 0.0 - bottom_mesh.topleft.vr[:] .= 0.0 + bottom_mesh.corner.r[:] .= rows[:] + bottom_mesh.corner.c[:] .= cols[:] + bottom_mesh.corner.ϕ[:] .= -Bottom_Offset + bottom_mesh.corner.vr[:] .= 0.0 + bottom_mesh.corner.vr[:] .= 0.0 ### diff --git a/src/io.jl b/src/io.jl index f0d6529..dc33af4 100644 --- a/src/io.jl +++ b/src/io.jl @@ -8,12 +8,12 @@ $(SIGNATURES) function convert(::Meshes.SimpleMesh, mesh::FaceMesh) height, width = size(mesh) - points = Meshes.Point3.([mesh.topleft[ci] for ci ∈ CartesianIndices(mesh.topleft)]) + points = Meshes.Point3.([mesh.corners[ci] for ci ∈ CartesianIndices(mesh.corners)]) top_connections = - [connect(mesh.toptriangles[ci]) for ci ∈ CartesianIndices(mesh.topleft)] + [connect(mesh.toptriangles[ci]) for ci ∈ CartesianIndices(mesh.corners)] bot_connections = - [connect(mesh.bottriangles[ci]) for ci ∈ CartesianIndices(mesh.topleft)] + [connect(mesh.bottriangles[ci]) for ci ∈ CartesianIndices(mesh.corners)] return SimpleMesh(points, vcat(top_connections, bot_connections)) end diff --git a/src/plots.jl b/src/plots.jl index 0b9c4b6..55cc38c 100644 --- a/src/plots.jl +++ b/src/plots.jl @@ -17,10 +17,10 @@ function plot_as_quiver( vrs = Float64[] vcs = Float64[] - ϕ = -mesh.topleft.h + ϕ = -mesh.corners.ϕ - vrm = reverser ? mesh.topleft.vr .* scale : -mesh.topleft.vr .* scale - vcm = reversec ? -mesh.topleft.vc .* scale : mesh.topleft.vc .* scale + vrm = reverser ? mesh.corners.vr .* scale : -mesh.corners.vr .* scale + vcm = reversec ? -mesh.corners.vc .* scale : mesh.corners.vc .* scale vrm = clamp.(vrm, -max_length, max_length) vcm = clamp.(vcm, -max_length, max_length) diff --git a/src/scratchpad.jl b/src/scratchpad.jl index 3e91a0a..47de745 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -6,20 +6,21 @@ image = Images.load("./examples/cat_posing.jpg"); # Check current working direct using CausticsEngineering mesh, imageBW = engineer_caustics(image); + Gray.(imageBW) -mesh.topleft.r[1:10, 1:10] -mesh.topleft.c[1:10, 1:10] -mesh.topleft.h[1:10, 1:10] -mesh.topleft.vr[1:10, 1:10] -mesh.topleft.vc[1:10, 1:10] +mesh.pixel.r[1:10, 1:10] +mesh.pixel.c[1:10, 1:10] +mesh.pixel.ϕ[1:10, 1:10] +mesh.pixel.vr[1:10, 1:10] +mesh.pixel.vc[1:10, 1:10] mesh.toptriangles[1:10] mesh.bottriangles[1:10] -mesh.topleft.r[250:260, 250:260] -mesh.topleft.c[250:260, 250:260] -mesh.topleft.h[250:260, 250:260] +mesh.pixel.r[250:260, 250:260] +mesh.pixel.c[250:260, 250:260] +mesh.pixel.ϕ[250:260, 250:260] using Test @@ -63,7 +64,7 @@ end c = t[1] -f.topleft(c) +f.pixel(c) t = CausticsEngineering.top_triangle3D(f, CartesianIndex(1, 1)) diff --git a/src/utilities.jl b/src/utilities.jl index 93ce1a0..9e94e00 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -1,18 +1,19 @@ """ $(TYPEDEF) -## Coordinates +## Coordinates. Represent the data of each topleft corner of a pixel. +## posts/fences: One more corner than number of pixels. """ struct Vertex3D r::Float64 c::Float64 - h::Float64 + ϕ::Float64 vr::Float64 vc::Float64 - Vertex3D(r, c, h, vr, vc) = new(r, c, h, vr, vc) + Vertex3D(r, c, ϕ, vr, vc) = new(r, c, ϕ, vr, vc) Vertex3D() = new(0.0, 0.0, 0.0, 0.0, 0.0) end @@ -22,8 +23,7 @@ $(SIGNATURES) function dist(p1::Tuple{Float64,Float64,Float64}, p2::Tuple{Float64,Float64,Float64}) dr = p2[1] - p1[1] dc = p2[2] - p1[2] - dh = p2[3] - p1[3] - return sqrt(dr^2 + dc^2 + dh^2) + return sqrt(dr^2 + dc^2) end """ @@ -31,34 +31,11 @@ $(SIGNATURES) """ function dist(p1::Vertex3D, p2::Vertex3D) dr = p2.r - p1.r - @assert 0.0 <= abs(dr) <= 1e6 "Distance (row coordinate = $(dr)) between $(p1) and $(p2) makes no sense " - dc = p2.c - p1.c - @assert 0.0 <= abs(dc) <= 1e6 "Distance (col coordinate = $(dc)) between $(p1) and $(p2) makes no sense " - - dh = p2.h - p1.h - @assert 0.0 <= abs(dh) <= 1e6 "Distance (height coordinate = $(dh)) between $(p1) and $(p2) makes no sense " - - return sqrt(dr^2 + dc^2 + dh^2) + return sqrt(dr^2 + dc^2) end -# """ -# $(SIGNATURES) -# """ -# function area( -# p1::Tuple{Float64,Float64,Float64}, -# p2::Tuple{Float64,Float64,Float64}, -# p3::Tuple{Float64,Float64,Float64}, -# ) -# a = dist(p1, p2) -# b = dist(p2, p3) -# c = dist(p3, p1) -# s = (a + b + c) / 2.0 - -# return sqrt(s * (s - a) * (s - b) * (s - c)) -# end - """ $(SIGNATURES) """ @@ -75,27 +52,13 @@ function area(v1::Vertex3D, v2::Vertex3D, v3::Vertex3D) end -""" -$(SIGNATURES) - -A midpoint is the average between two points -""" -midpoint(p1::Vertex3D, p2::Vertex3D) = - Vertex3D((p1.r + p2.r) / 2.0, (p1.c + p2.c) / 2.0, (p1.h + p2.h) / 2.0, 0.0, 0.0) - - """ $(SIGNATURES) Centroid of three points. """ -centroid(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) = Vertex3D( - (p1.r + p2.r + p3.r) / 3.0, - (p1.c + p2.c + p3.c) / 3.0, - (p1.h + p2.h + p3.h) / 3.0, - 0, - 0, -) +centroid(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) = + Vertex3D((p1.r + p2.r + p3.r) / 3.0, (p1.c + p2.c + p3.c) / 3.0, 0.0, 0.0, 0.0) """ @@ -129,7 +92,9 @@ mutable struct FieldVertex3D r::AbstractMatrix{Float64} c::AbstractMatrix{Float64} - h::AbstractMatrix{Float64} + + # Velocity potential at each corner + ϕ::AbstractMatrix{Float64} vr::AbstractMatrix{Float64} vc::AbstractMatrix{Float64} @@ -137,29 +102,29 @@ mutable struct FieldVertex3D rows_numbers::AbstractMatrix{Float64} cols_numbers::AbstractMatrix{Float64} - # FieldVertex3D(size, mr, mc, mh, mvr, mvc, rows_numbers, cols_numbers) = new(size, mr, mc, mh, mvr, mvc, rows_numbers, cols_numbers) + # FieldVertex3D(size, mr, mc, mϕ, mvr, mvc, rows_numbers, cols_numbers) = new(size, mr, mc, mϕ, mvr, mvc, rows_numbers, cols_numbers) end - +# Information about each corner surrounding a pixel. Posts&fences warning!!! function FieldVertex3D(height, width) - # mr = zeros(Float64, height + 1, width + 1) - # my = zeros(Float64, height + 1, width + 1) - # mh = zeros(Float64, height + 1, width + 1) - - # mvr = zeros(Float64, height + 1, width + 1) - # mvc = zeros(Float64, height + 1, width + 1) - rows_numbers = repeat(Float64.(1:height+1), 1, width + 1) cols_numbers = repeat(Float64.(1:width+1)', height + 1, 1) - mr = rows_numbers + rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 - mc = cols_numbers + rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 - mh = rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 - mvr = rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 - mvc = rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 + mr = rows_numbers + mc = cols_numbers + mϕ = zeros(Float64, height + 1, width + 1) + + mvr = zeros(Float64, height + 1, width + 1) + mvc = zeros(Float64, height + 1, width + 1) - fv = FieldVertex3D((height, width), mr, mc, mh, mvr, mvc, rows_numbers, cols_numbers) + # mr = rows_numbers + rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 + # mc = cols_numbers + rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 + # mϕ = rand(Float64, height, width) ./ 1_000 .- 0.5 / 1_000 + # mvr = rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 + # mvc = rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 + + fv = FieldVertex3D((height, width), mr, mc, mϕ, mvr, mvc, rows_numbers, cols_numbers) reset_border_values!(fv) return fv end @@ -170,21 +135,20 @@ $(SIGNATURES) Return the dimension of the mesh as the number of rectangles. It does not return the number of corner points. """ -function reset_border_values!(topleft::FieldVertex3D) +function reset_border_values!(corners::FieldVertex3D) # Reset the border at the fixed values fixed coordinates. - topleft.r[1, :] .= topleft.rows_numbers[1, :] - topleft.r[end, :] .= topleft.rows_numbers[end, :] - topleft.r[:, 1] .= topleft.rows_numbers[:, 1] - topleft.r[:, end] .= topleft.rows_numbers[:, end] - - topleft.c[1, :] .= topleft.cols_numbers[1, :] - topleft.c[end, :] .= topleft.cols_numbers[end, :] - topleft.c[:, 1] .= topleft.cols_numbers[:, 1] - topleft.c[:, end] .= topleft.cols_numbers[:, end] - - fill_borders!(topleft.h, 0.0) - fill_borders!(topleft.vr, 0.0) - fill_borders!(topleft.vc, 0.0) + corners.r[1, :] .= corners.rows_numbers[1, :] + corners.r[end, :] .= corners.rows_numbers[end, :] + corners.r[:, 1] .= corners.rows_numbers[:, 1] + corners.r[:, end] .= corners.rows_numbers[:, end] + + corners.c[1, :] .= corners.cols_numbers[1, :] + corners.c[end, :] .= corners.cols_numbers[end, :] + corners.c[:, 1] .= corners.cols_numbers[:, 1] + corners.c[:, end] .= corners.cols_numbers[:, end] + + fill_borders!(corners.vr, 0.0) + fill_borders!(corners.vc, 0.0) end @@ -201,7 +165,7 @@ function Vertex3D(fv::FieldVertex3D, row, col) Vertex3D( fv.r[row, col], fv.y[row, col], - fv.h[row, col], + fv.ϕ[row, col], fv.vr[row, col], fv.vc[row, col], ) @@ -233,7 +197,7 @@ of triangles rather than corners coming from different rectangles. """ struct FaceMesh size::Tuple{Int,Int} - topleft::FieldVertex3D + corners::FieldVertex3D toptriangles::AbstractMatrix{Tuple{Tuple{Int,Int},Tuple{Int,Int},Tuple{Int,Int}}} bottriangles::AbstractMatrix{Tuple{Tuple{Int,Int},Tuple{Int,Int},Tuple{Int,Int}}} @@ -241,7 +205,7 @@ struct FaceMesh FaceMesh(s, tl, tt, bt) = new(s, tl, tt, bt) function FaceMesh(height::Int, width::Int) - m_topleft = FieldVertex3D(height, width) + m_corner = FieldVertex3D(height, width) t_triangles = Matrix{Tuple{Tuple{Int,Int},Tuple{Int,Int},Tuple{Int,Int}}}( undef, height, @@ -258,7 +222,7 @@ struct FaceMesh b_triangles[row, col] = ((row, col + 1), (row + 1, col), (row + 1, col + 1)) end - return FaceMesh((height, width), m_topleft, t_triangles, b_triangles) + return FaceMesh((height, width), m_corner, t_triangles, b_triangles) end end @@ -309,30 +273,30 @@ function triangle3D(mesh::FaceMesh, row::Int, col::Int, side = Union{:top,:botto t2_row, t2_col = t[2] t3_row, t3_col = t[3] - r1 = mesh.topleft.r[t1_row, t1_col] - c1 = mesh.topleft.c[t1_row, t1_col] - h1 = mesh.topleft.h[t1_row, t1_col] - vr1 = mesh.topleft.vr[t1_row, t1_col] - vc1 = mesh.topleft.vc[t1_row, t1_col] - @assert r1^2 + c1^2 + h1^2 <= 1e12 "Coordinate $(r1), $(c1), $(h1) of point #1 at $(row), $(col) side = $(side) makes no sense " - - r2 = mesh.topleft.r[t2_row, t2_col] - c2 = mesh.topleft.c[t2_row, t2_col] - h2 = mesh.topleft.h[t2_row, t2_col] - vr2 = mesh.topleft.vr[t2_row, t2_col] - vc2 = mesh.topleft.vc[t2_row, t2_col] - @assert r2^2 + c2^2 + h2^2 <= 1e12 "Coordinate $(r2), $(c2), $(h2) of point #2 at $(row), $(col) side = $(side) makes no sense " - - r3 = mesh.topleft.r[t3_row, t3_col] - c3 = mesh.topleft.c[t3_row, t3_col] - h3 = mesh.topleft.h[t3_row, t3_col] - vr3 = mesh.topleft.vr[t3_row, t3_col] - vc3 = mesh.topleft.vc[t3_row, t3_col] - @assert r3^2 + c3^2 + h3^2 <= 1e12 "Coordinate $(r3), $(c3), $(h3) of point #3 at $(row), $(col) side = $(side) makes no sense " - - p1 = Vertex3D(r1, c1, h1, vr1, vc1) - p2 = Vertex3D(r2, c2, h2, vr2, vc2) - p3 = Vertex3D(r3, c3, h3, vr3, vc3) + r1 = mesh.corners.r[t1_row, t1_col] + c1 = mesh.corners.c[t1_row, t1_col] + ϕ1 = mesh.corners.ϕ[t1_row, t1_col] + vr1 = mesh.corners.vr[t1_row, t1_col] + vc1 = mesh.corners.vc[t1_row, t1_col] + @assert r1^2 + c1^2 + ϕ1^2 <= 1e12 "Coordinate $(r1), $(c1), $(ϕ1) of point #1 at $(row), $(col), side = $(side) makes no sense " + + r2 = mesh.corners.r[t2_row, t2_col] + c2 = mesh.corners.c[t2_row, t2_col] + ϕ2 = mesh.corners.ϕ[t2_row, t2_col] + vr2 = mesh.corners.vr[t2_row, t2_col] + vc2 = mesh.corners.vc[t2_row, t2_col] + @assert r2^2 + c2^2 + ϕ2^2 <= 1e12 "Coordinate $(r2), $(c2), $(ϕ2) of point #2 at $(row), $(col), side = $(side) makes no sense " + + r3 = mesh.corners.r[t3_row, t3_col] + c3 = mesh.corners.c[t3_row, t3_col] + ϕ3 = mesh.corners.ϕ[t3_row, t3_col] + vr3 = mesh.corners.vr[t3_row, t3_col] + vc3 = mesh.corners.vc[t3_row, t3_col] + @assert r3^2 + c3^2 + ϕ3^2 <= 1e12 "Coordinate $(r3), $(c3), $(ϕ3) of point #3 at $(row), $(col), side = $(side) makes no sense " + + p1 = Vertex3D(r1, c1, ϕ1, vr1, vc1) + p2 = Vertex3D(r2, c2, ϕ2, vr2, vc2) + p3 = Vertex3D(r3, c3, ϕ3, vr3, vc3) return (p1, p2, p3) else # return (missing, missing, missing) @@ -402,4 +366,6 @@ function area(mesh::FaceMesh, row::Int, col::Int; side = Union{:top,:bottom}) end -max_sum_abs(m::AbstractMatrix) = (sum(abs.(m)) / length(m)) < 1_024 +average_absolute(m::AbstractMatrix) = (sum(abs.(m)) / length(m)) < 1e10 + +smallest_positive(x1::Float64, x2::Float64) = min(max(x1, 0, 0), max(x2, 0.0)) From 5802b2a18869e0826d08baa6526ca1695cc75723 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Thu, 9 Sep 2021 14:07:53 +0200 Subject: [PATCH 18/58] Refactoring ongoing. Snapshot 12 --- src/create_mesh.jl | 372 +++++++++++++++++++++++++++------------------ src/plots.jl | 2 +- src/scratchpad.jl | 105 +++++++++++++ src/utilities.jl | 20 ++- 4 files changed, 346 insertions(+), 153 deletions(-) diff --git a/src/create_mesh.jl b/src/create_mesh.jl index eaaea2d..83aed5f 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -11,14 +11,14 @@ function engineer_caustics(source_image) # cover each image corner with a triangle. mesh = FaceMesh(height, width) # println("Mesh creation: ") - # r_check = 1 - # c_check = 1 - # println( - # "\tCoordinates: $(mesh.corners.r[r_check, c_check]) , $(mesh.corners.c[r_check, c_check]) , $(mesh.corners.ϕ[r_check, c_check])", - # ) - # println( - # "\tVelocities: $(mesh.corners.vr[r_check, c_check]) , $(mesh.corners.vc[r_check, c_check])", - # ) + r_check = 256 + c_check = 256 + println( + "\tCoordinates: $(mesh.corners.r[r_check, c_check]) , $(mesh.corners.c[r_check, c_check]) , $(mesh.corners.ϕ[r_check, c_check])", + ) + println( + "\tVelocities: $(mesh.corners.vr[r_check, c_check]) , $(mesh.corners.vc[r_check, c_check])", + ) # The energy going through the lens is equal to the amount of energy on the caustics total_energy_lens = height * width * 1 # 1 unit of energy per corner @@ -29,11 +29,22 @@ function engineer_caustics(source_image) # original image. imageBW = imageBW .* correction_ratio - for i ∈ 1:5 - println("\nSTARTING VERTICAL ITERATION $(i) ---") + start_max_update = 1_000.0 + max_update = start_max_update + old_max_update = 2 * start_max_update + iteration_count = 0 + + # while 1e-6 < abs(max_update) < start_max_update + 1 && abs((max_update - old_max_update) / old_max_update) > 0.01 + while iteration_count < 1_024 + iteration_count += 1 + + println( + "\nSTARTING VERTICAL ITERATION $(iteration_count) --------------------------------------------", + ) - max_update = solve_velocity_potential!(mesh, imageBW, "it$(i)") - print("Vertical move max update = $(max_update)") + old_max_update = max_update + max_update = solve_velocity_potential!(mesh, imageBW, "it$(iteration_count)") + print("Vertical move max update = $(max_update) \n") # println( # "\tCoordinates: $(mesh.corners.r[r_check, c_check]) , $(mesh.corners.c[r_check, c_check]) , $(mesh.corners.ϕ[r_check, c_check])", @@ -41,13 +52,11 @@ function engineer_caustics(source_image) # println( # "\tVelocities: $(mesh.corners.vr[r_check, c_check]) , $(mesh.corners.vc[r_check, c_check])", # ) - - println("---------- ITERATION $(i): $(max_update)/n") end println("\nSTARTING HORIZONTAL ITERATION ---") - mesh.corners.ϕ, max_update = - move_horizontally(mesh, imageBW; f = 1.0, picture_width = Caustics_Side) + ϕ, max_update = move_horizontally(mesh, imageBW; f = 1.0, picture_width = Caustics_Side) + mesh.corners.ϕ .= ϕ println(" max update = $(max_update)") @@ -70,85 +79,108 @@ end """ $(SIGNATURES) + +ϕ is the _velocity potential_. The velocity represents the direction towards which the mesh vertices should move. +Zones of high luminosity should be covered with more triangles and should attract more vertices. """ function solve_velocity_potential!(mesh, image, suffix) # Remember mesh is (will be) `grid_definition x grid_definition` just like the image # `grid_definition x grid_definition`, so LJ is `grid_definition x grid_definition`. - # The idea is that: - # - any corner on the caustic projection receives light from a given 'rectangle' on the lens. - # - That rectangle is made of 2 triangles. area_distorted_corners = get_area_corners(mesh) @assert average_absolute(area_distorted_corners) """ - solve_velocity_potential: area_distorted_corners values seem too large - $(maximum(area_distorted_corners)) / $(minimum(area_distorted_corners)) + solve_velocity_potential: area_distorted_corners values seem too large + $(maximum(area_distorted_corners)) / $(minimum(area_distorted_corners)) - """ + """ + # Positive error => the triangle needs to shrink (less light) error_luminosity = Float64.(area_distorted_corners - image) @assert average_absolute(error_luminosity) """ - solve_velocity_potential: error_luminosity values seem too large - max/min error_luminosity = $(maximum(error_luminosity)) / $(minimum(error_luminosity)) - max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) + solve_velocity_potential: error_luminosity values seem too large + max/min error_luminosity = $(maximum(error_luminosity)) / $(minimum(error_luminosity)) - """ + """ # Save the loss image as a png plot_loss!(error_luminosity, suffix, image) - # ϕ is the _velocity potential_ - # ϕ is defined per corner - ϕ = zeros(Float64, size(mesh.corners.ϕ)) - # For the purpose of Poisson, we need to divergence to increase towards the inside: negative divergence for high luminosity - error_luminosity = -error_luminosity + # error_luminosity = -error_luminosity + + mesh_r = copy(mesh.corners.r) + mesh_c = copy(mesh.corners.c) + mesh_ϕ = copy(mesh.corners.ϕ) + height, width = size(mesh.corners.ϕ) - max_update = Inf + start_max_update = 1_000.0 + max_update = start_max_update + old_max_update = 2 * start_max_update iteration_count = 0 - for _ ∈ 1:5 + new_divergence = 0.0 + + # while 1e-6 < abs(max_update) < start_max_update + 1 && abs((max_update - old_max_update) / old_max_update) > 0.01 + # while sum(abs.(mesh.corners.ϕ - mesh_ϕ)) / (height * width) < 100 + while new_divergence < 20.0 iteration_count += 1 iteration_count % 100 == 0 && println("Converging for intensity: $(max_update)") + mesh.corners.ϕ[:, :] .-= sum(mesh.corners.ϕ) / (height * width) + old_max_update = max_update println( - "solve_velocity_potential: iteration count = $(iteration_count) -- ", - "max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) -- ", - "max/min mesh.corners.ϕ = $(maximum(mesh.corners.ϕ)) / $(minimum(mesh.corners.ϕ)) -- ", - "max_update = $(max_update)", + """ + solve_velocity_potential: + max/min mesh.corners.ϕ = $(maximum(mesh.corners.ϕ)) / $(minimum(mesh.corners.ϕ)) + iteration count = $(iteration_count), max_update = $(max_update) + new maximum divergence = $(new_divergence) + """, ) # Solve the Poisson equation where the divergence of the gradient of ϕ is equal to the luminosity loss. - ϕ, max_update = gradient_descent(ϕ, error_luminosity) - @assert average_absolute(ϕ) """ - - solve_velocity_potential: ϕ values seem too large - iteration count = $(iteration_count) - max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) - max/min mesh.corners.ϕ = $(maximum(mesh.corners.ϕ)) / $(minimum(mesh.corners.ϕ)) - - max/min error_luminosity = $(maximum(error_luminosity)) / $(minimum(error_luminosity)) - max_update = $(max_update) - - """ - + ϕ, max_update = gradient_descent(mesh.corners.ϕ, error_luminosity) + mesh.corners.ϕ[:, :] .= ϕ[:, :] + + @assert average_absolute(mesh.corners.ϕ) """ + + solve_velocity_potential: ϕ values seem too large + iteration count = $(iteration_count) + max/min mesh.corners.ϕ = $(maximum(mesh.corners.ϕ)) / $(minimum(mesh.corners.ϕ)) + + max/min error_luminosity = $(maximum(error_luminosity)) / $(minimum(error_luminosity)) + max_update = $(max_update) + + """ + new_divergence = maximum( + abs.( + mesh.corners.ϕ[begin+1:end, begin:end-1] .- + mesh_ϕ[begin:end-1, begin:end-1] .+ + mesh.corners.ϕ[begin:end-1, begin+1:end] .- + mesh_ϕ[begin:end-1, begin:end-1], + ), + ) + end - if abs(max_update) < 1e-6 || - abs((max_update - old_max_update) / old_max_update) < 0.01 - println( - "Convergence stopped at step $(iteraction_count) with ", - "max_update = $(max_update) -- ", - "max/min area_distorted_corners = $(maximum(area_distorted_corners)) / $(minimum(area_distorted_corners)) -- ", - "max error_luminosity = $(maximum(abs.(error_luminosity)))", - ) - break - end - end + # Relevel ϕ around its average. It doesn't matter for potential fields + mean_ϕ = sum(mesh.corners.ϕ) / length(mesh.corners.ϕ) + mesh.corners.ϕ .-= mean_ϕ - mesh.corners.ϕ .= ϕ + println( + """ + Convergence stopped at step $(iteration_count) with + max_update = $(max_update) + max/min area_distorted_corners = $(maximum(area_distorted_corners)) / $(minimum(area_distorted_corners)) + max error_luminosity = $(maximum(abs.(error_luminosity))) + Average mesh changes on ϕ = $(sum(abs.(mesh.corners.ϕ - mesh_ϕ)) / (height * width)) + max ϕ divergence = $(maximum(abs.(mesh.corners.ϕ[begin+1:end, begin:end-1] .- mesh_ϕ[begin:end-1, begin:end-1] .+ + mesh.corners.ϕ[begin:end-1, begin+1:end] .- mesh_ϕ[begin:end-1, begin:end-1]))) + + """, + ) # Now we need to march the x,y locations in our mesh according to this gradient! # Tasks are a control flow feature that allows computations to be suspended and resumed in a flexible manner. @@ -156,7 +188,7 @@ function solve_velocity_potential!(mesh, image, suffix) march_mesh!(mesh) save_stl!( - matrix_to_mesh(ϕ * 0.02), + matrix_to_mesh(mesh.corners.ϕ * 0.02), "./examples/phi_$(suffix).obj", reverse = false, flipxy = true, @@ -202,14 +234,14 @@ function move_horizontally( d_row = mesh.corners.rows_numbers - mesh.corners.r d_col = mesh.corners.cols_numbers - mesh.corners.c + # The focal length is in meters. H is in corners. + H = f / Meters_Per_Pixel + # true_H is the real distance beteen the surface of the lens and the projection # H is the initial distance from the surface of the carved face to the projection screen. # H is constant and does not account for the change in heights due to carving. - # The focal length is in meters. H is in corners. # Note: Higher location means closer to the caustics => negative sign - H = f / Meters_Per_corner - - true_H = similar(mesh.corners.ϕ) + true_H = zeros(Float64, size(mesh.corners.ϕ)) @. true_H[:] = -mesh.corners.ϕ[:] + H # Normals. @@ -224,33 +256,40 @@ function move_horizontally( @. div_row[1:end, 1:end] = N_row[2:end, 1:end-1] - N_row[1:end-1, 1:end-1] @. div_col[1:end, 1:end] = N_col[1:end-1, 2:end] - N_col[1:end-1, 1:end-1] - divergence_direction = zeros(Float64, size(div_row)) - divergence_direction[1:height, 1:width] = div_row + div_col - @assert average_absolute(divergence_direction) "ALERT: horiz. Δ divergence_direction is too large - max/min = $(maximum(divergence_direction)) / $(minimum(divergence_direction))" + # divergence_direction = zeros(Float64, size(div_row)) + divergence_direction = div_row + div_col + @assert average_absolute(divergence_direction) """ - println("Have all the divergences") + ALERT: horiz. Δ divergence_direction seem too large + max/min = $(maximum(divergence_direction)) / $(minimum(divergence_direction)) + """ - corner_heights = zeros(Float64, size(mesh.corners.ϕ)) - max_update = 1_000.0 - iteration_count = 0 - while true - iteration_count += 1 - iteration_count % 100 == 0 && println("Converging for divergence: $(max_update)") + corner_heights, max_update = gradient_descent(corner_heights, -divergence_direction) - old_max_update = max_update - corner_heights, max_update = gradient_descent(corner_heights, -divergence_direction) - @assert average_absolute(corner_heights) "ALERT: horiz. Δ corner_heights is too large - max/min corner_heights = $(maximum(corner_heights)) / $(minimum(corner_heights))" + @assert average_absolute(corner_heights) """ + ALERT: horiz. Δ corner_heights is too large + max/min corner_heights = $(maximum(corner_heights)) / $(minimum(corner_heights)) + """ - if abs(max_update) < 1e-6 || - abs((max_update - old_max_update) / old_max_update) < 0.01 - println( - "Convergence stopped improving at step $(iteration_count) ", - "with max_update of $(max_update)", - ) - break - end - end + println( + "Convergence horiz. Δ stopped improving at step $(iteration_count) ", + "with max_update of $(max_update)", + ) + + + # println(""" + # Convergence stopped at step $(iteration_count) with + # max_update = $(max_update) + # max/min area_distorted_corners = $(maximum(area_distorted_corners)) / $(minimum(area_distorted_corners)) + # max error_luminosity = $(maximum(abs.(error_luminosity))) + + # Average mesh changes on row = $(sum(abs.(mesh.corners.r - mesh_r)) / (height * width)) -- CHECK == 0.0 + # Average mesh changes on col = $(sum(abs.(mesh.corners.c - mesh_c)) / (height * width)) -- CHECK == 0.0 + # Average mesh changes on ϕ = $(sum(abs.(mesh.corners.ϕ - mesh_ϕ)) / (height * width)) + + # """ + # ) # saveObj(matrix_to_mesh(h / 10), "./examples/heightmap.obj") return corner_heights, max_update @@ -273,29 +312,27 @@ function gradient_descent(ϕ::Matrix{Float64}, ∇ϕ::Matrix{Float64}) # Ensure that border conditions are as they should fill_borders!(∇ϕ, 0.0) - fill_borders!(ϕ, 0.0) + # fill_borders!(ϕ, 0.0) @assert average_absolute(ϕ) """ - Relaxation: ϕ values seem too large - max/min ∇ϕ = $(maximum(∇ϕ)) / $(minimum(∇ϕ)) - max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) + Relaxation: ϕ values seem too large + max/min ∇ϕ = $(maximum(∇ϕ)) / $(minimum(∇ϕ)) + max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) - """ + """ @assert average_absolute(∇ϕ) """ - Relaxation: ∇²ϕ values seem too large - max/min ∇ϕ = $(maximum(∇ϕ)) / $(minimum(∇ϕ)) - max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) - - """ + Relaxation: ∇²ϕ values seem too large + max/min ∇ϕ = $(maximum(∇ϕ)) / $(minimum(∇ϕ)) + max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) + """ @assert any(isnan.(ϕ)) == false "Relaxation: calling with a ϕ that contains NaN!!" @assert any(isnan.(∇ϕ)) == false "Relaxation: calling with a ∇ϕ that contains NaN!!" - # ϕ is of the same size as corners = number of corners + 1 height_corners, width_corners = size(ϕ) height_pixels, width_pixels = size(∇ϕ) @@ -328,33 +365,57 @@ function gradient_descent(ϕ::Matrix{Float64}, ∇ϕ::Matrix{Float64}) # Target position. The target is the current height map smoothed by averaging to which the # flow is added. # This has to converge towards the ∇ϕ. Difference to calculate speed of the descent. - δ = (flow_up + flow_down + flow_left + flow_right) + ∇ϕ + # δ = (flow_up + flow_down + flow_left + flow_right) + ∇ϕ + + # δ is the difference between the desired divergence and the current one + # High ∇ϕ means that the triangles are too bright. + δ = ∇ϕ - (flow_up + flow_down + flow_left + flow_right) @assert average_absolute(δ) """ - Relaxation: ∇ϕ_error as (current - target) seem too large - max/min target ∇ϕ = $(maximum(∇ϕ)) / $(minimum(∇ϕ)) - max/min ∇ϕ_error = $(maximum(δ)) / $(minimum(δ)) + Relaxation: ∇ϕ_error as (current - target) seem too large + max/min target ∇ϕ = $(maximum(∇ϕ)) / $(minimum(∇ϕ)) + max/min ∇ϕ_error = $(maximum(δ)) / $(minimum(δ)) - max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) - max/min padded_ϕ = $(maximum(padded_ϕ)) / $(minimum(padded_ϕ)) - max/min flow_up = $(maximum(flow_up)) / $(minimum(flow_up)) - max/min flow_down = $(maximum(flow_down)) / $(minimum(flow_down)) - max/min flow_left = $(maximum(flow_left)) / $(minimum(flow_left)) - max/min flow_right = $(maximum(flow_right)) / $(minimum(flow_right)) + max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) + max/min padded_ϕ = $(maximum(padded_ϕ)) / $(minimum(padded_ϕ)) + max/min flow_up = $(maximum(flow_up)) / $(minimum(flow_up)) + max/min flow_down = $(maximum(flow_down)) / $(minimum(flow_down)) + max/min flow_left = $(maximum(flow_left)) / $(minimum(flow_left)) + max/min flow_right = $(maximum(flow_right)) / $(minimum(flow_right)) - """ + """ # @. target_map[height_div, width_div] += ∇ϕ / 4.0 # fill_borders!(∇ϕ_error, 0.0) # Let the heightmap converge towards the target at a slow rate = gradient descent. # @. ϕ += 0.2 * ∇ϕ_error + + maximum_δ = maximum(abs.(δ)) + max_correction_ratio = 2.0 + + if 1.94 / 4.0 * maximum_δ < max_correction_ratio + correction_ratio = 1.94 / 4.0 + else + correction_ratio = max_correction_ratio / maximum_δ + end + + # High ∇ϕ (loss function) means that the triangles are too bright + # High brightness => triangle are too wide + # Too wide => need velocity towards the centre + # Velocity toward the centre => divergence should be negative + + # Negative divergence means that the field should increase towards the inside + + # δ > 0 => divergence of ϕ needs to increase + + # Increase @. ϕ[1:height_pixels, 1:width_pixels] += - 1.94 / 40.0 * δ[1:height_pixels, 1:width_pixels] + correction_ratio * δ[1:height_pixels, 1:width_pixels] @assert !any(isnan.(ϕ)) "Relaxation: Updated ϕ contains NaN!!" - max_update = maximum(abs.(1.94 / 40.0 * δ)) + max_update = correction_ratio * maximum(abs.(δ)) return ϕ, max_update end @@ -463,7 +524,7 @@ function find_maximum_t(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) # C will never end up on the line AB. # Very unlikely with Float64. # Negative numbers are filtered out when calculating the minimum jiggle ratio - return 1e-10 + return -1.0 end @@ -479,10 +540,9 @@ $(SIGNATURES) """ function march_mesh!(mesh::FaceMesh) - ϕ = mesh.corners.ϕ - height, width = size(ϕ) + height, width = size(mesh.corners.ϕ) - ∇ϕᵤ, ∇ϕᵥ = ∇(ϕ) + ∇ϕᵤ, ∇ϕᵥ = ∇(mesh.corners.ϕ) # println("Min/Max of values of ϕ: $(minimum(ϕ)) / $(maximum(ϕ))") # println("Sum of values of ∇ϕᵤ: $( sum(∇ϕᵤ) )") # println("Sum of values of ∇ϕᵥ: $( sum(∇ϕᵥ) )") @@ -499,7 +559,6 @@ function march_mesh!(mesh::FaceMesh) # Just in case... reset_border_values!(mesh.corners) - reset_border_values!(mesh.corners) # Basically infinity time to shrink a triangle to nothing. min_positive_t = Inf @@ -510,49 +569,70 @@ function march_mesh!(mesh::FaceMesh) mesh_r = copy(mesh.corners.r) mesh_c = copy(mesh.corners.c) - mesh_h = copy(mesh.corners.ϕ) + mesh_ϕ = copy(mesh.corners.ϕ) # Get the time, at that velocity, for the area of the triangle to be nil. # We are only interested by positive values to only move in the direction of the gradient - list_triangles = vcat( - [triangle3D(mesh, row, col, :top) for row ∈ 1:height-1, col ∈ 1:width-1], - [triangle3D(mesh, row, col, :bottom) for row ∈ 1:height-1, col ∈ 1:width-1], - ) - list_maximum_t = find_maximum_t.(list_triangles) - min_positive_t = minimum(list_maximum_t) + # list_triangles = vcat( + # [triangle3D(mesh, row, col, :top) for row ∈ 1:height-1, col ∈ 1:width-1], + # [triangle3D(mesh, row, col, :bottom) for row ∈ 1:height-1, col ∈ 1:width-1], + # ) + # list_maximum_t = [time for time ∈ find_maximum_t.(list_triangles) + # if !isnan(time) && time > 0.0 && time < 10.0] + + # if !isempty(list_maximum_t) + # min_positive_t = minimum(list_maximum_t) + + # # @assert all(typeof.(t1) .== Float64) && all(typeof.(t2) .== Float64) "March mesh: Maximum times are not numerical at $(row), $(col)" + + # δ = min_positive_t / 2.0 + # mesh.corners.r -= δ .* ∇ϕᵤ + # mesh.corners.c -= δ .* ∇ϕᵥ + # end - # @assert all(typeof.(t1) .== Float64) && all(typeof.(t2) .== Float64) "March mesh: Maximum times are not numerical at $(row), $(col)" + for row ∈ 1:height-1, col ∈ 1:width-1 + list_triangles = + [triangle3D(mesh, row, col, :top), triangle3D(mesh, row, col, :bottom)] + list_maximum_t = [ + time for time ∈ find_maximum_t.(list_triangles) if + !isnan(time) && time > 0.0 && time < 10.0 + ] - δ = min_positive_t / 2.0 - mesh.corners.r -= δ .* ∇ϕᵤ - mesh.corners.c -= δ .* ∇ϕᵥ + if !isempty(list_maximum_t) + min_positive_t = minimum(list_maximum_t) + + # @assert all(typeof.(t1) .== Float64) && all(typeof.(t2) .== Float64) "March mesh: Maximum times are not numerical at $(row), $(col)" + + max_shift = max(abs(∇ϕᵤ[row, col]), abs(∇ϕᵥ[row, col])) + + # No shift more than 0.5 pixels + δ = min(min_positive_t / 2.0, 5.0 / max_shift) + mesh.corners.r[row, col] = + clamp(mesh.corners.r[row, col] + δ * ∇ϕᵤ[row, col], 1, height - 1) + mesh.corners.c[row, col] = + clamp(mesh.corners.c[row, col] + δ * ∇ϕᵥ[row, col], 1, width - 1) + end + end - # reset_border_values!(mesh.corner) # Reset the border at the fixed values fixed coordinates. reset_border_values!(mesh.corners) + # δ = $(δ) + # first minimum ts: $(list_maximum_t[1:5]) + println( """ - - March mash: - δ = $(δ) - first minimum ts: $(list_maximum_t[1:5]) - Average mesh changes on row = $(sum(abs.(mesh.corners.r - mesh_r)) / (height * width)) - Average mesh changes on col = $(sum(abs.(mesh.corners.c - mesh_c)) / (height * width)) - Average mesh changes on height = $(sum(abs.(mesh.corners.ϕ - mesh_h)) / (height * width)) + March mesh: + max/min Vu = $(maximum(abs.(∇ϕᵤ))) / $(minimum(abs.(∇ϕᵤ))) + max/min Vv = $(maximum(abs.(∇ϕᵥ))) / $(minimum(abs.(∇ϕᵥ))) + Average mesh changes on row = $(sum(abs.(mesh.corners.r - mesh_r)) / (height * width)) + Average mesh changes on col = $(sum(abs.(mesh.corners.c - mesh_c)) / (height * width)) """, ) - # Modify the mesh triangles but ensuring that we are far from destroying any of them with a nil area. - # Use the maximum change possible (negative or positive) - # δ = min_positive_t / 2.0 - # println( - # "\tMarch mesh with average factor $(sum(list_min_pos_t) / length(list_min_pos_t))\n", - # ) - # println("Overall maximum variations:") # println("\tOverall min_positive_t: $(min_positive_t)") # println("\tOverall max_negative_t: $(max_negative_t)") @@ -608,8 +688,8 @@ TO REFACTOR. """ function create_solid( mesh::FaceMesh; - bottom_offset = Bottom_Offset / Meters_Per_corner, - top_offset = Top_Offset / Meters_Per_corner, + bottom_offset = Bottom_Offset / Meters_Per_Pixel, + top_offset = Top_Offset / Meters_Per_Pixel, ) height, width = size(mesh) diff --git a/src/plots.jl b/src/plots.jl index 55cc38c..fc4b27c 100644 --- a/src/plots.jl +++ b/src/plots.jl @@ -4,7 +4,7 @@ $(SIGNATURES) function plot_as_quiver( mesh::FaceMesh; stride = 4, - scale = 300, + scale = 30, max_length = 2, flipxy = false, reverser = false, diff --git a/src/scratchpad.jl b/src/scratchpad.jl index 47de745..bf394b3 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -82,3 +82,108 @@ using StructArrays aa = StructArrays() aa[:].a = 0 + + +[1, 2, 3] |> filter(isnan) + + +begin + r1, c1, ϕ1, vr1, vc1 = (rand(5) .- 0.5) .* 20 + r2, c2, ϕ2, vr2, vc2 = (rand(5) .- 0.5) .* 20 + r3, c3, ϕ3, vr3, vc3 = (rand(5) .- 0.5) .* 20 + + vertex1 = Vertex3D(r1, c1, ϕ1, vr1, vc1) + vertex2 = Vertex3D(r2, c2, ϕ2, vr2, vc2) + vertex3 = Vertex3D(r3, c3, ϕ3, vr3, vc3) + + println( + CausticsEngineering.area(vertex1, vertex2, vertex3), + " ", + CausticsEngineering.find_maximum_t(vertex1, vertex2, vertex3), + ) +end + + +r1, c1, ϕ1, vr1, vc1 = (rand(5) .- 0.5) .* 20 +r2, c2, ϕ2, vr2, vc2 = (rand(5) .- 0.5) .* 20 +r3, c3, ϕ3, vr3, vc3 = (rand(5) .- 0.5) .* 20 + +p1 = Vertex3D(r1, c1, ϕ1, vr1, vc1) +p2 = Vertex3D(r2, c2, ϕ2, vr2, vc2) +p3 = Vertex3D(r3, c3, ϕ3, vr3, vc3) + +# To make the calculation simpler, everything is translated so that A is at the +# origin of the plane and its velocity is nil. +Br = p2.r - p1.r +Bc = p2.c - p1.c +Cr = p3.r - p1.r +Cc = p3.c - p1.c + +t_vBr = p2.vr - p1.vr +t_vBc = p2.vc - p1.vc +t_vCr = p3.vr - p1.vr +t_vCc = p3.vc - p1.vc + +# After this, given that Ar = Ac = t_vAr = t_vAc = 0, the area is nil iff +# (Br + t_vBr) (Cc + t_vCc ) - (Cr + t_vCr) (Bc + t_vBc) = 0. +# After expansion and reshuffling to have a quadratic equation where t +# is the variable, the coefficients of that equation are: +a = t_vCc * t_vBr - t_vBc * t_vCr +b = -Bc * t_vCr - Cr * t_vBc + Br * t_vCc + Cc * t_vBr +c = Br * Cc - Cr * Bc + +discriminant = b^2 - 4a * c +d = discriminant >= 0.0 ? sqrt(discriminant) : 0 +t1 = (-b - d) / 2a +t2 = (-b + d) / 2a +t1, t2, CausticsEngineering.smallest_positive((-b - d) / 2a, (-b + d) / 2a) + + +Vertex3D() + + + + +a = Vertex3D( + 489.20336199266757, + 190.09282140997482, + -58505.12856934825, + -39628.63636211195, + -50804.04679723241, +) +b = Vertex3D( + 490.30273062001396, + 189.42556748453276, + 29305.470378387537, + -10020.45529953039, + 48181.962585623834, +) +c = Vertex3D( + 489.89918140614986, + 189.67049879639754, + -18876.492207236297, + 39648.76478266787, + -65706.41461026447, +) +CausticsEngineering.find_maximum_t(a, b, c) + +a = Vertex3D(30.0, 271.0, 0.8354160335261099, -0.053188093456838725, -0.00538632666184502) +b = Vertex3D(31.0, 270.0, 0.8353725644270783, -0.005828514543554375, -0.05323156255587036) +c = Vertex3D( + 30.499999997149644, + 270.5, + 0.8886041269829487, + 0.04690021252675358, + 0.04690021225938901, +) +CausticsEngineering.find_maximum_t(a, b, c) + +ab = CausticsEngineering.dist(a, b) +ac = CausticsEngineering.dist(a, c) +cb = CausticsEngineering.dist(c, b) + +s = (ab + ac + cb) / 2.0 + +s - ab +s - ab +s - ab diff --git a/src/utilities.jl b/src/utilities.jl index 9e94e00..224f3c7 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -45,10 +45,10 @@ function area(v1::Vertex3D, v2::Vertex3D, v3::Vertex3D) c = dist(v3, v1) s = (a + b + c) / 2.0 - surface = s * (s - a) * (s - b) * (s - c) + surface = max(s * (s - a) * (s - b) * (s - c), 1 / 100.0) @assert surface >= 0.0 "Negative surface for $(v1), $(v2), $(v3)" - return sqrt(s * (s - a) * (s - b) * (s - c)) + return sqrt(surface) end @@ -262,6 +262,8 @@ Converts a triangle as a triplet of references to mesh vertices to a triplet of """ function triangle3D(mesh::FaceMesh, row::Int, col::Int, side = Union{:top,:bottom}) height, width = size(mesh) + max_distance_sq = ((height + 1) * (width + 1))^2 + if 1 <= row <= height && 1 <= col <= width if side == :top t = mesh.toptriangles[row, col] @@ -278,21 +280,21 @@ function triangle3D(mesh::FaceMesh, row::Int, col::Int, side = Union{:top,:botto ϕ1 = mesh.corners.ϕ[t1_row, t1_col] vr1 = mesh.corners.vr[t1_row, t1_col] vc1 = mesh.corners.vc[t1_row, t1_col] - @assert r1^2 + c1^2 + ϕ1^2 <= 1e12 "Coordinate $(r1), $(c1), $(ϕ1) of point #1 at $(row), $(col), side = $(side) makes no sense " + @assert r1^2 + c1^2 <= max_distance_sq "Coordinate $(r1), $(c1), $(ϕ1) of point #1 at $(row), $(col), side = $(side) makes no sense " r2 = mesh.corners.r[t2_row, t2_col] c2 = mesh.corners.c[t2_row, t2_col] ϕ2 = mesh.corners.ϕ[t2_row, t2_col] vr2 = mesh.corners.vr[t2_row, t2_col] vc2 = mesh.corners.vc[t2_row, t2_col] - @assert r2^2 + c2^2 + ϕ2^2 <= 1e12 "Coordinate $(r2), $(c2), $(ϕ2) of point #2 at $(row), $(col), side = $(side) makes no sense " + @assert r2^2 + c2^2 <= max_distance_sq "Coordinate $(r2), $(c2), $(ϕ2) of point #2 at $(row), $(col), side = $(side) makes no sense " r3 = mesh.corners.r[t3_row, t3_col] c3 = mesh.corners.c[t3_row, t3_col] ϕ3 = mesh.corners.ϕ[t3_row, t3_col] vr3 = mesh.corners.vr[t3_row, t3_col] vc3 = mesh.corners.vc[t3_row, t3_col] - @assert r3^2 + c3^2 + ϕ3^2 <= 1e12 "Coordinate $(r3), $(c3), $(ϕ3) of point #3 at $(row), $(col), side = $(side) makes no sense " + @assert r3^2 + c3^2 <= max_distance_sq "Coordinate $(r3), $(c3), $(ϕ3) of point #3 at $(row), $(col), side = $(side) makes no sense " p1 = Vertex3D(r1, c1, ϕ1, vr1, vc1) p2 = Vertex3D(r2, c2, ϕ2, vr2, vc2) @@ -368,4 +370,10 @@ end average_absolute(m::AbstractMatrix) = (sum(abs.(m)) / length(m)) < 1e10 -smallest_positive(x1::Float64, x2::Float64) = min(max(x1, 0, 0), max(x2, 0.0)) +function smallest_positive(x1::Float64, x2::Float64) + x1 < 0.0 && x2 < 0.0 && return -1.0 + x1 >= 0.0 && x2 < 0.0 && return x1 + x1 < 0.0 && x2 >= 0.0 && return x2 + x1 >= 0.0 && x2 >= 0.0 && return min(x1, x2) + return -1.0 +end From 80409c48427d1f9024684fc6da09761dbc5bec75 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Fri, 10 Sep 2021 00:15:20 +0200 Subject: [PATCH 19/58] Refactoring. Snapshot 13 --- src/create_mesh.jl | 161 ++++++++++++++++++++++++++------------------- src/plots.jl | 18 ++--- 2 files changed, 99 insertions(+), 80 deletions(-) diff --git a/src/create_mesh.jl b/src/create_mesh.jl index 83aed5f..51ff467 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -21,21 +21,29 @@ function engineer_caustics(source_image) ) # The energy going through the lens is equal to the amount of energy on the caustics - total_energy_lens = height * width * 1 # 1 unit of energy per corner + total_energy_lens = height * width * 1 # 1 unit of energy per pixel total_energy_caustics = sum(imageBW) - correction_ratio = (width * height) / sum(imageBW) + correction_ratio = sum(imageBW) / (width * height) # imageBW is `grid_definition x grid_definition` and is normalised to the same (sort of) _energy_ as the # original image. - imageBW = imageBW .* correction_ratio + imageBW = imageBW ./ correction_ratio + # start_max_update has no particular meeting. + # It is basically the initial max_update. But then is used to initialise other variables so that + # not to stop the `while` loop on the first iteration start_max_update = 1_000.0 max_update = start_max_update old_max_update = 2 * start_max_update iteration_count = 0 - # while 1e-6 < abs(max_update) < start_max_update + 1 && abs((max_update - old_max_update) / old_max_update) > 0.01 - while iteration_count < 1_024 + while ( + 1e-6 < abs(max_update) < start_max_update + 1 && + abs((max_update - old_max_update) / old_max_update) > 0.01 && + iteration_count < 1_024 + ) + # while iteration_count < 1_024 + iteration_count += 1 println( @@ -95,7 +103,6 @@ function solve_velocity_potential!(mesh, image, suffix) """ - # Positive error => the triangle needs to shrink (less light) error_luminosity = Float64.(area_distorted_corners - image) @assert average_absolute(error_luminosity) """ @@ -106,25 +113,34 @@ function solve_velocity_potential!(mesh, image, suffix) """ # Save the loss image as a png - plot_loss!(error_luminosity, suffix, image) + println("Loss:") + println("\tMinimum loss: $(minimum(error_luminosity))") + println("\tMaximum loss: $(maximum(error_luminosity))") + plot_scalar_field!(error_luminosity, suffix * "_loss", image) # For the purpose of Poisson, we need to divergence to increase towards the inside: negative divergence for high luminosity # error_luminosity = -error_luminosity - mesh_r = copy(mesh.corners.r) mesh_c = copy(mesh.corners.c) mesh_ϕ = copy(mesh.corners.ϕ) height, width = size(mesh.corners.ϕ) + # start_max_update has no particular meeting. + # It is basically the initial max_update. But then is used to initialise other variables so that + # not to stop the `while` loop on the first iteration start_max_update = 1_000.0 max_update = start_max_update old_max_update = 2 * start_max_update iteration_count = 0 new_divergence = 0.0 - # while 1e-6 < abs(max_update) < start_max_update + 1 && abs((max_update - old_max_update) / old_max_update) > 0.01 - # while sum(abs.(mesh.corners.ϕ - mesh_ϕ)) / (height * width) < 100 - while new_divergence < 20.0 + while ( + 1e-6 < abs(max_update) < start_max_update + 1 && + abs((max_update - old_max_update) / old_max_update) > 0.01 && + new_divergence < 20.0 + ) + + # while sum(abs.(mesh.corners.ϕ - mesh_ϕ)) / (height * width) < 100 iteration_count += 1 iteration_count % 100 == 0 && println("Converging for intensity: $(max_update)") @@ -141,7 +157,7 @@ function solve_velocity_potential!(mesh, image, suffix) ) # Solve the Poisson equation where the divergence of the gradient of ϕ is equal to the luminosity loss. - ϕ, max_update = gradient_descent(mesh.corners.ϕ, error_luminosity) + ϕ, max_update = propagate_poisson(mesh.corners.ϕ, error_luminosity) mesh.corners.ϕ[:, :] .= ϕ[:, :] @assert average_absolute(mesh.corners.ϕ) """ @@ -179,7 +195,7 @@ function solve_velocity_potential!(mesh, image, suffix) max ϕ divergence = $(maximum(abs.(mesh.corners.ϕ[begin+1:end, begin:end-1] .- mesh_ϕ[begin:end-1, begin:end-1] .+ mesh.corners.ϕ[begin:end-1, begin+1:end] .- mesh_ϕ[begin:end-1, begin:end-1]))) - """, + """, ) # Now we need to march the x,y locations in our mesh according to this gradient! @@ -213,8 +229,6 @@ function solve_velocity_potential!(mesh, image, suffix) end - - """ $(SIGNATURES) """ @@ -264,7 +278,7 @@ function move_horizontally( max/min = $(maximum(divergence_direction)) / $(minimum(divergence_direction)) """ - corner_heights, max_update = gradient_descent(corner_heights, -divergence_direction) + corner_heights, max_update = propagate_poisson(corner_heights, -divergence_direction) @assert average_absolute(corner_heights) """ @@ -300,57 +314,78 @@ end $(SIGNATURES) This function implements successive over relaxation for a matrix and its associated error matrix -There is a hardcoded assumption of Neumann boundary conditions--that the derivative across the +There is a hardcoded assumption of Neumann boundary conditions -- that the derivative across the boundary must be zero in all cases. See: https://math.stackexchange.com/questions/3790299/how-to-iteratively-solve-poissons-equation-with-no-boundary-conditions -- ϕ is the potential to solve subject to the Poisson equation and is the same size as the corners (posts) -- target is ∇²ϕ and is of the size of the pixels (fences) +- ϕ is the potential to be solved subject to the Poisson equation and is the same size as the corners (posts) +- target is ∇ϕ and is of the size of the pixels (fences) + +In order of how to think about the flow of the program: + +- High ∇ϕ (intensity loss function for the velocity potential) means that the triangles are too bright +- High brightness => triangle are too wide: a wide triangle collects a large amount of light and focuses is + onto a signle pixel of the caustics. +- Too wide => need velocity towards the centroid of the triangle to bring its corners closer and decrease its + surface. +- Velocity toward the centre => divergence of the velocities should be negative. That is ∇²ϕ < 0. +- The higher ∇ϕ (the actual loss given a particular target caustics), the lower ∇²ϕ (of the current estimated ϕ) + should be. + +In order to reduce the error, the error informs how to change the estimated ϕ. + +- +δ > 0 => divergence of ϕ needs to increase + """ -function gradient_descent(ϕ::Matrix{Float64}, ∇ϕ::Matrix{Float64}) +function propagate_poisson(ϕ::Matrix{Float64}, ∇²ϕ::Matrix{Float64}) # Ensure that border conditions are as they should - fill_borders!(∇ϕ, 0.0) + fill_borders!(∇²ϕ, 0.0) # fill_borders!(ϕ, 0.0) @assert average_absolute(ϕ) """ Relaxation: ϕ values seem too large - max/min ∇ϕ = $(maximum(∇ϕ)) / $(minimum(∇ϕ)) + max/min ∇ϕ = $(maximum(∇²ϕ)) / $(minimum(∇²ϕ)) max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) """ - @assert average_absolute(∇ϕ) """ + @assert average_absolute(∇²ϕ) """ Relaxation: ∇²ϕ values seem too large - max/min ∇ϕ = $(maximum(∇ϕ)) / $(minimum(∇ϕ)) + max/min ∇²ϕ = $(maximum(∇²ϕ)) / $(minimum(∇²ϕ)) max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) """ - @assert any(isnan.(ϕ)) == false "Relaxation: calling with a ϕ that contains NaN!!" - @assert any(isnan.(∇ϕ)) == false "Relaxation: calling with a ∇ϕ that contains NaN!!" + @assert any(isnan.(ϕ)) == false "Relaxation: calling with a ϕ that contains NaN!!" + @assert any(isnan.(∇²ϕ)) == false "Relaxation: calling with a ∇²ϕ that contains NaN!!" # ϕ is of the same size as corners = number of corners + 1 height_corners, width_corners = size(ϕ) - height_pixels, width_pixels = size(∇ϕ) + height_pixels, width_pixels = size(∇²ϕ) + + # From the velocity potential field ϕ, we calculate its gradient (the velocity), then its divergence. + # This is then compared to the intensity loss + # Laplacian # Embed matrix within a larger matrix for better vectorization and avoid duplicated code - # Size of ϕ/corner is h, w. Padded matrix adds 1 row/col after + # Padded matrix adds 1 row/col after the size of ϕ. # ϕ is inserted in padded matrix within 1:height_corners+1 x 1:width_corners+1. - # The rest of the padded matrix (the borders) are set at 0.0. + # The rest of the padded matrix (its borders) are set at 0.0. padded_ϕ = zeros(Float64, height_corners + 1, width_corners + 1) padded_ϕ[1:height_corners, 1:width_corners] .= ϕ # Those values are all of ϕ's size and represent the _flow_ in each direction - flow_up = zeros(Float64, size(∇ϕ)) - flow_down = zeros(Float64, size(∇ϕ)) - flow_left = zeros(Float64, size(∇ϕ)) - flow_right = zeros(Float64, size(∇ϕ)) + flow_up = zeros(Float64, size(∇²ϕ)) + flow_down = zeros(Float64, size(∇²ϕ)) + flow_left = zeros(Float64, size(∇²ϕ)) + flow_right = zeros(Float64, size(∇²ϕ)) flow_up[1:end, 1:end] .= padded_ϕ[1:end-2, 2:end-1] - padded_ϕ[2:end-1, 2:end-1] flow_down[1:end, 1:end] .= padded_ϕ[3:end, 2:end-1] - padded_ϕ[2:end-1, 2:end-1] @@ -362,20 +397,21 @@ function gradient_descent(ϕ::Matrix{Float64}, ∇ϕ::Matrix{Float64}) fill_borders!(flow_left, 0.0) fill_borders!(flow_right, 0.0) - # Target position. The target is the current height map smoothed by averaging to which the - # flow is added. + # Target position. The target is the current height map smoothed by averaging to which the flow is added. # This has to converge towards the ∇ϕ. Difference to calculate speed of the descent. - # δ = (flow_up + flow_down + flow_left + flow_right) + ∇ϕ + # δ = (flow_up + flow_down + flow_left + flow_right) + ∇²ϕ - # δ is the difference between the desired divergence and the current one - # High ∇ϕ means that the triangles are too bright. - δ = ∇ϕ - (flow_up + flow_down + flow_left + flow_right) + # δ is the difference between the divergence of the intensity loss (in the case of the velocity potential) + # and the current one for the current field ϕ (divergence of its gradient). + # + # High intensity loss ∇ϕ means that the triangles are too bright, too large. + δ = ∇²ϕ - (flow_up + flow_down + flow_left + flow_right) @assert average_absolute(δ) """ - Relaxation: ∇ϕ_error as (current - target) seem too large - max/min target ∇ϕ = $(maximum(∇ϕ)) / $(minimum(∇ϕ)) - max/min ∇ϕ_error = $(maximum(δ)) / $(minimum(δ)) + Relaxation: ∇²ϕ_error as (current - target) seem too large + max/min target ∇²ϕ = $(maximum(∇²ϕ)) / $(minimum(∇²ϕ)) + max/min ∇²ϕ_error = $(maximum(δ)) / $(minimum(δ)) max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) max/min padded_ϕ = $(maximum(padded_ϕ)) / $(minimum(padded_ϕ)) @@ -386,11 +422,11 @@ function gradient_descent(ϕ::Matrix{Float64}, ∇ϕ::Matrix{Float64}) """ - # @. target_map[height_div, width_div] += ∇ϕ / 4.0 - # fill_borders!(∇ϕ_error, 0.0) + # @. target_map[height_div, width_div] += ∇²ϕ / 4.0 + # fill_borders!(∇²ϕ_error, 0.0) # Let the heightmap converge towards the target at a slow rate = gradient descent. - # @. ϕ += 0.2 * ∇ϕ_error + # @. ϕ += 0.2 * ∇²ϕ_error maximum_δ = maximum(abs.(δ)) max_correction_ratio = 2.0 @@ -401,15 +437,6 @@ function gradient_descent(ϕ::Matrix{Float64}, ∇ϕ::Matrix{Float64}) correction_ratio = max_correction_ratio / maximum_δ end - # High ∇ϕ (loss function) means that the triangles are too bright - # High brightness => triangle are too wide - # Too wide => need velocity towards the centre - # Velocity toward the centre => divergence should be negative - - # Negative divergence means that the field should increase towards the inside - - # δ > 0 => divergence of ϕ needs to increase - # Increase @. ϕ[1:height_pixels, 1:width_pixels] += correction_ratio * δ[1:height_pixels, 1:width_pixels] @@ -448,29 +475,25 @@ end """ $(SIGNATURES) """ -function quantify_loss(D, suffix, img) - println("Loss:") - println("\tMinimum loss: $(minimum(D))") - println("\tMaximum loss: $(maximum(D))") - - normalised_D_max = D ./ maximum(D) - normalised_D_min = D ./ minimum(D) +function plot_scalar_field(scalar_field, suffix, img) + normalised_D_max = scalar_field ./ maximum(scalar_field) + normalised_D_min = scalar_field ./ minimum(scalar_field) - blue = zeros(size(D)) - blue[D.>0] = normalised_D_max[D.>0] - red = zeros(size(D)) - red[D.<0] = -normalised_D_min[D.<0] - green = zeros(size(D)) + blue = zeros(size(scalar_field)) + blue[scalar_field.>0] = normalised_D_max[scalar_field.>0] + red = zeros(size(scalar_field)) + red[scalar_field.<0] = -normalised_D_min[scalar_field.<0] + green = zeros(size(scalar_field)) rgbImg = RGB.(red, green, blue)' - save("./examples/loss_$(suffix).png", map(clamp01nan, rgbImg)) + save("./examples/$(suffix)_loss.png", map(clamp01nan, rgbImg)) println("Saving output image:") println(typeof(img)) - E = Gray.(D) + E = Gray.(scalar_field) println(typeof(E)) outputImg = img - E - save("./examples/actual_$(suffix).png", outputImg) + save("./examples/$(suffix)_actual.png", outputImg) end diff --git a/src/plots.jl b/src/plots.jl index fc4b27c..1846527 100644 --- a/src/plots.jl +++ b/src/plots.jl @@ -120,19 +120,15 @@ end """ $(SIGNATURES) """ -function plot_loss!(D, suffix, img) - println("Loss:") - println("\tMinimum loss: $(minimum(D))") - println("\tMaximum loss: $(maximum(D))") - - blue = zeros(size(D)) - blue[D.>0] = D[D.>0] - red = zeros(size(D)) - red[D.<0] = -D[D.<0] - green = zeros(size(D)) +function plot_scalar_field!(field, filename, img) + blue = zeros(size(field)) + blue[field.>0] = field[field.>0] + red = zeros(size(field)) + red[field.<0] = -field[field.<0] + green = zeros(size(field)) rgbImg = RGB.(red, green, blue)' - save("./examples/loss_$(suffix).png", map(clamp01nan, rgbImg)) + save("./examples/$(filename).png", map(clamp01nan, rgbImg)) # println("Saving output image:") # println(typeof(img)) From a85c0485bfb7af5c241ff22fab5f3a66303ee32c Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Fri, 10 Sep 2021 15:55:29 +0200 Subject: [PATCH 20/58] Refactoring. Snapshot 14 --- .gitignore | 1 + src/CausticsEngineering.jl | 5 +- src/create_mesh.jl | 393 ++++--------------------------------- src/io.jl | 53 +++++ src/math_utilities.jl | 47 +++++ src/mesh.jl | 260 ++++++++++++++++++++++++ src/plots.jl | 26 +++ src/scratchpad.jl | 56 ++++++ src/utilities.jl | 74 +++---- 9 files changed, 521 insertions(+), 394 deletions(-) create mode 100644 src/math_utilities.jl create mode 100644 src/mesh.jl diff --git a/.gitignore b/.gitignore index 5376b6d..3ab70c5 100644 --- a/.gitignore +++ b/.gitignore @@ -6,6 +6,7 @@ *.jl.*.cov *.obj +it*.png loss*.png diff --git a/src/CausticsEngineering.jl b/src/CausticsEngineering.jl index 58fd949..7b8ef6d 100644 --- a/src/CausticsEngineering.jl +++ b/src/CausticsEngineering.jl @@ -8,6 +8,8 @@ gr() include("parameters.jl") include("utilities.jl") +include("math_utilities.jl") +include("mesh.jl") include("io.jl") include("plots.jl") @@ -25,6 +27,7 @@ function main() return engineer_caustics(img) end -export Vertex3D, FieldVertex3D, FaceMesh, main, engineer_caustics +export Meters_Per_Pixel, + Vertex3D, FieldVertex3D, FaceMesh, main, engineer_caustics, create_solid end # End module diff --git a/src/create_mesh.jl b/src/create_mesh.jl index 51ff467..19d4864 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -11,14 +11,6 @@ function engineer_caustics(source_image) # cover each image corner with a triangle. mesh = FaceMesh(height, width) # println("Mesh creation: ") - r_check = 256 - c_check = 256 - println( - "\tCoordinates: $(mesh.corners.r[r_check, c_check]) , $(mesh.corners.c[r_check, c_check]) , $(mesh.corners.ϕ[r_check, c_check])", - ) - println( - "\tVelocities: $(mesh.corners.vr[r_check, c_check]) , $(mesh.corners.vc[r_check, c_check])", - ) # The energy going through the lens is equal to the amount of energy on the caustics total_energy_lens = height * width * 1 # 1 unit of energy per pixel @@ -42,8 +34,6 @@ function engineer_caustics(source_image) abs((max_update - old_max_update) / old_max_update) > 0.01 && iteration_count < 1_024 ) - # while iteration_count < 1_024 - iteration_count += 1 println( @@ -53,13 +43,6 @@ function engineer_caustics(source_image) old_max_update = max_update max_update = solve_velocity_potential!(mesh, imageBW, "it$(iteration_count)") print("Vertical move max update = $(max_update) \n") - - # println( - # "\tCoordinates: $(mesh.corners.r[r_check, c_check]) , $(mesh.corners.c[r_check, c_check]) , $(mesh.corners.ϕ[r_check, c_check])", - # ) - # println( - # "\tVelocities: $(mesh.corners.vr[r_check, c_check]) , $(mesh.corners.vc[r_check, c_check])", - # ) end println("\nSTARTING HORIZONTAL ITERATION ---") @@ -67,19 +50,6 @@ function engineer_caustics(source_image) mesh.corners.ϕ .= ϕ println(" max update = $(max_update)") - - - println("$(mesh.corners.vr[r_check, c_check]) , $(mesh.corners.vc[r_check, c_check])") - - - # solidMesh = create_solid(mesh) - # save_stl!( - # solidMesh, - # "./examples/original_image.obj", - # scale = Float64(1 / Grid_Definition * Artifact_Size), - # scaleh = Float64(1 / Grid_Definition * Artifact_Size), - # ) - return mesh, imageBW end @@ -156,7 +126,8 @@ function solve_velocity_potential!(mesh, image, suffix) """, ) - # Solve the Poisson equation where the divergence of the gradient of ϕ is equal to the luminosity loss. + # Solve the Poisson equation where the divergence of the gradient of ϕ is equal to the luminosity error. + # High error => Too much luminosity. ϕ, max_update = propagate_poisson(mesh.corners.ϕ, error_luminosity) mesh.corners.ϕ[:, :] .= ϕ[:, :] @@ -278,35 +249,18 @@ function move_horizontally( max/min = $(maximum(divergence_direction)) / $(minimum(divergence_direction)) """ - corner_heights, max_update = propagate_poisson(corner_heights, -divergence_direction) + true_H, max_update = propagate_poisson(true_H, -divergence_direction) - @assert average_absolute(corner_heights) """ + @assert average_absolute(true_H) """ ALERT: horiz. Δ corner_heights is too large - max/min corner_heights = $(maximum(corner_heights)) / $(minimum(corner_heights)) + max/min corner_heights = $(maximum(true_H)) / $(minimum(true_H)) """ - println( - "Convergence horiz. Δ stopped improving at step $(iteration_count) ", - "with max_update of $(max_update)", - ) - - - # println(""" - # Convergence stopped at step $(iteration_count) with - # max_update = $(max_update) - # max/min area_distorted_corners = $(maximum(area_distorted_corners)) / $(minimum(area_distorted_corners)) - # max error_luminosity = $(maximum(abs.(error_luminosity))) - - # Average mesh changes on row = $(sum(abs.(mesh.corners.r - mesh_r)) / (height * width)) -- CHECK == 0.0 - # Average mesh changes on col = $(sum(abs.(mesh.corners.c - mesh_c)) / (height * width)) -- CHECK == 0.0 - # Average mesh changes on ϕ = $(sum(abs.(mesh.corners.ϕ - mesh_ϕ)) / (height * width)) - - # """ - # ) + println("Convergence horiz. Δ stopped with max_update of $(max_update)") # saveObj(matrix_to_mesh(h / 10), "./examples/heightmap.obj") - return corner_heights, max_update + return true_H, max_update end @@ -343,8 +297,6 @@ function propagate_poisson(ϕ::Matrix{Float64}, ∇²ϕ::Matrix{Float64}) # Ensure that border conditions are as they should fill_borders!(∇²ϕ, 0.0) - # fill_borders!(ϕ, 0.0) - @assert average_absolute(ϕ) """ Relaxation: ϕ values seem too large @@ -373,63 +325,36 @@ function propagate_poisson(ϕ::Matrix{Float64}, ∇²ϕ::Matrix{Float64}) # Laplacian + # Those values are all of ϕ's size and represent the second order approximation of the + # Laplacian of ϕ. + Lϕ = laplacian(ϕ) + @assert average_absolute(Lϕ) """ - # Embed matrix within a larger matrix for better vectorization and avoid duplicated code - # Padded matrix adds 1 row/col after the size of ϕ. - # ϕ is inserted in padded matrix within 1:height_corners+1 x 1:width_corners+1. - # The rest of the padded matrix (its borders) are set at 0.0. - padded_ϕ = zeros(Float64, height_corners + 1, width_corners + 1) - padded_ϕ[1:height_corners, 1:width_corners] .= ϕ - - # Those values are all of ϕ's size and represent the _flow_ in each direction - flow_up = zeros(Float64, size(∇²ϕ)) - flow_down = zeros(Float64, size(∇²ϕ)) - flow_left = zeros(Float64, size(∇²ϕ)) - flow_right = zeros(Float64, size(∇²ϕ)) - - flow_up[1:end, 1:end] .= padded_ϕ[1:end-2, 2:end-1] - padded_ϕ[2:end-1, 2:end-1] - flow_down[1:end, 1:end] .= padded_ϕ[3:end, 2:end-1] - padded_ϕ[2:end-1, 2:end-1] - flow_left[1:end, 1:end] .= padded_ϕ[2:end-1, 1:end-2] - padded_ϕ[2:end-1, 2:end-1] - flow_right[1:end, 1:end] .= padded_ϕ[2:end-1, 3:end] - padded_ϕ[2:end-1, 2:end-1] - - fill_borders!(flow_up, 0.0) - fill_borders!(flow_down, 0.0) - fill_borders!(flow_left, 0.0) - fill_borders!(flow_right, 0.0) - - # Target position. The target is the current height map smoothed by averaging to which the flow is added. - # This has to converge towards the ∇ϕ. Difference to calculate speed of the descent. - # δ = (flow_up + flow_down + flow_left + flow_right) + ∇²ϕ + Relaxation: Laplacian of ϕ a seem too large + max/min target Lϕ = $(maximum(Lϕ)) / $(minimum(Lϕ)) + max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) + + """ # δ is the difference between the divergence of the intensity loss (in the case of the velocity potential) # and the current one for the current field ϕ (divergence of its gradient). # - # High intensity loss ∇ϕ means that the triangles are too bright, too large. - δ = ∇²ϕ - (flow_up + flow_down + flow_left + flow_right) - + # High intensity loss ∇²ϕ means that the triangles are too bright, too large. + # This has to converge towards the ∇²ϕ. Difference to calculate speed of the descent. + δ = Lϕ - ∇²ϕ @assert average_absolute(δ) """ - Relaxation: ∇²ϕ_error as (current - target) seem too large - max/min target ∇²ϕ = $(maximum(∇²ϕ)) / $(minimum(∇²ϕ)) - max/min ∇²ϕ_error = $(maximum(δ)) / $(minimum(δ)) - + Relaxation: difference between intensity loss and estimated Laplacian seem too large + max/min δ = $(maximum(δ)) / $(minimum(δ)) + max/min target Lϕ = $(maximum(Lϕ)) / $(minimum(Lϕ)) max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) - max/min padded_ϕ = $(maximum(padded_ϕ)) / $(minimum(padded_ϕ)) - max/min flow_up = $(maximum(flow_up)) / $(minimum(flow_up)) - max/min flow_down = $(maximum(flow_down)) / $(minimum(flow_down)) - max/min flow_left = $(maximum(flow_left)) / $(minimum(flow_left)) - max/min flow_right = $(maximum(flow_right)) / $(minimum(flow_right)) """ - # @. target_map[height_div, width_div] += ∇²ϕ / 4.0 - # fill_borders!(∇²ϕ_error, 0.0) - - # Let the heightmap converge towards the target at a slow rate = gradient descent. - # @. ϕ += 0.2 * ∇²ϕ_error - maximum_δ = maximum(abs.(δ)) - max_correction_ratio = 2.0 + + # We limit the changes of the potential to a maximum + max_correction_ratio = 10.0 if 1.94 / 4.0 * maximum_δ < max_correction_ratio correction_ratio = 1.94 / 4.0 @@ -437,7 +362,12 @@ function propagate_poisson(ϕ::Matrix{Float64}, ∇²ϕ::Matrix{Float64}) correction_ratio = max_correction_ratio / maximum_δ end - # Increase + # if δ > 0, the intensity loss is too high, or the Laplacian is too high at that point. + # => increase flow towards outside + # => decrease the flow towards the inside. + # => increase divergence of the flow + # => increase the height of the potential there so that gradient are locally increasing + # => correction has to be of the same sign as δ. @. ϕ[1:height_pixels, 1:width_pixels] += correction_ratio * δ[1:height_pixels, 1:width_pixels] @assert !any(isnan.(ϕ)) "Relaxation: Updated ϕ contains NaN!!" @@ -448,111 +378,6 @@ function propagate_poisson(ϕ::Matrix{Float64}, ∇²ϕ::Matrix{Float64}) end -""" -$(SIGNATURES) - -A Mesh is a collection of triangles. The brightness flowing through a given triangle is just proportional to its -area in the x, y plane. h is ignored. - -The function returns a matrix with the quantity of light coming from each 'rectangle' around a corner. That 'rectangle' -has been shifted and flexed around. -""" -function get_area_corners(mesh::FaceMesh) - height, width = size(mesh) - - top_tri_area = - [area(triangle3D(mesh, row, col, :top)...) for row ∈ 1:height, col ∈ 1:width] - @assert !any(isnan.(top_tri_area)) "get_area_corners: NaN area in top triangles." - - bot_tri_area = - [area(triangle3D(mesh, row, col, :bottom)...) for row ∈ 1:height, col ∈ 1:width] - @assert !any(isnan.(top_tri_area)) "get_area_corners: NaN area in bottom triangles." - - return top_tri_area + bot_tri_area -end - - -""" -$(SIGNATURES) -""" -function plot_scalar_field(scalar_field, suffix, img) - normalised_D_max = scalar_field ./ maximum(scalar_field) - normalised_D_min = scalar_field ./ minimum(scalar_field) - - blue = zeros(size(scalar_field)) - blue[scalar_field.>0] = normalised_D_max[scalar_field.>0] - red = zeros(size(scalar_field)) - red[scalar_field.<0] = -normalised_D_min[scalar_field.<0] - green = zeros(size(scalar_field)) - - rgbImg = RGB.(red, green, blue)' - save("./examples/$(suffix)_loss.png", map(clamp01nan, rgbImg)) - - println("Saving output image:") - println(typeof(img)) - E = Gray.(scalar_field) - println(typeof(E)) - outputImg = img - E - save("./examples/$(suffix)_actual.png", outputImg) -end - - - - -""" -$(SIGNATURES) - -Given 3 points and their velocities, calculate the time `t` required to bring the area of that triangle to zero -""" -function find_maximum_t(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) - # Three points A, B and C, with coordinates (x, y) - # The area of a triangle is 1/2 * [ Ax (By - Cy) + Bx (Cy - Ay) + Cx (Ay - By)] - # where each point of the triangle is where it will be after time t - # i.e. a point goes from P to P+tV where V is the velocity of that point. - # Notation is here B -> B + t_vB - - # To make the calculation simpler, everything is translated so that A is at the - # origin of the plane and its velocity is nil. - Br = p2.r - p1.r - Bc = p2.c - p1.c - Cr = p3.r - p1.r - Cc = p3.c - p1.c - - t_vBr = p2.vr - p1.vr - t_vBc = p2.vc - p1.vc - t_vCr = p3.vr - p1.vr - t_vCc = p3.vc - p1.vc - - # After this, given that Ar = Ac = t_vAr = t_vAc = 0, the area is nil iff - # (Br + t_vBr) (Cc + t_vCc ) - (Cr + t_vCr) (Bc + t_vBc) = 0. - # After expansion and reshuffling to have a quadratic equation where t - # is the variable, the coefficients of that equation are: - a = t_vCc * t_vBr - t_vBc * t_vCr - b = -Bc * t_vCr - Cr * t_vBc + Br * t_vCc + Cc * t_vBr - c = Br * Cc - Cr * Bc - - # if a = 0, this is just a linear equation. - if a == 0 && b != 0 - return smallest_positive(-c / b, c / b) - else - discriminant = b^2 - 4a * c - - # If there is a solution - if discriminant >= 0 - d = sqrt(discriminant) - return smallest_positive((-b - d) / 2a, (-b + d) / 2a) - end - end - # There can be no solution if, after translation, B abd C move in parallel direction. - # C will never end up on the line AB. - # Very unlikely with Float64. - # Negative numbers are filtered out when calculating the minimum jiggle ratio - return -1.0 -end - - -find_maximum_t(p::Tuple{Vertex3D,Vertex3D,Vertex3D}) = find_maximum_t(p[1], p[2], p[3]) - """ $(SIGNATURES) @@ -596,24 +421,6 @@ function march_mesh!(mesh::FaceMesh) # Get the time, at that velocity, for the area of the triangle to be nil. # We are only interested by positive values to only move in the direction of the gradient - - # list_triangles = vcat( - # [triangle3D(mesh, row, col, :top) for row ∈ 1:height-1, col ∈ 1:width-1], - # [triangle3D(mesh, row, col, :bottom) for row ∈ 1:height-1, col ∈ 1:width-1], - # ) - # list_maximum_t = [time for time ∈ find_maximum_t.(list_triangles) - # if !isnan(time) && time > 0.0 && time < 10.0] - - # if !isempty(list_maximum_t) - # min_positive_t = minimum(list_maximum_t) - - # # @assert all(typeof.(t1) .== Float64) && all(typeof.(t2) .== Float64) "March mesh: Maximum times are not numerical at $(row), $(col)" - - # δ = min_positive_t / 2.0 - # mesh.corners.r -= δ .* ∇ϕᵤ - # mesh.corners.c -= δ .* ∇ϕᵥ - # end - for row ∈ 1:height-1, col ∈ 1:width-1 list_triangles = [triangle3D(mesh, row, col, :top), triangle3D(mesh, row, col, :bottom)] @@ -629,8 +436,9 @@ function march_mesh!(mesh::FaceMesh) max_shift = max(abs(∇ϕᵤ[row, col]), abs(∇ϕᵥ[row, col])) - # No shift more than 0.5 pixels - δ = min(min_positive_t / 2.0, 5.0 / max_shift) + # No shift more than 20 pixels + max_pixel_move = 20.0 + δ = min(min_positive_t / 2.0, max_pixel_move / max_shift) mesh.corners.r[row, col] = clamp(mesh.corners.r[row, col] + δ * ∇ϕᵤ[row, col], 1, height - 1) mesh.corners.c[row, col] = @@ -642,9 +450,6 @@ function march_mesh!(mesh::FaceMesh) # Reset the border at the fixed values fixed coordinates. reset_border_values!(mesh.corners) - # δ = $(δ) - # first minimum ts: $(list_maximum_t[1:5]) - println( """ March mesh: @@ -656,11 +461,6 @@ function march_mesh!(mesh::FaceMesh) """, ) - # println("Overall maximum variations:") - # println("\tOverall min_positive_t: $(min_positive_t)") - # println("\tOverall max_negative_t: $(max_negative_t)") - # println("\tUsing δ: $(δ)") - # saveObj(mesh, "gateau.obj") end @@ -680,128 +480,3 @@ function ∇(ϕ::Matrix{Float64}) return ∇ϕᵤ, ∇ϕᵥ end - - -""" -$(SIGNATURES) - -This function will take a `grid_definition x grid_definition` matrix and returns a -`grid_definition x grid_definition` mesh. - -""" -function matrix_to_mesh(ϕ::Matrix{Float64}) - height, width = size(ϕ) - - mesh = FaceMesh(height, width) - - # 1 more corner than corners! Therefore compiler needs to specify exact indices. - mesh.corners.ϕ[1:height, 1:width] .= ϕ[1:height, 1:width] - - # The borders' height is forced at 0. - reset_border_values!(mesh.corners) - - return mesh -end - - -""" -$(SIGNATURES) - -TO REFACTOR. -""" -function create_solid( - mesh::FaceMesh; - bottom_offset = Bottom_Offset / Meters_Per_Pixel, - top_offset = Top_Offset / Meters_Per_Pixel, -) - height, width = size(mesh) - - - ### - ### Top mesh - ### - # List top mesh top triangles - list_triangles_top_top = [top_triangles(mesh, r, c) for r ∈ 1:height, c ∈ 1:width] - - # List top mesh bottom triangles - list_triangles_top_bottom = [bottom_triangle(mesh, r, c) for r ∈ 1:height, c ∈ 1:width] - - - ### - ### Botttom mesh - ### - # Build the bottom surface which is prepopulated by its constructor. However, its height is incorrect. - - # Coordinates on the caustics - rows = repeat(Float64.(1:height), 1, width) - cols = repeat(Float64.(1:width)', height, 1) - - bottom_mesh = FaceMesh(height, width) - bottom_mesh.corner.r[:] .= rows[:] - bottom_mesh.corner.c[:] .= cols[:] - bottom_mesh.corner.ϕ[:] .= -Bottom_Offset - bottom_mesh.corner.vr[:] .= 0.0 - bottom_mesh.corner.vr[:] .= 0.0 - - - ### - ### Side meshes - ### - # Build triangles to create side meshes and close the mesh - # The mesh is made of a single top/bottom triangles joining the bottom face - # and the top face. - - # (Looking from above), left side. - - list_triangles = [] - col = 1 - for row = 1:height - count += 1 - - ll = (row - 1) * width + col - ul = ll + totalNodes / 2 - lr = row * width + col - ur = lr + totalNodes / 2 - triangles[2*count-1] = Triangle(ll, ul, ur) - triangles[2*count] = Triangle(ur, lr, ll) - end - - mesh_right = FaceMesh(height, 1) - for row = 1:(height-1) - count += 1 - - ll = (row - 1) * width + col - ul = ll + totalNodes / 2 - lr = row * width + col - ur = lr + totalNodes / 2 - triangles[2*count-1] = Triangle(ll, ur, ul) - triangles[2*count] = Triangle(ur, ll, lr) - end - - mesh_up = FaceMesh(1, width) - row = 1 - for col = 2:width - count += 1 - - ll = (row - 1) * width + col - ul = ll + totalNodes / 2 - lr = (row - 1) * width + (col - 1) - ur = lr + totalNodes / 2 - triangles[2*count-1] = Triangle(ll, ul, ur) - triangles[2*count] = Triangle(ur, lr, ll) - end - - mesh_down = FaceMesh(1, width) - for col = 2:width - count += 1 - - ll = (row - 1) * width + col - ul = ll + totalNodes / 2 - lr = (row - 1) * width + (col - 1) - ur = lr + totalNodes / 2 - triangles[2*count-1] = Triangle(ll, ur, ul) - triangles[2*count] = Triangle(ur, ll, lr) - end - - return RectangleMesh(nodeList, nodeArrarowBottom, triangles, width, height) -end diff --git a/src/io.jl b/src/io.jl index dc33af4..90e4fdd 100644 --- a/src/io.jl +++ b/src/io.jl @@ -1,6 +1,15 @@ using FileIO, MeshIO +# Utility function to name a vertex +vertex_name(face::String, row::Int64, col::Int64)::String = "Vertex_$(name)_$(row)_$(col)" + +# Utility functions to create the names +triangle_name(face::String, row::Int64, col::Int64, side::Union{Symbol,Symbol})::String = + "Tri_$(face)_$(row)_$(col)_$(side)" + + + """ $(SIGNATURES) @@ -75,6 +84,50 @@ function save_stl!( end +""" +$(SIGNATURES) + +""" +function save_stl!( + triangle_index::AbstractDict{}, + vertex_index::AbstractDict{}, + filename::String; + scale = 1.0, + scaleh = 1.0, + reverse = false, + flipxy = false, +) + + open(filename, "w") do io + println(io, "solid engineered_caustics") + + for i ∈ 1:length(vertex_index) + if flipxy + println( + io, + "v $(vertex_index[2] * scale) $(vertex_index[1] * scale) $(vertex_index[3] * scaleh)", + ) + else + println( + io, + "v $(vertex_index[1] * scale) $(vertex_index[2] * scale) $(vertex_index[3] * scaleh)", + ) + end + end + + for i ∈ 1:length(triangle_index) + println( + io, + "f $(triangle_index[i][1]) $(triangle_index[i][2]) $(triangle_index[i][3])", + ) + end + + println(io, "endsolid engineered_caustics") + end +end + + + """ $(SIGNATURES) diff --git a/src/math_utilities.jl b/src/math_utilities.jl new file mode 100644 index 0000000..53bf16e --- /dev/null +++ b/src/math_utilities.jl @@ -0,0 +1,47 @@ +""" +$(SIGNATURES) +""" +average_absolute(m::AbstractMatrix) = (sum(abs.(m)) / length(m)) < 1e10 + + +""" +$(SIGNATURES) +""" +function smallest_positive(x1::Float64, x2::Float64) + x1 < 0.0 && x2 < 0.0 && return -1.0 + x1 >= 0.0 && x2 < 0.0 && return x1 + x1 < 0.0 && x2 >= 0.0 && return x2 + x1 >= 0.0 && x2 >= 0.0 && return min(x1, x2) + return -1.0 +end + + +""" +$(SIGNATURES) + +Calculate the second-order Laplace operator by convolution of a kernel. +""" +function laplacian(ϕ::AbstractMatrix{Float64}) + height, width = size(ϕ) + height -= 1 + width -= 1 + + # Embed matrix within a larger matrix for better vectorization and avoid duplicated code + # Padded matrix adds 1 row/col after the size of ϕ. + # ϕ is inserted in padded matrix within 1:1+height+1 x 1:1+width+1. + # The rest of the padded matrix (its borders) are set at 0.0. + padded_ϕ = zeros(Float64, 1 + height + 1, 1 + width + 1) + padded_ϕ[2:height+1, 2:width+1] .= ϕ[1:height, 1:width] + + # The Laplace operator can be calculated by convolving a kernel. + # See https://www.wikiwand.com/en/Discrete_Laplace_operator for simple example in 2D + kernel = ([[0.0 1.0 0.0]; [1.0 -4.0 1.0]; [0.0 1.0 0.0]]) + + # Convolution + ∇²ϕ = zeros(Float64, height, width) + for row ∈ 1:height, col ∈ 1:width + ∇²ϕ[row, height] = sum(padded_ϕ[row:row+2, col:col+2] .* kernel[1:3, 1:3]) + end + + return ∇²ϕ +end diff --git a/src/mesh.jl b/src/mesh.jl new file mode 100644 index 0000000..b7cf652 --- /dev/null +++ b/src/mesh.jl @@ -0,0 +1,260 @@ +""" +$(SIGNATURES) + +Given 3 points and their velocities, calculate the time `t` required to bring the area of that triangle to zero +""" +function find_maximum_t(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) + # Three points A, B and C, with coordinates (x, y) + # The area of a triangle is 1/2 * [ Ax (By - Cy) + Bx (Cy - Ay) + Cx (Ay - By)] + # where each point of the triangle is where it will be after time t + # i.e. a point goes from P to P+tV where V is the velocity of that point. + # Notation is here B -> B + t_vB + + # To make the calculation simpler, everything is translated so that A is at the + # origin of the plane and its velocity is nil. + Br = p2.r - p1.r + Bc = p2.c - p1.c + Cr = p3.r - p1.r + Cc = p3.c - p1.c + + t_vBr = p2.vr - p1.vr + t_vBc = p2.vc - p1.vc + t_vCr = p3.vr - p1.vr + t_vCc = p3.vc - p1.vc + + # After this, given that Ar = Ac = t_vAr = t_vAc = 0, the area is nil iff + # (Br + t_vBr) (Cc + t_vCc ) - (Cr + t_vCr) (Bc + t_vBc) = 0. + # After expansion and reshuffling to have a quadratic equation where t + # is the variable, the coefficients of that equation are: + a = t_vCc * t_vBr - t_vBc * t_vCr + b = -Bc * t_vCr - Cr * t_vBc + Br * t_vCc + Cc * t_vBr + c = Br * Cc - Cr * Bc + + # if a = 0, this is just a linear equation. + if a == 0 && b != 0 + return smallest_positive(-c / b, c / b) + else + discriminant = b^2 - 4a * c + + # If there is a solution + if discriminant >= 0 + d = sqrt(discriminant) + return smallest_positive((-b - d) / 2a, (-b + d) / 2a) + end + end + # There can be no solution if, after translation, B abd C move in parallel direction. + # C will never end up on the line AB. + # Very unlikely with Float64. + # Negative numbers are filtered out when calculating the minimum jiggle ratio + return -1.0 +end + +find_maximum_t(p::Tuple{Vertex3D,Vertex3D,Vertex3D}) = find_maximum_t(p[1], p[2], p[3]) + + + + +""" +$(SIGNATURES) + +This function will take a `grid_definition x grid_definition` matrix and returns a +`grid_definition x grid_definition` mesh. + +""" +function matrix_to_mesh(ϕ::Matrix{Float64}) + height, width = size(ϕ) + + mesh = FaceMesh(height, width) + + # 1 more corner than corners! Therefore compiler needs to specify exact indices. + mesh.corners.ϕ[1:height, 1:width] .= ϕ[1:height, 1:width] + + # The borders' height is forced at 0. + reset_border_values!(mesh.corners) + + return mesh +end + + +""" +$(SIGNATURES) + +Create a mash of the solid block to be carved. +Imagining a mid-plane where the heightmap is carved, start with a block whose lower plane is +bottom_distance away and the highr plane is top_distance above. +The distances are measured in meters and converted to pixels when necessary. + +The final mesh is a vector of vertices each with an ID number and a position. + +""" +function create_solid_as_dict( + mesh::FaceMesh; + bottom_distance = Bottom_Offset, + top_distance = Top_Offset, +) + + height, width = size(mesh) + bottom_offset = bottom_distance / Meters_Per_Pixel + top_offset = top_distance / Meters_Per_Pixel + + # To do this, we use several dictionaries before saving + # Dictionary 1: Triangle to 3 strings each naming a triangle vertex. + # Dictionary 2: Named vertex to its x, y, z coordinates. + # Dictionary 3: Named vertex to a unique numerical index. + triangle_dict = Dict{String,Vector{String}}() + vertex_dict = Dict{String,Tuple{Float64,Float64,Float64}}() + + mesh_height, mesh_width = size(mesh.corners.ϕ) + for row ∈ 1:mesh_height-1, col ∈ 1:mesh_width-1 + + # Top face, add vertices, top and bottom triangles + for side ∈ [:top, :bottom] + side_name = side == :top ? "Top" : "Bottom" + t = side == :top ? mesh.toptriangles[row, col] : mesh.bottriangles[row, col] + + # Add the vertices 1 by 1 + vertices_names = ["", "", ""] + for i ∈ 1:3 + v_row, v_col = t[i] + r = mesh.corners.r[v_row, v_col] + c = mesh.corners.c[v_row, v_col] + ϕ = mesh.corners.ϕ[v_row, v_col] + name = vertex_name("Top", row, col) + vertices_names[i] = name + vertex_dict[name] = (r, c, ϕ) + end + + # Add the triangle + triangle_dict[triangle_name(side_name, row, col, side)] = vertices_names + end + + # Bottom face + v_coord_top = [(row, col), (row + 1, col), (row, col + 1)] + vertices_names_top = ["", "", ""] + + v_coord_bot = [(row, col + 1), (row + 1, col), (row + 1, col + 1)] + vertices_names_bot = ["", "", ""] + + # Add the vertices 1 by one + for i ∈ 1:3 + (v_row, v_col) = v_coord_top[i] + name = vertex_name("Bottom", v_row, v_col) + vertices_names_top[i] = name + vertex_dict[name] = + (Float64(v_row), Float64(v_col), Float64(-bottom_offset * 0)) + + (v_row, v_col) = v_coord_bot[i] + name = vertex_name("Bottom", v_row, v_col) + vertices_names_bot[i] = name + vertex_dict[name] = (Float64(v_row), Float64(v_col), Float64(-bottom_offset)) + end + + # Add the triangles + triangle_dict[triangle_name("Bottom", row, col, :top)] = vertices_names_top + triangle_dict[triangle_name("Bottom", row, col, :bottom)] = vertices_names_bot + end + + + ### + ### Side meshes + ### + # Build triangles to create side meshes and close the mesh + # The mesh is made of a single couple top/bottom triangles joining the bottom face + # and the top face. + # All the vertices already exist + + # (Looking from above), west/east sides. + for (col, face_name) ∈ [(1, "West"), (width, "East")] + for row = 1:height-1 + + v_coord_top = [(:top, row, col), (:bottom, row, col), (:top, row + 1, col)] + vertices_names_top = ["", "", ""] + for i ∈ 1:3 + vertices_names_top[i] = vertex_name( + (v_coord_top[i][1] == :top ? "Top" : "Bottom"), + v_coord_top[i][2], + v_coord_top[i][3], + ) + end + + v_coord_bot = + [(:top, row + 1, col), (:bottom, row + 1, col), (:bottom, row, col)] + vertices_names_bot = ["", "", ""] + for i ∈ 1:3 + vertices_names_bot[i] = vertex_name( + (v_coord_bot[i][1] == :top ? "Top" : "Bottom"), + v_coord_bot[i][2], + v_coord_bot[i][3], + ) + end + + # Add the triangles + triangle_dict[triangle_name(face_name, row, col, :top)] = vertices_names_top + triangle_dict[triangle_name(face_name, row, col, :bottom)] = vertices_names_bot + end + end + + # (Looking from above), north/south sides. + for (row, face_name) ∈ [(1, "North"), (height, "South")] + for col ∈ 1:width-1 + + v_coord_top = [(:top, row, col), (:bottom, row, col), (:top, row, col + 1)] + vertices_names_top = ["", "", ""] + for i ∈ 1:3 + vertices_names_top[i] = vertex_name( + (v_coord_top[i][1] == :top ? "Top" : "Bottom"), + v_coord_top[i][2], + v_coord_top[i][3], + ) + end + + v_coord_bot = [(:top, row, col + 1), (:bottom, row, col + 1), (:top, row, col)] + vertices_names_bot = ["", "", ""] + for i ∈ 1:3 + vertices_names_bot[i] = vertex_name( + (v_coord_bot[i][1] == :top ? "Top" : "Bottom"), + v_coord_bot[i][2], + v_coord_bot[i][3], + ) + end + + + # Add the triangles + triangle_dict[triangle_name(face_name, row, col, :top)] = vertices_names_top + triangle_dict[triangle_name(face_name, row, col, :bottom)] = vertices_names_bot + end + end + + return triangle_dict, vertex_dict +end + + +""" +$(SIGNATURES) + +""" +function create_solid( + mesh::FaceMesh; + bottom_distance = Bottom_Offset, + top_distance = Top_Offset, +) + + triangle_dict, vertex_dict = + create_solid(mesh; bottom_distance = Bottom_Offset, top_distance = Top_Offset) + index_dict = Dict(String, Int64)() + + count = 0 + for k ∈ keys(vertex_dict) + count += 1 + index_dict[k] = count + end + + vertex_index = [(index_dict[v], v[1], v[2], v[3]) for (k, v) ∈ values(vertex_dict)] + triangle_index = [ + (index_dict[v[1]], index_dict[v[2]], index_dict[v[3]]) for + v ∈ values(triangle_dict) + ] + + return triangle_dict, vertex_dict, triangle_index, vertex_index + +end diff --git a/src/plots.jl b/src/plots.jl index 1846527..781cafd 100644 --- a/src/plots.jl +++ b/src/plots.jl @@ -137,3 +137,29 @@ function plot_scalar_field!(field, filename, img) # outputImg = img - E # save("./examples/actual_$(suffix).png", outputImg) end + + + +""" +$(SIGNATURES) +""" +function plot_scalar_field(scalar_field, suffix, img) + normalised_D_max = scalar_field ./ maximum(scalar_field) + normalised_D_min = scalar_field ./ minimum(scalar_field) + + blue = zeros(size(scalar_field)) + blue[scalar_field.>0] = normalised_D_max[scalar_field.>0] + red = zeros(size(scalar_field)) + red[scalar_field.<0] = -normalised_D_min[scalar_field.<0] + green = zeros(size(scalar_field)) + + rgbImg = RGB.(red, green, blue)' + save("./examples/$(suffix)_loss.png", map(clamp01nan, rgbImg)) + + println("Saving output image:") + println(typeof(img)) + E = Gray.(scalar_field) + println(typeof(E)) + outputImg = img - E + save("./examples/$(suffix)_actual.png", outputImg) +end diff --git a/src/scratchpad.jl b/src/scratchpad.jl index bf394b3..d52eca7 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -6,6 +6,22 @@ image = Images.load("./examples/cat_posing.jpg"); # Check current working direct using CausticsEngineering mesh, imageBW = engineer_caustics(image); +triangle_dict, vertex_dict, triangle_index, vertex_index = create_solid(mesh) + +save_stl!( + triangle_index, vertex_index, + "./examples/result_mesh.obj", + scale = Float64(Meters_Per_Pixel), + scaleh = Float64(Meters_Per_Pixel), +) + + + + + + + + Gray.(imageBW) @@ -187,3 +203,43 @@ s = (ab + ac + cb) / 2.0 s - ab s - ab s - ab + +[[0 1 0], [1 -4 1], [0 1 0]] + + + flow_up = zeros(Float64, size(∇²ϕ)) + flow_down = zeros(Float64, size(∇²ϕ)) + flow_left = zeros(Float64, size(∇²ϕ)) + flow_right = zeros(Float64, size(∇²ϕ)) + + flow_up[1:end, 1:end] .= padded_ϕ[1:end-2, 2:end-1] - padded_ϕ[2:end-1, 2:end-1] + flow_down[1:end, 1:end] .= padded_ϕ[3:end, 2:end-1] - padded_ϕ[2:end-1, 2:end-1] + flow_left[1:end, 1:end] .= padded_ϕ[2:end-1, 1:end-2] - padded_ϕ[2:end-1, 2:end-1] + flow_right[1:end, 1:end] .= padded_ϕ[2:end-1, 3:end] - padded_ϕ[2:end-1, 2:end-1] + + fill_borders!(flow_up, 0.0) + fill_borders!(flow_down, 0.0) + fill_borders!(flow_left, 0.0) + fill_borders!(flow_right, 0.0) + + + + +end + +ϕ + +k = ([[0.0 1.0 0.0]; [1.0 -4.0 1.0]; [0.0 1.0 0.0]]) + +m = [[0.0 1.0 0.0 4.0]; [1.0 -4.0 1.0 2.0]; [0.0 1.0 0.0 3.0]; [1.0 -4.0 1.0 2.0]] +p = zeros(Float64, 4, 4) + + +p[1, 1] = sum(m[1:3, 1:3] .* k) +p + +vertex_dict = Dict{String, Tuple{Float64, Float64, Float64}}() + +name = "a" +vertex_dict[name] = (1.0, 1.0, 1.0) +vertex_dict \ No newline at end of file diff --git a/src/utilities.jl b/src/utilities.jl index 224f3c7..9f58951 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -162,13 +162,7 @@ function Vertex3D(fv::FieldVertex3D, row, col) height, width = size(fv) if (1 <= row <= height + 1) && (1 <= col <= width + 1) - Vertex3D( - fv.r[row, col], - fv.y[row, col], - fv.ϕ[row, col], - fv.vr[row, col], - fv.vc[row, col], - ) + Vertex3D(fv.r[row, col], fv.y[row, col], fv.ϕ[row, col], fv.vr[row, col], fv.vc[row, col]) else missing end @@ -206,16 +200,8 @@ struct FaceMesh function FaceMesh(height::Int, width::Int) m_corner = FieldVertex3D(height, width) - t_triangles = Matrix{Tuple{Tuple{Int,Int},Tuple{Int,Int},Tuple{Int,Int}}}( - undef, - height, - width, - ) - b_triangles = Matrix{Tuple{Tuple{Int,Int},Tuple{Int,Int},Tuple{Int,Int}}}( - undef, - height, - width, - ) + t_triangles = Matrix{Tuple{Tuple{Int,Int},Tuple{Int,Int},Tuple{Int,Int}}}(undef, height, width) + b_triangles = Matrix{Tuple{Tuple{Int,Int},Tuple{Int,Int},Tuple{Int,Int}}}(undef, height, width) for row ∈ 1:height, col ∈ 1:width t_triangles[row, col] = ((row, col), (row + 1, col), (row, col + 1)) @@ -227,9 +213,6 @@ struct FaceMesh end - - - """ $(SIGNATURES) @@ -246,10 +229,7 @@ struct Triangle points::Tuple{Int,Int,Int} function Triangle(mesh::FaceMesh) - return Triangle( - mesh, - Tuple(mesh.as_index(1, 1), mesh.as_index(2, 1), mesh.as_index(1, 2)), - ) + return Triangle(mesh, Tuple(mesh.as_index(1, 1), mesh.as_index(2, 1), mesh.as_index(1, 2))) end end @@ -306,9 +286,7 @@ function triangle3D(mesh::FaceMesh, row::Int, col::Int, side = Union{:top,:botto end end -triangle3D(mesh::FaceMesh, ci::CartesianIndex{2}, side = Union{:top,:bottom}) = - triangle3D(mesh, ci[1], ci[2], side) - +triangle3D(mesh::FaceMesh, ci::CartesianIndex{2}, side = Union{:top,:bottom}) = triangle3D(mesh, ci[1], ci[2], side) """ @@ -368,12 +346,40 @@ function area(mesh::FaceMesh, row::Int, col::Int; side = Union{:top,:bottom}) end -average_absolute(m::AbstractMatrix) = (sum(abs.(m)) / length(m)) < 1e10 +""" +$(TYPEDEF) +""" +struct MeshVertex + id::Int64 + tri::Vertex3D +end + + +""" +$(TYPEDEF) +""" +struct MeshTriangle + tri::Tuple{Int64} +end + + +""" +$(SIGNATURES) + +A Mesh is a collection of triangles. The brightness flowing through a given triangle is just proportional to its +area in the x, y plane. h is ignored. + +The function returns a matrix with the quantity of light coming from each 'rectangle' around a corner. That 'rectangle' +has been shifted and flexed around. +""" +function get_area_corners(mesh::FaceMesh) + height, width = size(mesh) + + top_tri_area = [area(triangle3D(mesh, row, col, :top)...) for row ∈ 1:height, col ∈ 1:width] + @assert !any(isnan.(top_tri_area)) "get_area_corners: NaN area in top triangles." + + bot_tri_area = [area(triangle3D(mesh, row, col, :bottom)...) for row ∈ 1:height, col ∈ 1:width] + @assert !any(isnan.(top_tri_area)) "get_area_corners: NaN area in bottom triangles." -function smallest_positive(x1::Float64, x2::Float64) - x1 < 0.0 && x2 < 0.0 && return -1.0 - x1 >= 0.0 && x2 < 0.0 && return x1 - x1 < 0.0 && x2 >= 0.0 && return x2 - x1 >= 0.0 && x2 >= 0.0 && return min(x1, x2) - return -1.0 + return top_tri_area + bot_tri_area end From 6392ad5a18ded8e48694c3f2b2901e974270d39e Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Fri, 10 Sep 2021 21:48:05 +0200 Subject: [PATCH 21/58] Refactoring. Snapshot 15 --- src/CausticsEngineering.jl | 21 +++- src/create_mesh.jl | 8 +- src/io.jl | 4 +- src/mesh.jl | 34 ++++- src/scratchpad.jl | 249 ++++--------------------------------- src/utilities.jl | 34 +++-- 6 files changed, 103 insertions(+), 247 deletions(-) diff --git a/src/CausticsEngineering.jl b/src/CausticsEngineering.jl index 7b8ef6d..8af0e6e 100644 --- a/src/CausticsEngineering.jl +++ b/src/CausticsEngineering.jl @@ -27,7 +27,24 @@ function main() return engineer_caustics(img) end -export Meters_Per_Pixel, - Vertex3D, FieldVertex3D, FaceMesh, main, engineer_caustics, create_solid +export + # Constants + Meters_Per_Pixel, + Bottom_Offset, + Top_Offset, + + # Types + Vertex3D, + FieldVertex3D, + FaceMesh, + + # Mesh + create_solid, + create_solid_as_dict, + + # Main procedures + main, + engineer_caustics + end # End module diff --git a/src/create_mesh.jl b/src/create_mesh.jl index 19d4864..82a92e2 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -107,7 +107,7 @@ function solve_velocity_potential!(mesh, image, suffix) while ( 1e-6 < abs(max_update) < start_max_update + 1 && abs((max_update - old_max_update) / old_max_update) > 0.01 && - new_divergence < 20.0 + new_divergence < 100.0 ) # while sum(abs.(mesh.corners.ϕ - mesh_ϕ)) / (height * width) < 100 @@ -175,16 +175,16 @@ function solve_velocity_potential!(mesh, image, suffix) march_mesh!(mesh) save_stl!( - matrix_to_mesh(mesh.corners.ϕ * 0.02), + matrix_to_mesh(mesh.corners.ϕ * 0.01), "./examples/phi_$(suffix).obj", reverse = false, - flipxy = true, + flipxy = false, ) # plot_as_quiver(ϕ * -1.0, stride=30, scale=1.0, max_length=200, flipxy=true, reverser=false, reversec=false) plot_as_quiver( mesh, - stride = 30, + stride = 20, scale = 1.0, max_length = 200, flipxy = true, diff --git a/src/io.jl b/src/io.jl index 90e4fdd..6843693 100644 --- a/src/io.jl +++ b/src/io.jl @@ -89,8 +89,8 @@ $(SIGNATURES) """ function save_stl!( - triangle_index::AbstractDict{}, - vertex_index::AbstractDict{}, + triangle_index::AbstractVector{}, + vertex_index::AbstractVector{}, filename::String; scale = 1.0, scaleh = 1.0, diff --git a/src/mesh.jl b/src/mesh.jl index b7cf652..5c1878e 100644 --- a/src/mesh.jl +++ b/src/mesh.jl @@ -239,17 +239,43 @@ function create_solid( top_distance = Top_Offset, ) - triangle_dict, vertex_dict = - create_solid(mesh; bottom_distance = Bottom_Offset, top_distance = Top_Offset) - index_dict = Dict(String, Int64)() + triangle_dict, vertex_dict = create_solid_as_dict( + mesh; + bottom_distance = Bottom_Offset, + top_distance = Top_Offset, + ) + + _, _, triangle_index, vertex_index = create_solid( + triangle_dict, + vertex_dict; + bottom_distance = bottom_distance, + top_distance = top_distance, + ) + return triangle_dict, vertex_dict, triangle_index, vertex_index +end + + + +""" +$(SIGNATURES) + +""" +function create_solid( + triangle_dict::Dict{String,Vector{String}}, + vertex_dict::Dict{String,Tuple{Float64,Float64,Float64}}; + bottom_distance = Bottom_Offset, + top_distance = Top_Offset, +) + + index_dict = Dict{String,Int64}() count = 0 for k ∈ keys(vertex_dict) count += 1 index_dict[k] = count end - vertex_index = [(index_dict[v], v[1], v[2], v[3]) for (k, v) ∈ values(vertex_dict)] + vertex_index = [(index_dict[k], v[1], v[2], v[3]) for (k, v) ∈ vertex_dict] triangle_index = [ (index_dict[v[1]], index_dict[v[2]], index_dict[v[3]]) for v ∈ values(triangle_dict) diff --git a/src/scratchpad.jl b/src/scratchpad.jl index d52eca7..2b04ec4 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -6,240 +6,33 @@ image = Images.load("./examples/cat_posing.jpg"); # Check current working direct using CausticsEngineering mesh, imageBW = engineer_caustics(image); -triangle_dict, vertex_dict, triangle_index, vertex_index = create_solid(mesh) - -save_stl!( - triangle_index, vertex_index, - "./examples/result_mesh.obj", - scale = Float64(Meters_Per_Pixel), - scaleh = Float64(Meters_Per_Pixel), +CausticsEngineering.plot_as_quiver( + mesh, + stride = 20, + scale = 1.0, + max_length = 20, + flipxy = true, + reverser = false, + reversec = false, ) +triangle_dict, vertex_dict = + create_solid_as_dict(mesh; bottom_distance = Bottom_Offset, top_distance = Top_Offset) - - - - - -Gray.(imageBW) - -mesh.pixel.r[1:10, 1:10] -mesh.pixel.c[1:10, 1:10] -mesh.pixel.ϕ[1:10, 1:10] -mesh.pixel.vr[1:10, 1:10] -mesh.pixel.vc[1:10, 1:10] - -mesh.toptriangles[1:10] -mesh.bottriangles[1:10] - -mesh.pixel.r[250:260, 250:260] -mesh.pixel.c[250:260, 250:260] -mesh.pixel.ϕ[250:260, 250:260] - - -using Test - -t3 = ( - CausticsEngineering.Vertex3D(5.0, 5.0, 0.01, 0.1, -2.0), - CausticsEngineering.Vertex3D(6.0, 5.0, 0.01, 0.1, 2.0), - CausticsEngineering.Vertex3D(5.5, 5.5, 0.01, 0.5, -3.0), +_, _, triangle_index, vertex_index = create_solid( + triangle_dict, + vertex_dict; + bottom_distance = Bottom_Offset, + top_distance = Top_Offset, ) -CausticsEngineering.find_maximum_t(t3) - - -typeof(CartesianIndex(3, 5)[1]) - -t = Matrix{Tuple{CartesianIndex(2),CartesianIndex(2),CartesianIndex(2)}}(undef, 2, 2) - -t[1, 1] = (CartesianIndex(1, 1), CartesianIndex(2, 1), CartesianIndex(1, 2)) -typeof((CartesianIndex(1, 1), CartesianIndex(2, 1), CartesianIndex(1, 2))) - - -f.toptriangles[CartesianIndex(5, 5)] - -f = FaceMesh(5, 5); -v3 = CausticsEngineering.top_triangle3D(f, CartesianIndex(5, 5)) -CausticsEngineering.find_maximum_t(v3) - -v3 = CausticsEngineering.top_triangle3D(f, CartesianIndex(5, 5)) -CausticsEngineering.area(v3...) - -v3 = CausticsEngineering.bot_triangle3D(f, CartesianIndex(5, 5)) -CausticsEngineering.area(v3...) - -CausticsEngineering.get_pixel_area(f) - -for _ = 1:100 - h = rand(Float64, (10, 10)) - d = rand(Float64, (10, 10)) - print(CausticsEngineering.relax(h, d)) -end - -c = t[1] - -f.pixel(c) - -t = CausticsEngineering.top_triangle3D(f, CartesianIndex(1, 1)) - - - -# Indexing structs -struct TT - a::Int - b::Int -end - -using StructArrays - - -aa = StructArrays() - -aa[:].a = 0 - - -[1, 2, 3] |> filter(isnan) - - -begin - r1, c1, ϕ1, vr1, vc1 = (rand(5) .- 0.5) .* 20 - r2, c2, ϕ2, vr2, vc2 = (rand(5) .- 0.5) .* 20 - r3, c3, ϕ3, vr3, vc3 = (rand(5) .- 0.5) .* 20 - vertex1 = Vertex3D(r1, c1, ϕ1, vr1, vc1) - vertex2 = Vertex3D(r2, c2, ϕ2, vr2, vc2) - vertex3 = Vertex3D(r3, c3, ϕ3, vr3, vc3) - - println( - CausticsEngineering.area(vertex1, vertex2, vertex3), - " ", - CausticsEngineering.find_maximum_t(vertex1, vertex2, vertex3), - ) -end - - -r1, c1, ϕ1, vr1, vc1 = (rand(5) .- 0.5) .* 20 -r2, c2, ϕ2, vr2, vc2 = (rand(5) .- 0.5) .* 20 -r3, c3, ϕ3, vr3, vc3 = (rand(5) .- 0.5) .* 20 - -p1 = Vertex3D(r1, c1, ϕ1, vr1, vc1) -p2 = Vertex3D(r2, c2, ϕ2, vr2, vc2) -p3 = Vertex3D(r3, c3, ϕ3, vr3, vc3) - -# To make the calculation simpler, everything is translated so that A is at the -# origin of the plane and its velocity is nil. -Br = p2.r - p1.r -Bc = p2.c - p1.c -Cr = p3.r - p1.r -Cc = p3.c - p1.c - -t_vBr = p2.vr - p1.vr -t_vBc = p2.vc - p1.vc -t_vCr = p3.vr - p1.vr -t_vCc = p3.vc - p1.vc - -# After this, given that Ar = Ac = t_vAr = t_vAc = 0, the area is nil iff -# (Br + t_vBr) (Cc + t_vCc ) - (Cr + t_vCr) (Bc + t_vBc) = 0. -# After expansion and reshuffling to have a quadratic equation where t -# is the variable, the coefficients of that equation are: -a = t_vCc * t_vBr - t_vBc * t_vCr -b = -Bc * t_vCr - Cr * t_vBc + Br * t_vCc + Cc * t_vBr -c = Br * Cc - Cr * Bc - -discriminant = b^2 - 4a * c -d = discriminant >= 0.0 ? sqrt(discriminant) : 0 -t1 = (-b - d) / 2a -t2 = (-b + d) / 2a -t1, t2, CausticsEngineering.smallest_positive((-b - d) / 2a, (-b + d) / 2a) - - -Vertex3D() - - - - -a = Vertex3D( - 489.20336199266757, - 190.09282140997482, - -58505.12856934825, - -39628.63636211195, - -50804.04679723241, -) -b = Vertex3D( - 490.30273062001396, - 189.42556748453276, - 29305.470378387537, - -10020.45529953039, - 48181.962585623834, -) -c = Vertex3D( - 489.89918140614986, - 189.67049879639754, - -18876.492207236297, - 39648.76478266787, - -65706.41461026447, -) -CausticsEngineering.find_maximum_t(a, b, c) - -a = Vertex3D(30.0, 271.0, 0.8354160335261099, -0.053188093456838725, -0.00538632666184502) -b = Vertex3D(31.0, 270.0, 0.8353725644270783, -0.005828514543554375, -0.05323156255587036) -c = Vertex3D( - 30.499999997149644, - 270.5, - 0.8886041269829487, - 0.04690021252675358, - 0.04690021225938901, +CausticsEngineering.save_stl!( + triangle_index, + vertex_index, + "./examples/result_mesh.obj", + scale = Float64(Meters_Per_Pixel), + scaleh = Float64(Meters_Per_Pixel), ) -CausticsEngineering.find_maximum_t(a, b, c) - -ab = CausticsEngineering.dist(a, b) -ac = CausticsEngineering.dist(a, c) -cb = CausticsEngineering.dist(c, b) - -s = (ab + ac + cb) / 2.0 - -s - ab -s - ab -s - ab - -[[0 1 0], [1 -4 1], [0 1 0]] - - - flow_up = zeros(Float64, size(∇²ϕ)) - flow_down = zeros(Float64, size(∇²ϕ)) - flow_left = zeros(Float64, size(∇²ϕ)) - flow_right = zeros(Float64, size(∇²ϕ)) - - flow_up[1:end, 1:end] .= padded_ϕ[1:end-2, 2:end-1] - padded_ϕ[2:end-1, 2:end-1] - flow_down[1:end, 1:end] .= padded_ϕ[3:end, 2:end-1] - padded_ϕ[2:end-1, 2:end-1] - flow_left[1:end, 1:end] .= padded_ϕ[2:end-1, 1:end-2] - padded_ϕ[2:end-1, 2:end-1] - flow_right[1:end, 1:end] .= padded_ϕ[2:end-1, 3:end] - padded_ϕ[2:end-1, 2:end-1] - - fill_borders!(flow_up, 0.0) - fill_borders!(flow_down, 0.0) - fill_borders!(flow_left, 0.0) - fill_borders!(flow_right, 0.0) - - - - -end - -ϕ - -k = ([[0.0 1.0 0.0]; [1.0 -4.0 1.0]; [0.0 1.0 0.0]]) - -m = [[0.0 1.0 0.0 4.0]; [1.0 -4.0 1.0 2.0]; [0.0 1.0 0.0 3.0]; [1.0 -4.0 1.0 2.0]] -p = zeros(Float64, 4, 4) - - -p[1, 1] = sum(m[1:3, 1:3] .* k) -p - -vertex_dict = Dict{String, Tuple{Float64, Float64, Float64}}() - -name = "a" -vertex_dict[name] = (1.0, 1.0, 1.0) -vertex_dict \ No newline at end of file diff --git a/src/utilities.jl b/src/utilities.jl index 9f58951..675ba32 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -162,7 +162,13 @@ function Vertex3D(fv::FieldVertex3D, row, col) height, width = size(fv) if (1 <= row <= height + 1) && (1 <= col <= width + 1) - Vertex3D(fv.r[row, col], fv.y[row, col], fv.ϕ[row, col], fv.vr[row, col], fv.vc[row, col]) + Vertex3D( + fv.r[row, col], + fv.y[row, col], + fv.ϕ[row, col], + fv.vr[row, col], + fv.vc[row, col], + ) else missing end @@ -200,8 +206,16 @@ struct FaceMesh function FaceMesh(height::Int, width::Int) m_corner = FieldVertex3D(height, width) - t_triangles = Matrix{Tuple{Tuple{Int,Int},Tuple{Int,Int},Tuple{Int,Int}}}(undef, height, width) - b_triangles = Matrix{Tuple{Tuple{Int,Int},Tuple{Int,Int},Tuple{Int,Int}}}(undef, height, width) + t_triangles = Matrix{Tuple{Tuple{Int,Int},Tuple{Int,Int},Tuple{Int,Int}}}( + undef, + height, + width, + ) + b_triangles = Matrix{Tuple{Tuple{Int,Int},Tuple{Int,Int},Tuple{Int,Int}}}( + undef, + height, + width, + ) for row ∈ 1:height, col ∈ 1:width t_triangles[row, col] = ((row, col), (row + 1, col), (row, col + 1)) @@ -229,7 +243,10 @@ struct Triangle points::Tuple{Int,Int,Int} function Triangle(mesh::FaceMesh) - return Triangle(mesh, Tuple(mesh.as_index(1, 1), mesh.as_index(2, 1), mesh.as_index(1, 2))) + return Triangle( + mesh, + Tuple(mesh.as_index(1, 1), mesh.as_index(2, 1), mesh.as_index(1, 2)), + ) end end @@ -286,7 +303,8 @@ function triangle3D(mesh::FaceMesh, row::Int, col::Int, side = Union{:top,:botto end end -triangle3D(mesh::FaceMesh, ci::CartesianIndex{2}, side = Union{:top,:bottom}) = triangle3D(mesh, ci[1], ci[2], side) +triangle3D(mesh::FaceMesh, ci::CartesianIndex{2}, side = Union{:top,:bottom}) = + triangle3D(mesh, ci[1], ci[2], side) """ @@ -375,10 +393,12 @@ has been shifted and flexed around. function get_area_corners(mesh::FaceMesh) height, width = size(mesh) - top_tri_area = [area(triangle3D(mesh, row, col, :top)...) for row ∈ 1:height, col ∈ 1:width] + top_tri_area = + [area(triangle3D(mesh, row, col, :top)...) for row ∈ 1:height, col ∈ 1:width] @assert !any(isnan.(top_tri_area)) "get_area_corners: NaN area in top triangles." - bot_tri_area = [area(triangle3D(mesh, row, col, :bottom)...) for row ∈ 1:height, col ∈ 1:width] + bot_tri_area = + [area(triangle3D(mesh, row, col, :bottom)...) for row ∈ 1:height, col ∈ 1:width] @assert !any(isnan.(top_tri_area)) "get_area_corners: NaN area in bottom triangles." return top_tri_area + bot_tri_area From 5c835c4218834fa5fc15f5847352dd8aae2f5b74 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Sat, 11 Sep 2021 12:29:42 +0200 Subject: [PATCH 22/58] Refactoring - Looks like working --- .gitignore | 4 +++ Project.toml | 5 +++ src/CausticsEngineering.jl | 6 ++++ src/create_mesh.jl | 16 +++++---- src/io.jl | 33 ++++++++---------- src/mesh.jl | 22 +++++++++--- src/scratchpad.jl | 71 ++++++++++++++++++++++++++++++++------ 7 files changed, 116 insertions(+), 41 deletions(-) diff --git a/.gitignore b/.gitignore index 3ab70c5..e99552d 100644 --- a/.gitignore +++ b/.gitignore @@ -35,3 +35,7 @@ Manifest.toml *.tmp *.temp + + + +src/debug_script.jl diff --git a/Project.toml b/Project.toml index 1919c58..d29b150 100644 --- a/Project.toml +++ b/Project.toml @@ -4,15 +4,20 @@ authors = ["Matt Ferraro", "Emmanuel Rialland"] version = "0.1.0" [deps] +CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0" Debugger = "31a5f54b-26ea-5ae9-a837-f05ce5417438" DocStringExtensions = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae" Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4" DocumenterTools = "35a29f4d-8980-5a13-9543-d66fff28ecb8" FileIO = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549" +GLMakie = "e9467ef8-e4e7-5192-8a1a-b1aee30e663a" +GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326" Images = "916415d5-f1e6-5110-898d-aaa5f9f070e0" JuliaFormatter = "98e50ef6-434e-11e9-1051-2b60c6c9e899" MeshIO = "7269a6da-0436-5bbc-96c2-40638cbb6118" +MeshViz = "9ecf9c4f-6e5a-4b5e-83ae-06f2c7a661d8" Meshes = "eacbb407-ea5a-433e-ab97-5258b1ca43fa" +Plotly = "58dd65bb-95f3-509e-9936-c39a10fdeae7" Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" Revise = "295af30f-e4ad-537b-8983-00126c2a3abe" diff --git a/src/CausticsEngineering.jl b/src/CausticsEngineering.jl index 8af0e6e..8548f9a 100644 --- a/src/CausticsEngineering.jl +++ b/src/CausticsEngineering.jl @@ -42,6 +42,12 @@ export create_solid, create_solid_as_dict, + # Plotting + plot_as_quiver, + + # I/O + save_obj!, + # Main procedures main, engineer_caustics diff --git a/src/create_mesh.jl b/src/create_mesh.jl index 82a92e2..af6de9f 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -10,18 +10,16 @@ function engineer_caustics(source_image) # mesh is the same size as the image with an extra row/column to have coordinates to # cover each image corner with a triangle. mesh = FaceMesh(height, width) - # println("Mesh creation: ") - # The energy going through the lens is equal to the amount of energy on the caustics + # The total energy going through the lens is equal to the amount of energy on the caustics total_energy_lens = height * width * 1 # 1 unit of energy per pixel total_energy_caustics = sum(imageBW) correction_ratio = sum(imageBW) / (width * height) - # imageBW is `grid_definition x grid_definition` and is normalised to the same (sort of) _energy_ as the - # original image. + # imageBW is normalised to the same (sort of) _energy_ as the original image. imageBW = imageBW ./ correction_ratio - # start_max_update has no particular meeting. + # start_max_update has no particular meing. # It is basically the initial max_update. But then is used to initialise other variables so that # not to stop the `while` loop on the first iteration start_max_update = 1_000.0 @@ -50,6 +48,10 @@ function engineer_caustics(source_image) mesh.corners.ϕ .= ϕ println(" max update = $(max_update)") + # Move the around a nil average. + mean_ϕ = sum(mesh.corners.ϕ) / length(mesh.corners.ϕ) + mesh.corners.ϕ = mesh.corners.ϕ .- mean_ϕ + return mesh, imageBW end @@ -174,7 +176,7 @@ function solve_velocity_potential!(mesh, image, suffix) # We mention them here only for completeness; for a full discussion see Asynchronous Programming. march_mesh!(mesh) - save_stl!( + save_obj!( matrix_to_mesh(mesh.corners.ϕ * 0.01), "./examples/phi_$(suffix).obj", reverse = false, @@ -194,7 +196,7 @@ function solve_velocity_potential!(mesh, image, suffix) # plot_as_quiver(ϕ * -1.0, stride=30, scale=1.0, max_length=200, flipxy=true, reversex=false, reversey=false) # saveObj(matrix_to_mesh(D * 10), "D_$(suffix).obj") - save_stl!(mesh, "./examples/mesh_$(suffix).obj", flipxy = true) + save_obj!(mesh, "./examples/mesh_$(suffix).obj", flipxy = true) return max_update end diff --git a/src/io.jl b/src/io.jl index 6843693..0c61d6d 100644 --- a/src/io.jl +++ b/src/io.jl @@ -38,7 +38,7 @@ The format difinition is sourced from [https://en.wikipedia.org/wiki/STL_(file_f TO REFACTOR. """ -function save_stl!( +function save_obj!( mesh::FaceMesh, filename::String; scale = 1.0, @@ -88,9 +88,9 @@ end $(SIGNATURES) """ -function save_stl!( - triangle_index::AbstractVector{}, - vertex_index::AbstractVector{}, +function save_obj!( + triangle_index, + vertex_index::AbstractMatrix{Float64}, filename::String; scale = 1.0, scaleh = 1.0, @@ -101,25 +101,22 @@ function save_stl!( open(filename, "w") do io println(io, "solid engineered_caustics") - for i ∈ 1:length(vertex_index) + xs = vertex_index[:, 1] + ys = vertex_index[:, 2] + zs = vertex_index[:, 3] + for i ∈ 1:length(xs) if flipxy - println( - io, - "v $(vertex_index[2] * scale) $(vertex_index[1] * scale) $(vertex_index[3] * scaleh)", - ) + println(io, "v $(ys[i] * scale) $(xs[i][1] * scale) $(zs[i] * scaleh)") else - println( - io, - "v $(vertex_index[1] * scale) $(vertex_index[2] * scale) $(vertex_index[3] * scaleh)", - ) + println(io, "v $(xs[i] * scale) $(ys[i][1] * scale) $(zs[i] * scaleh)") end end - for i ∈ 1:length(triangle_index) - println( - io, - "f $(triangle_index[i][1]) $(triangle_index[i][2]) $(triangle_index[i][3])", - ) + t1 = triangle_index[1] + t2 = triangle_index[2] + t3 = triangle_index[3] + for i ∈ 1:length(t1) + println(io, "f $(t1[i]) $(t2[i]) $(t3[i])") end println(io, "endsolid engineered_caustics") diff --git a/src/mesh.jl b/src/mesh.jl index 5c1878e..f295b42 100644 --- a/src/mesh.jl +++ b/src/mesh.jl @@ -269,13 +269,25 @@ function create_solid( ) index_dict = Dict{String,Int64}() - count = 0 - for k ∈ keys(vertex_dict) - count += 1 - index_dict[k] = count + index_of_vertex = 0 + for name ∈ keys(vertex_dict) + index_of_vertex += 1 + index_dict[name] = index_of_vertex end - vertex_index = [(index_dict[k], v[1], v[2], v[3]) for (k, v) ∈ vertex_dict] + vertex_index = Vector{Tuple{Float64,Float64,Float64}}(undef, length(vertex_dict)) + # For each vertex using its name and coordinates + for (name, v) ∈ vertex_dict + # Determine the index of the vertex + i = index_dict[name] + x = v[1] + y = v[2] + z = v[3] + vertex_index[i] = (x, y, z) + end + + # The connections are listed as a tuple of 3 arrays. + # First array contains the first point of a triangle, and so on triangle_index = [ (index_dict[v[1]], index_dict[v[2]], index_dict[v[3]]) for v ∈ values(triangle_dict) diff --git a/src/scratchpad.jl b/src/scratchpad.jl index 2b04ec4..fe99999 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -6,7 +6,22 @@ image = Images.load("./examples/cat_posing.jpg"); # Check current working direct using CausticsEngineering mesh, imageBW = engineer_caustics(image); -CausticsEngineering.plot_as_quiver( + +# Check a few values to make sure they make sense +mesh.corners.r +minimum(mesh.corners.vr) +maximum(mesh.corners.vr) + +mesh.corners.c +minimum(mesh.corners.vc) +maximum(mesh.corners.vc) + +minimum(mesh.corners.ϕ) +maximum(mesh.corners.ϕ) +mean_ϕ = sum(mesh.corners.ϕ) / length(mesh.corners.ϕ) + +# Plot the last vector field +plot_as_quiver( mesh, stride = 20, scale = 1.0, @@ -17,22 +32,56 @@ CausticsEngineering.plot_as_quiver( ) +# Generate dictionaries and arrays containing the vertices and triangles. +triangle_dict, vertex_dict, triangle_index, vertex_index = + create_solid(mesh; bottom_distance = Bottom_Offset, top_distance = Top_Offset) -triangle_dict, vertex_dict = - create_solid_as_dict(mesh; bottom_distance = Bottom_Offset, top_distance = Top_Offset) -_, _, triangle_index, vertex_index = create_solid( - triangle_dict, - vertex_dict; - bottom_distance = Bottom_Offset, - top_distance = Top_Offset, -) +# Can be done in 2 steps +# +# triangle_dict, vertex_dict = create_solid_as_dict( +# mesh; +# bottom_distance = Bottom_Offset, +# top_distance = Top_Offset +# ) +# +# # Generate array or coordinates and indices usable to create traditional mesh objects +# _, _, triangle_index, vertex_index = create_solid( +# triangle_dict, +# vertex_dict; +# bottom_distance = Bottom_Offset, +# top_distance = Top_Offset, +# ) -CausticsEngineering.save_stl!( +# Save as an obj file +save_obj!( triangle_index, vertex_index, - "./examples/result_mesh.obj", + "./examples/result_cat_mesh.obj", scale = Float64(Meters_Per_Pixel), scaleh = Float64(Meters_Per_Pixel), ) + + +# Convert to a mesh structure +using Meshes + +# 2D Mesh +vertex_index2D = [(v[1], v[2]) for v ∈ vertex_index] +vertices2 = Meshes.Point2.(vertex_index2D) +cat_mesh2D = Meshes.SimpleMesh(vertices, connections) + +# 3D Mesh +vertices = Meshes.Point3.(vertex_index) +connections = Meshes.connect.(triangle_index) +cat_mesh = Meshes.SimpleMesh(vertices, connections) + + +# NOT WORKING... +using MeshViz + +# Explicitly import the preferred backend (depending on use case) +import CairoMakie +MeshViz.viz(cat_mesh) +MeshViz.viz(cat_mesh2D) From 4332b8025bad48b653afb275a83327425f38cebe Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Sat, 11 Sep 2021 14:38:13 +0200 Subject: [PATCH 23/58] Refactoring - Looks like working --- src/create_mesh.jl | 13 ----------- src/io.jl | 56 ---------------------------------------------- src/utilities.jl | 30 ++----------------------- 3 files changed, 2 insertions(+), 97 deletions(-) diff --git a/src/create_mesh.jl b/src/create_mesh.jl index af6de9f..cdccfda 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -112,7 +112,6 @@ function solve_velocity_potential!(mesh, image, suffix) new_divergence < 100.0 ) - # while sum(abs.(mesh.corners.ϕ - mesh_ϕ)) / (height * width) < 100 iteration_count += 1 iteration_count % 100 == 0 && println("Converging for intensity: $(max_update)") @@ -183,7 +182,6 @@ function solve_velocity_potential!(mesh, image, suffix) flipxy = false, ) - # plot_as_quiver(ϕ * -1.0, stride=30, scale=1.0, max_length=200, flipxy=true, reverser=false, reversec=false) plot_as_quiver( mesh, stride = 20, @@ -194,8 +192,6 @@ function solve_velocity_potential!(mesh, image, suffix) reversec = false, ) - # plot_as_quiver(ϕ * -1.0, stride=30, scale=1.0, max_length=200, flipxy=true, reversex=false, reversey=false) - # saveObj(matrix_to_mesh(D * 10), "D_$(suffix).obj") save_obj!(mesh, "./examples/mesh_$(suffix).obj", flipxy = true) return max_update @@ -261,7 +257,6 @@ function move_horizontally( println("Convergence horiz. Δ stopped with max_update of $(max_update)") - # saveObj(matrix_to_mesh(h / 10), "./examples/heightmap.obj") return true_H, max_update end @@ -288,12 +283,6 @@ In order of how to think about the flow of the program: - The higher ∇ϕ (the actual loss given a particular target caustics), the lower ∇²ϕ (of the current estimated ϕ) should be. -In order to reduce the error, the error informs how to change the estimated ϕ. - -- -δ > 0 => divergence of ϕ needs to increase - - """ function propagate_poisson(ϕ::Matrix{Float64}, ∇²ϕ::Matrix{Float64}) @@ -462,8 +451,6 @@ function march_mesh!(mesh::FaceMesh) """, ) - - # saveObj(mesh, "gateau.obj") end diff --git a/src/io.jl b/src/io.jl index 0c61d6d..d5d705b 100644 --- a/src/io.jl +++ b/src/io.jl @@ -28,62 +28,6 @@ function convert(::Meshes.SimpleMesh, mesh::FaceMesh) end - -""" -$(SIGNATURES) - -This function saves the mesh object in stl format. - -The format difinition is sourced from [https://en.wikipedia.org/wiki/STL_(file_format)](). - -TO REFACTOR. -""" -function save_obj!( - mesh::FaceMesh, - filename::String; - scale = 1.0, - scaleh = 1.0, - reverse = false, - flipxy = false, -) - - return - - height, width = size(mesh) - - open(filename, "w") do io - println(io, "solid engineered_caustics") - - for row ∈ 1:height, col ∈ 1:width - # Top triangle - top_triangle = top_triangle(mesh, row, col) - n = centroid(top_triangle) - - if flipxy - println(io, "v $(n.c * scale) $(n.r * scale) $(n.h * scaleh)") - else - println(io, "v $(n.r * scale) $(n.c * scale) $(n.h * scaleh)") - end - - # Bottom triangle - bot_triangle = bottom_triangle(mesh, row, col) - n = centroid(bot_triangle) - - if flipxy - println(io, "v $(n.y * scale) $(n.x * scale) $(n.z * scalez)") - else - println(io, "v $(n.x * scale) $(n.y * scale) $(n.z * scalez)") - end - end - - # CHECK what dims exactly represents. Number of triangles? - println(io, "dims $(2*mesh.width) $(2*mesh.height)") - - println(io, "endsolid engineered_caustics") - end -end - - """ $(SIGNATURES) diff --git a/src/utilities.jl b/src/utilities.jl index 675ba32..fc57df1 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -82,7 +82,7 @@ Origin is top left, going right and down .`x` goes horizontal and follows column # Velocity -Velocity vector along `x` and `y` (velocity along h not necessary). +Velocity vector along `row` and `col` (velocity along h not used). Implementation is a struc of arrays. Easier to vectorise. @@ -101,9 +101,6 @@ mutable struct FieldVertex3D rows_numbers::AbstractMatrix{Float64} cols_numbers::AbstractMatrix{Float64} - - # FieldVertex3D(size, mr, mc, mϕ, mvr, mvc, rows_numbers, cols_numbers) = new(size, mr, mc, mϕ, mvr, mvc, rows_numbers, cols_numbers) - end # Information about each corner surrounding a pixel. Posts&fences warning!!! @@ -118,12 +115,6 @@ function FieldVertex3D(height, width) mvr = zeros(Float64, height + 1, width + 1) mvc = zeros(Float64, height + 1, width + 1) - # mr = rows_numbers + rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 - # mc = cols_numbers + rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 - # mϕ = rand(Float64, height, width) ./ 1_000 .- 0.5 / 1_000 - # mvr = rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 - # mvc = rand(Float64, height + 1, width + 1) ./ 1_000 .- 0.5 / 1_000 - fv = FieldVertex3D((height, width), mr, mc, mϕ, mvr, mvc, rows_numbers, cols_numbers) reset_border_values!(fv) return fv @@ -364,28 +355,11 @@ function area(mesh::FaceMesh, row::Int, col::Int; side = Union{:top,:bottom}) end -""" -$(TYPEDEF) -""" -struct MeshVertex - id::Int64 - tri::Vertex3D -end - - -""" -$(TYPEDEF) -""" -struct MeshTriangle - tri::Tuple{Int64} -end - - """ $(SIGNATURES) A Mesh is a collection of triangles. The brightness flowing through a given triangle is just proportional to its -area in the x, y plane. h is ignored. +area in the r, r plane. h is ignored. The function returns a matrix with the quantity of light coming from each 'rectangle' around a corner. That 'rectangle' has been shifted and flexed around. From fd94975df9ed94732c0982b49c731d3820827f91 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Sun, 12 Sep 2021 11:32:12 +0200 Subject: [PATCH 24/58] Minor --- .gitignore | 1 + Project.toml | 4 +-- src/create_mesh.jl | 27 +++++-------------- src/plots.jl | 18 +++++-------- src/scratchpad.jl | 67 +++++++++++++++++++++++++++++++++++++--------- 5 files changed, 69 insertions(+), 48 deletions(-) diff --git a/.gitignore b/.gitignore index e99552d..7607609 100644 --- a/.gitignore +++ b/.gitignore @@ -39,3 +39,4 @@ Manifest.toml src/debug_script.jl +examples/personal \ No newline at end of file diff --git a/Project.toml b/Project.toml index d29b150..f1bd27d 100644 --- a/Project.toml +++ b/Project.toml @@ -1,7 +1,7 @@ name = "CausticsEngineering" uuid = "e17b973c-3eae-4e30-9cf2-ee583e3dfd43" authors = ["Matt Ferraro", "Emmanuel Rialland"] -version = "0.1.0" +version = "0.2.0" [deps] CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0" @@ -21,8 +21,6 @@ Plotly = "58dd65bb-95f3-509e-9936-c39a10fdeae7" Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" Revise = "295af30f-e4ad-537b-8983-00126c2a3abe" -StaticArrays = "90137ffa-7385-5640-81b9-e52037218182" -StructArrays = "09ab397b-f2b6-538f-b94a-2f83cf4a842a" [compat] julia = "1" diff --git a/src/create_mesh.jl b/src/create_mesh.jl index cdccfda..e33439f 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -28,9 +28,9 @@ function engineer_caustics(source_image) iteration_count = 0 while ( - 1e-6 < abs(max_update) < start_max_update + 1 && - abs((max_update - old_max_update) / old_max_update) > 0.01 && - iteration_count < 1_024 + 1e-8 < abs(max_update) < 10 * start_max_update && + abs((max_update - old_max_update) / old_max_update) > 1e-6 && + iteration_count < 100_000 ) iteration_count += 1 @@ -107,8 +107,8 @@ function solve_velocity_potential!(mesh, image, suffix) new_divergence = 0.0 while ( - 1e-6 < abs(max_update) < start_max_update + 1 && - abs((max_update - old_max_update) / old_max_update) > 0.01 && + 1e-9 < abs(max_update) < 10 * start_max_update && + abs((max_update - old_max_update) / old_max_update) > 1e-6 && new_divergence < 100.0 ) @@ -175,13 +175,6 @@ function solve_velocity_potential!(mesh, image, suffix) # We mention them here only for completeness; for a full discussion see Asynchronous Programming. march_mesh!(mesh) - save_obj!( - matrix_to_mesh(mesh.corners.ϕ * 0.01), - "./examples/phi_$(suffix).obj", - reverse = false, - flipxy = false, - ) - plot_as_quiver( mesh, stride = 20, @@ -192,8 +185,6 @@ function solve_velocity_potential!(mesh, image, suffix) reversec = false, ) - save_obj!(mesh, "./examples/mesh_$(suffix).obj", flipxy = true) - return max_update end @@ -345,7 +336,7 @@ function propagate_poisson(ϕ::Matrix{Float64}, ∇²ϕ::Matrix{Float64}) maximum_δ = maximum(abs.(δ)) # We limit the changes of the potential to a maximum - max_correction_ratio = 10.0 + max_correction_ratio = 5.0 if 1.94 / 4.0 * maximum_δ < max_correction_ratio correction_ratio = 1.94 / 4.0 @@ -382,9 +373,6 @@ function march_mesh!(mesh::FaceMesh) height, width = size(mesh.corners.ϕ) ∇ϕᵤ, ∇ϕᵥ = ∇(mesh.corners.ϕ) - # println("Min/Max of values of ϕ: $(minimum(ϕ)) / $(maximum(ϕ))") - # println("Sum of values of ∇ϕᵤ: $( sum(∇ϕᵤ) )") - # println("Sum of values of ∇ϕᵥ: $( sum(∇ϕᵥ) )") # For each point in the mesh we need to figure out its velocity @@ -392,7 +380,6 @@ function march_mesh!(mesh::FaceMesh) # I.e. velocity (Vx, Vy) = (0, 0) and the square of acrylate will remain # of the same size. # Warning: The indices are necessary because corner and ∇ϕ are of different sizes - # CHECK SIGNS! mesh.corners.vr .= -∇ϕᵤ mesh.corners.vc .= -∇ϕᵥ @@ -423,8 +410,6 @@ function march_mesh!(mesh::FaceMesh) if !isempty(list_maximum_t) min_positive_t = minimum(list_maximum_t) - # @assert all(typeof.(t1) .== Float64) && all(typeof.(t2) .== Float64) "March mesh: Maximum times are not numerical at $(row), $(col)" - max_shift = max(abs(∇ϕᵤ[row, col]), abs(∇ϕᵥ[row, col])) # No shift more than 20 pixels diff --git a/src/plots.jl b/src/plots.jl index 781cafd..c340820 100644 --- a/src/plots.jl +++ b/src/plots.jl @@ -122,24 +122,17 @@ $(SIGNATURES) """ function plot_scalar_field!(field, filename, img) blue = zeros(size(field)) - blue[field.>0] = field[field.>0] red = zeros(size(field)) - red[field.<0] = -field[field.<0] green = zeros(size(field)) + blue[field.>0] = field[field.>0] + red[field.<0] = -field[field.<0] + rgbImg = RGB.(red, green, blue)' save("./examples/$(filename).png", map(clamp01nan, rgbImg)) - - # println("Saving output image:") - # println(typeof(img)) - # E = Gray.(D) - # println(typeof(E)) - # outputImg = img - E - # save("./examples/actual_$(suffix).png", outputImg) end - """ $(SIGNATURES) """ @@ -148,11 +141,12 @@ function plot_scalar_field(scalar_field, suffix, img) normalised_D_min = scalar_field ./ minimum(scalar_field) blue = zeros(size(scalar_field)) - blue[scalar_field.>0] = normalised_D_max[scalar_field.>0] red = zeros(size(scalar_field)) - red[scalar_field.<0] = -normalised_D_min[scalar_field.<0] green = zeros(size(scalar_field)) + blue[scalar_field.>0] = normalised_D_max[scalar_field.>0] + red[scalar_field.<0] = -normalised_D_min[scalar_field.<0] + rgbImg = RGB.(red, green, blue)' save("./examples/$(suffix)_loss.png", map(clamp01nan, rgbImg)) diff --git a/src/scratchpad.jl b/src/scratchpad.jl index fe99999..5b40cbc 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -1,11 +1,15 @@ using Revise, Debugger using Images +using CausticsEngineering + image = Images.load("./examples/cat_posing.jpg"); # Check current working directory with pwd() +image = Images.load("./examples/personal/image.jpg"); # Check current working directory with pwd() +image = Images.load("./examples/personal/caricature.jpg"); # Check current working directory with pwd() -using CausticsEngineering -mesh, imageBW = engineer_caustics(image); +image = Images.load("./examples/personal/bilal.jpg"); # Check current working directory with pwd() +mesh, imageBW = engineer_caustics(image); # Check a few values to make sure they make sense mesh.corners.r @@ -24,7 +28,7 @@ mean_ϕ = sum(mesh.corners.ϕ) / length(mesh.corners.ϕ) plot_as_quiver( mesh, stride = 20, - scale = 1.0, + scale = 5.0, max_length = 20, flipxy = true, reverser = false, @@ -53,6 +57,10 @@ triangle_dict, vertex_dict, triangle_index, vertex_index = # top_distance = Top_Offset, # ) +# Area of all the distorted pixels +am = CausticsEngineering.get_area_corners(mesh) +maximum(am) +minimum(am) # Save as an obj file save_obj!( @@ -67,21 +75,56 @@ save_obj!( # Convert to a mesh structure using Meshes -# 2D Mesh -vertex_index2D = [(v[1], v[2]) for v ∈ vertex_index] -vertices2 = Meshes.Point2.(vertex_index2D) -cat_mesh2D = Meshes.SimpleMesh(vertices, connections) +# Zone to plot +row_min = 100.0 +row_max = 200.0 +col_min = 100.0 +col_max = 200.0 + +function clip_trangle_index( + triangle_index, + vertex_index; + row_min = 100.0, + row_max = 200.0, + col_min = 100.0, + col_max = 200.0, +) + + function is_in_zone(t)::Bool + p1, p2, p3 = t + v1_r, v1_c = vertex_index[p1] + v2_r, v2_c = vertex_index[p2] + v3_r, v3_c = vertex_index[p3] + + return row_min <= v1_r <= row_max && + col_min <= v1_c <= col_max && + row_min <= v2_r <= row_max && + col_min <= v2_c <= col_max && + row_min <= v3_r <= row_max && + col_min <= v3_c <= col_max + end + + return [t for t ∈ triangle_index if is_in_zone(t)] +end + +# Select relevant triangles +triangle_index3D = clip_trangle_index(triangle_index, vertex_index) +connections = Meshes.connect.(triangle_index3D) # 3D Mesh -vertices = Meshes.Point3.(vertex_index) -connections = Meshes.connect.(triangle_index) -cat_mesh = Meshes.SimpleMesh(vertices, connections) +vertices3D = Meshes.Point3.(vertex_index) +cat_mesh3D = Meshes.SimpleMesh(vertices3D, connections) + +# 2D Mesh +vertex_index2D = [(v[1], v[2]) for v ∈ vertex_index] +vertices2D = Meshes.Point2.(vertex_index2D) +cat_mesh2D = Meshes.SimpleMesh(vertices2D, connections) # NOT WORKING... using MeshViz # Explicitly import the preferred backend (depending on use case) -import CairoMakie -MeshViz.viz(cat_mesh) +import GLMakie +MeshViz.viz(cat_mesh3D) MeshViz.viz(cat_mesh2D) From 4c28798daf374cbef25150d0ce506e1463fc8efb Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Sun, 12 Sep 2021 21:52:49 +0200 Subject: [PATCH 25/58] Plotting bugs. Change of optimisation halting conditions. --- src/create_mesh.jl | 75 +++++++++++++++++----------- src/math_utilities.jl | 2 +- src/parameters.jl | 12 ++--- src/plots.jl | 111 ++++++++++++++++++++++-------------------- src/scratchpad.jl | 3 +- 5 files changed, 112 insertions(+), 91 deletions(-) diff --git a/src/create_mesh.jl b/src/create_mesh.jl index e33439f..0468afd 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -1,3 +1,4 @@ + """ $(SIGNATURES) """ @@ -7,6 +8,16 @@ function engineer_caustics(source_image) height, width = size(imageBW) println("Image size: $((height, width))") + # Set some global size parameters + global N_Pixel_Height = height + global N_Pixel_Width = width + + global Caustics_Height = Caustics_Long_Side + global Caustics_Width = Caustics_Height * N_Pixel_Width / N_Pixel_Height + + global Meters_Per_Pixel = Caustics_Height / N_Pixel_Height + + # mesh is the same size as the image with an extra row/column to have coordinates to # cover each image corner with a triangle. mesh = FaceMesh(height, width) @@ -28,9 +39,9 @@ function engineer_caustics(source_image) iteration_count = 0 while ( - 1e-8 < abs(max_update) < 10 * start_max_update && - abs((max_update - old_max_update) / old_max_update) > 1e-6 && - iteration_count < 100_000 + abs(max_update) > 1e-4 && + abs((max_update - old_max_update) / old_max_update) > 1e-4 && + iteration_count < 10_000 ) iteration_count += 1 @@ -44,9 +55,10 @@ function engineer_caustics(source_image) end println("\nSTARTING HORIZONTAL ITERATION ---") - ϕ, max_update = move_horizontally(mesh, imageBW; f = 1.0, picture_width = Caustics_Side) + + ϕ, max_update = move_horizontally(mesh, imageBW; f = 1.0) mesh.corners.ϕ .= ϕ - println(" max update = $(max_update)") + println("\tmax update = $(max_update)") # Move the around a nil average. mean_ϕ = sum(mesh.corners.ϕ) / length(mesh.corners.ϕ) @@ -104,12 +116,12 @@ function solve_velocity_potential!(mesh, image, suffix) max_update = start_max_update old_max_update = 2 * start_max_update iteration_count = 0 - new_divergence = 0.0 + new_divergence = Inf64 while ( - 1e-9 < abs(max_update) < 10 * start_max_update && - abs((max_update - old_max_update) / old_max_update) > 1e-6 && - new_divergence < 100.0 + abs(max_update) > 1e-4 && + abs((max_update - old_max_update) / old_max_update) > 1e-4 && + new_divergence >= 0.0 ) iteration_count += 1 @@ -144,10 +156,13 @@ function solve_velocity_potential!(mesh, image, suffix) """ new_divergence = maximum( abs.( - mesh.corners.ϕ[begin+1:end, begin:end-1] .- - mesh_ϕ[begin:end-1, begin:end-1] .+ - mesh.corners.ϕ[begin:end-1, begin+1:end] .- - mesh_ϕ[begin:end-1, begin:end-1], + ( + mesh.corners.ϕ[begin+1:end, begin:end-1] .- + mesh_ϕ[begin:end-1, begin:end-1] + ) .+ ( + mesh.corners.ϕ[begin:end-1, begin+1:end] .- + mesh_ϕ[begin:end-1, begin:end-1] + ), ), ) end @@ -177,10 +192,10 @@ function solve_velocity_potential!(mesh, image, suffix) plot_as_quiver( mesh, - stride = 20, + n_steps = 20, scale = 1.0, - max_length = 200, - flipxy = true, + max_length = height / 20, + flipxy = false, reverser = false, reversec = false, ) @@ -192,12 +207,7 @@ end """ $(SIGNATURES) """ -function move_horizontally( - mesh::FaceMesh, - image; - f = Focal_Length, - picture_width = Caustics_Side, -) +function move_horizontally(mesh::FaceMesh, image; f = Focal_Length) # height indexes rows, width indexes columns height, width = size(mesh) @@ -205,6 +215,7 @@ function move_horizontally( # Coordinates difference # Coordinates on the caustics = simple rectangular values in corners. # Coordinates on the lens face comes from corner field. + # d_row/d_col are _POSTS-SIZED_ d_row = mesh.corners.rows_numbers - mesh.corners.r d_col = mesh.corners.cols_numbers - mesh.corners.c @@ -215,22 +226,28 @@ function move_horizontally( # H is the initial distance from the surface of the carved face to the projection screen. # H is constant and does not account for the change in heights due to carving. # Note: Higher location means closer to the caustics => negative sign + # true_H is _POSTS_SIZED_ true_H = zeros(Float64, size(mesh.corners.ϕ)) @. true_H[:] = -mesh.corners.ϕ[:] + H # Normals. + # N_row/N_col are _POSTS_SIZED_ N_row = zeros(Float64, size(true_H)) N_col = zeros(Float64, size(true_H)) - @. N_row[:] = tan(atan(d_row[:] / true_H[:]) / (n₁ - n₂)) - @. N_col[:] = tan(atan(d_col[:] / true_H[:]) / (n₁ - n₂)) + @. N_row[1:end, 1:end] = + tan(atan(d_row[1:end, 1:end] / true_H[1:end, 1:end]) / (n₁ - n₂)) + @. N_col[1:end, 1:end] = + tan(atan(d_col[1:end, 1:end] / true_H[1:end, 1:end]) / (n₁ - n₂)) # We need to find the divergence of the Vector field described by Nx and Ny + # div_row/div_col are _FENCES_SIZED_ div_row = zeros(Float64, width, height) div_col = zeros(Float64, width, height) @. div_row[1:end, 1:end] = N_row[2:end, 1:end-1] - N_row[1:end-1, 1:end-1] @. div_col[1:end, 1:end] = N_col[1:end-1, 2:end] - N_col[1:end-1, 1:end-1] # divergence_direction = zeros(Float64, size(div_row)) + # divergence_direction is _FENCES_SIZED_ divergence_direction = div_row + div_col @assert average_absolute(divergence_direction) """ @@ -239,7 +256,6 @@ function move_horizontally( """ true_H, max_update = propagate_poisson(true_H, -divergence_direction) - @assert average_absolute(true_H) """ ALERT: horiz. Δ corner_heights is too large @@ -260,8 +276,8 @@ There is a hardcoded assumption of Neumann boundary conditions -- that the deriv boundary must be zero in all cases. See: https://math.stackexchange.com/questions/3790299/how-to-iteratively-solve-poissons-equation-with-no-boundary-conditions -- ϕ is the potential to be solved subject to the Poisson equation and is the same size as the corners (posts) -- target is ∇ϕ and is of the size of the pixels (fences) +- ϕ is the potential to be solved subject to the Poisson equation and is the same size as the corners (_POSTS_SIZED_) +- target is ∇ϕ and is of the size in pixels (_FENCES_SIZED_) In order of how to think about the flow of the program: @@ -412,8 +428,9 @@ function march_mesh!(mesh::FaceMesh) max_shift = max(abs(∇ϕᵤ[row, col]), abs(∇ϕᵥ[row, col])) - # No shift more than 20 pixels - max_pixel_move = 20.0 + # No shift more than 100 pixels + max_pixel_move = 10.0 + δ = min(min_positive_t / 2.0, max_pixel_move / max_shift) mesh.corners.r[row, col] = clamp(mesh.corners.r[row, col] + δ * ∇ϕᵤ[row, col], 1, height - 1) diff --git a/src/math_utilities.jl b/src/math_utilities.jl index 53bf16e..3271353 100644 --- a/src/math_utilities.jl +++ b/src/math_utilities.jl @@ -40,7 +40,7 @@ function laplacian(ϕ::AbstractMatrix{Float64}) # Convolution ∇²ϕ = zeros(Float64, height, width) for row ∈ 1:height, col ∈ 1:width - ∇²ϕ[row, height] = sum(padded_ϕ[row:row+2, col:col+2] .* kernel[1:3, 1:3]) + ∇²ϕ[row, col] = sum(padded_ϕ[row:row+2, col:col+2] .* kernel[1:3, 1:3]) end return ∇²ϕ diff --git a/src/parameters.jl b/src/parameters.jl index afbd201..d99b17a 100644 --- a/src/parameters.jl +++ b/src/parameters.jl @@ -19,14 +19,14 @@ const Bottom_Offset = 0.02 # 2 centimeters ## Optics const Focal_Length = 1.0 # meters -const Caustics_Side = 0.1 # m -const Caustics_Height = Caustics_Side - +const Caustics_Long_Side = 0.20 # m +global Caustics_Height = Caustics_Long_Side +global Caustics_Width = Caustics_Long_Side # Caustics picture -const N_Pixel_Side = 512 -const N_Pixel_Height = N_Pixel_Side -const N_Pixel_Width = N_Pixel_Side +global N_Pixel_Side = 512 +global N_Pixel_Height = N_Pixel_Side +global N_Pixel_Width = N_Pixel_Side global Meters_Per_Pixel = Caustics_Height / N_Pixel_Height diff --git a/src/plots.jl b/src/plots.jl index c340820..893bfb0 100644 --- a/src/plots.jl +++ b/src/plots.jl @@ -1,41 +1,46 @@ + """ $(SIGNATURES) """ function plot_as_quiver( mesh::FaceMesh; - stride = 4, + n_steps = 20, scale = 30, - max_length = 2, + max_length = N_Pixel_Width / n_steps, flipxy = false, reverser = false, reversec = false, ) height, width = size(mesh) - rs = Float64[] - cs = Float64[] - vrs = Float64[] - vcs = Float64[] + stride = Int64(ceil(max(height, width) / n_steps)) + row_s = Float64[] + col_s = Float64[] + v_rows = Float64[] + v_cols = Float64[] + + # Ensure that gradient arrows point reflect change of luminosity + # (outward flow = bigger cells = more luminosity) ϕ = -mesh.corners.ϕ - vrm = reverser ? mesh.corners.vr .* scale : -mesh.corners.vr .* scale - vcm = reversec ? -mesh.corners.vc .* scale : mesh.corners.vc .* scale + mat_vr = (reverser ? 1 : -1) .* mesh.corners.vr .* scale + mat_vc = (reversec ? -1 : 1) .* mesh.corners.vc .* scale - vrm = clamp.(vrm, -max_length, max_length) - vcm = clamp.(vcm, -max_length, max_length) + mat_vr = clamp.(mat_vr, -max_length, max_length) + mat_vc = clamp.(mat_vc, -max_length, max_length) for row = 1:stride:height, col = 1:stride:width - reverser ? push!(rs, row) : push!(rs, -row) - reversec ? push!(cs, -col) : push!(cs, col) + reverser ? push!(row_s, row) : push!(row_s, -row) + reversec ? push!(col_s, -col) : push!(col_s, col) - push!(vrs, vrm[row, col]) - push!(vcs, vcm[row, col]) + push!(v_rows, mat_vr[row, col]) + push!(v_cols, mat_vc[row, col]) end q = - flipxy ? quiver(cs, rs, quiver = (vcs, vrs), aspect_ratio = :equal) : - quiver(rs, cs, quiver = (vrs, vcs), aspect_ratio = :equal) + flipxy ? quiver(col_s, row_s, quiver = (v_cols, v_rows)) : + quiver(row_s, col_s, quiver = (v_rows, v_cols)) display(q) end @@ -46,41 +51,40 @@ $(SIGNATURES) """ function plot_as_quiver( ϕ; - stride = 4, + n_steps = 20, scale = 300, max_length = 2, flipxy = false, - reversey = false, - reversex = false, + reverser = false, + reversec = false, ) - h, w = size(ϕ) - xs = Float64[] - ys = Float64[] - us = Float64[] - vs = Float64[] + height, width = size(ϕ) + stride = Int64(ceil(max(height, width) / n_steps)) - for x = 1:stride:w, y = 1:stride:h - reversex ? push!(xs, x) : push!(xs, -x) - reversey ? push!(ys, -y) : push!(ys, y) + row_s = Float64[] + col_s = Float64[] + Δrow = Float64[] + Δcol = Float64[] - p1 = ϕ[y, x] - u = (ϕ[y, x+1] - ϕ[y, x]) * scale - v = (ϕ[y+1, x] - ϕ[y, x]) * scale + for row = 1:stride:height, col = 1:stride:width + reverser ? push!(row_s, col) : push!(row_s, -col) + reversec ? push!(col_s, -row) : push!(col_s, row) - u = -u + p1 = ϕ[row, col] + dr = (-(ϕ[row, col+1] - ϕ[row, col]) * scale) + dc = (ϕ[row+1, col] - ϕ[row, col]) * scale - reversey && (v = -v) - reversex && (u = -u) + reverser && (dr = -dr) + reversec && (dc = -dc) - # println(u, v) - u >= 0 ? push!(us, min(u, max_length)) : push!(us, max(u, -max_length)) - v >= 0 ? push!(vs, min(v, max_length)) : push!(vs, max(v, -max_length)) + dr >= 0 ? push!(Δrow, min(dr, max_length)) : push!(Δrow, max(dr, -max_length)) + dc >= 0 ? push!(Δcol, min(dc, max_length)) : push!(Δcol, max(dc, -max_length)) end q = - flipxy ? quiver(ys, xs, quiver = (vs, us), aspect_ratio = :equal) : - quiver(xs, ys, quiver = (us, vs), aspect_ratio = :equal) + flipxy ? quiver(col_s, row_s, quiver = (Δcol, Δrow)) : + quiver(row_s, col_s, quiver = (Δrow, Δcol)) display(q) end @@ -89,28 +93,29 @@ end """ $(SIGNATURES) """ -function plot_velocities_as_quiver(vx, vy; stride = 4, scale = 300, max_length = 2) - h, w = size(vx) +function plot_velocities_as_quiver(vr, vc; n_steps = 20, scale = 300, max_length = 2) - xs = Float64[] - ys = Float64[] - us = Float64[] - vs = Float64[] + height, width = size(vr) + stride = Int64(ceil(max(height, width) / n_steps)) - for x = 1:stride:w, y = 1:stride:h - push!(xs, x) - push!(ys, h - y) + row_s = Float64[] + col_s = Float64[] + Δrow = Float64[] + Δcol = Float64[] - u = max(vx[x, y], 0.001) - v = max(vy[x, y], 0.001) + dr = max.(vr, 0.001) + dc = max.(vc, 0.001) + + for row = 1:stride:height, col = 1:stride:width + push!(row_s, height - row) + push!(col_s, col) - push!(us, u) - push!(vs, v) - # println(u, ": ", v) + push!(Δrow, dr[row, col]) + push!(Δcol, dc[row, col]) end # readline() - q = quiver(xs, ys, quiver = (us, vs), aspect_ratio = :equal) + q = quiver(row_s, col_s, quiver = (Δrow, Δcol), aspect_ratio = :equal) display(q) readline() end diff --git a/src/scratchpad.jl b/src/scratchpad.jl index 5b40cbc..8cc7025 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -4,10 +4,9 @@ using Images using CausticsEngineering image = Images.load("./examples/cat_posing.jpg"); # Check current working directory with pwd() -image = Images.load("./examples/personal/image.jpg"); # Check current working directory with pwd() image = Images.load("./examples/personal/caricature.jpg"); # Check current working directory with pwd() - image = Images.load("./examples/personal/bilal.jpg"); # Check current working directory with pwd() +image = Images.load("./examples/personal/image.jpg"); # Check current working directory with pwd() mesh, imageBW = engineer_caustics(image); From 4a1a06493b35c44b9290838532ec03227a2d3da5 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Mon, 13 Sep 2021 13:21:00 +0200 Subject: [PATCH 26/58] Plotting bugs. Change of optimisation halting conditions. Corrected bugs for non-square images. --- src/create_mesh.jl | 105 ++++++++++++++++++++++++++------------------- src/plots.jl | 76 +++++++++++++++++--------------- src/scratchpad.jl | 16 +++---- src/utilities.jl | 1 + 4 files changed, 111 insertions(+), 87 deletions(-) diff --git a/src/create_mesh.jl b/src/create_mesh.jl index 0468afd..50f0764 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -1,6 +1,7 @@ """ $(SIGNATURES) + """ function engineer_caustics(source_image) imageBW = Float64.(Gray.(source_image)) @@ -39,8 +40,8 @@ function engineer_caustics(source_image) iteration_count = 0 while ( - abs(max_update) > 1e-4 && - abs((max_update - old_max_update) / old_max_update) > 1e-4 && + abs(max_update) > 1e-2 && + abs((max_update - old_max_update) / old_max_update) > 0.0 && iteration_count < 10_000 ) iteration_count += 1 @@ -58,7 +59,7 @@ function engineer_caustics(source_image) ϕ, max_update = move_horizontally(mesh, imageBW; f = 1.0) mesh.corners.ϕ .= ϕ - println("\tmax update = $(max_update)") + println("\t Horizontal max update = $(max_update)") # Move the around a nil average. mean_ϕ = sum(mesh.corners.ϕ) / length(mesh.corners.ϕ) @@ -75,7 +76,7 @@ $(SIGNATURES) ϕ is the _velocity potential_. The velocity represents the direction towards which the mesh vertices should move. Zones of high luminosity should be covered with more triangles and should attract more vertices. """ -function solve_velocity_potential!(mesh, image, suffix) +function solve_velocity_potential!(mesh, image, prefix) # Remember mesh is (will be) `grid_definition x grid_definition` just like the image # `grid_definition x grid_definition`, so LJ is `grid_definition x grid_definition`. @@ -100,7 +101,7 @@ function solve_velocity_potential!(mesh, image, suffix) println("Loss:") println("\tMinimum loss: $(minimum(error_luminosity))") println("\tMaximum loss: $(maximum(error_luminosity))") - plot_scalar_field!(error_luminosity, suffix * "_loss", image) + save_plot_scalar_field!(error_luminosity, prefix * "_loss", image) # For the purpose of Poisson, we need to divergence to increase towards the inside: negative divergence for high luminosity # error_luminosity = -error_luminosity @@ -116,12 +117,13 @@ function solve_velocity_potential!(mesh, image, suffix) max_update = start_max_update old_max_update = 2 * start_max_update iteration_count = 0 - new_divergence = Inf64 + new_divergence_max = 1_000.0 + new_divergence_mean = 1_000.0 while ( - abs(max_update) > 1e-4 && - abs((max_update - old_max_update) / old_max_update) > 1e-4 && - new_divergence >= 0.0 + abs(max_update) > 0.0 && + abs((max_update - old_max_update) / old_max_update) >= 0.01 && + new_divergence_max >= 0.0 ) iteration_count += 1 @@ -135,7 +137,8 @@ function solve_velocity_potential!(mesh, image, suffix) solve_velocity_potential: max/min mesh.corners.ϕ = $(maximum(mesh.corners.ϕ)) / $(minimum(mesh.corners.ϕ)) iteration count = $(iteration_count), max_update = $(max_update) - new maximum divergence = $(new_divergence) + new mean divergence = $(new_divergence_mean) + new maximum divergence = $(new_divergence_max) """, ) @@ -154,7 +157,7 @@ function solve_velocity_potential!(mesh, image, suffix) max_update = $(max_update) """ - new_divergence = maximum( + new_divergence = abs.( ( mesh.corners.ϕ[begin+1:end, begin:end-1] .- @@ -163,8 +166,11 @@ function solve_velocity_potential!(mesh, image, suffix) mesh.corners.ϕ[begin:end-1, begin+1:end] .- mesh_ϕ[begin:end-1, begin:end-1] ), - ), - ) + ) + + new_divergence_max = maximum(new_divergence) + new_divergence_mean = sum(new_divergence) / length(new_divergence) + end @@ -190,15 +196,7 @@ function solve_velocity_potential!(mesh, image, suffix) # We mention them here only for completeness; for a full discussion see Asynchronous Programming. march_mesh!(mesh) - plot_as_quiver( - mesh, - n_steps = 20, - scale = 1.0, - max_length = height / 20, - flipxy = false, - reverser = false, - reversec = false, - ) + plot_as_quiver(mesh, n_steps = 30, scale = 1.0, max_length = height / 20) return max_update end @@ -255,7 +253,8 @@ function move_horizontally(mesh::FaceMesh, image; f = Focal_Length) max/min = $(maximum(divergence_direction)) / $(minimum(divergence_direction)) """ - true_H, max_update = propagate_poisson(true_H, -divergence_direction) + true_H, max_update = + propagate_poisson(true_H, -divergence_direction; clamp_correction = false) @assert average_absolute(true_H) """ ALERT: horiz. Δ corner_heights is too large @@ -291,7 +290,11 @@ In order of how to think about the flow of the program: should be. """ -function propagate_poisson(ϕ::Matrix{Float64}, ∇²ϕ::Matrix{Float64}) +function propagate_poisson( + ϕ::Matrix{Float64}, + ∇²ϕ::Matrix{Float64}; + clamp_correction = true, +) # Ensure that border conditions are as they should fill_borders!(∇²ϕ, 0.0) @@ -326,13 +329,13 @@ function propagate_poisson(ϕ::Matrix{Float64}, ∇²ϕ::Matrix{Float64}) # Those values are all of ϕ's size and represent the second order approximation of the # Laplacian of ϕ. Lϕ = laplacian(ϕ) - @assert average_absolute(Lϕ) """ + # @assert average_absolute(Lϕ) """ - Relaxation: Laplacian of ϕ a seem too large - max/min target Lϕ = $(maximum(Lϕ)) / $(minimum(Lϕ)) - max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) + # Relaxation: Laplacian of ϕ a seem too large + # max/min target Lϕ = $(maximum(Lϕ)) / $(minimum(Lϕ)) + # max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) - """ + # """ # δ is the difference between the divergence of the intensity loss (in the case of the velocity potential) # and the current one for the current field ϕ (divergence of its gradient). @@ -349,15 +352,28 @@ function propagate_poisson(ϕ::Matrix{Float64}, ∇²ϕ::Matrix{Float64}) """ - maximum_δ = maximum(abs.(δ)) - - # We limit the changes of the potential to a maximum - max_correction_ratio = 5.0 - - if 1.94 / 4.0 * maximum_δ < max_correction_ratio - correction_ratio = 1.94 / 4.0 - else - correction_ratio = max_correction_ratio / maximum_δ + # Default correction ratio to adjust δ is 1.94/ 4.0 + correction_ratio = 1.94 / 4.0 + + # Calculate the average δ that will be used to limit average changes to 5 pixels + if clamp_correction + abs_δ = abs.(δ) + maximum_δ = maximum(abs_δ) + μ_δ = sum(abs_δ) / length(abs_δ) + + # We limit the changes of the potential to a maximum + max_correction_max = 20.0 + max_correction_μ = 5.0 + max_correction_in_between = 10.0 + + if maximum_δ > max_correction_max + correction_ratio = min(correction_ratio, max_correction_max / maximum_δ) + elseif μ_δ > max_correction_μ + correction_ratio = min(correction_ratio, max_correction_μ / μ_δ) + elseif (μ_δ + maximum_δ) / 2 > max_correction_in_between + correction_ratio = + min(correction_ratio, max_correction_in_between / ((μ_δ + maximum_δ) / 2)) + end end # if δ > 0, the intensity loss is too high, or the Laplacian is too high at that point. @@ -420,7 +436,7 @@ function march_mesh!(mesh::FaceMesh) [triangle3D(mesh, row, col, :top), triangle3D(mesh, row, col, :bottom)] list_maximum_t = [ time for time ∈ find_maximum_t.(list_triangles) if - !isnan(time) && time > 0.0 && time < 10.0 + !isnan(time) && time > 0.0 && time < 1e6 ] if !isempty(list_maximum_t) @@ -429,13 +445,14 @@ function march_mesh!(mesh::FaceMesh) max_shift = max(abs(∇ϕᵤ[row, col]), abs(∇ϕᵥ[row, col])) # No shift more than 100 pixels - max_pixel_move = 10.0 + max_pixel_move = 100.0 δ = min(min_positive_t / 2.0, max_pixel_move / max_shift) - mesh.corners.r[row, col] = - clamp(mesh.corners.r[row, col] + δ * ∇ϕᵤ[row, col], 1, height - 1) - mesh.corners.c[row, col] = - clamp(mesh.corners.c[row, col] + δ * ∇ϕᵥ[row, col], 1, width - 1) + δ_row = clamp.(δ * ∇ϕᵤ[row, col], -max_pixel_move, max_pixel_move) + δ_col = clamp.(δ * ∇ϕᵥ[row, col], -max_pixel_move, max_pixel_move) + + mesh.corners.r[row, col] = clamp(mesh.corners.r[row, col] + δ_row, 1, height) + mesh.corners.c[row, col] = clamp(mesh.corners.c[row, col] + δ_col, 1, width) end end diff --git a/src/plots.jl b/src/plots.jl index 893bfb0..710dfd7 100644 --- a/src/plots.jl +++ b/src/plots.jl @@ -7,7 +7,7 @@ function plot_as_quiver( n_steps = 20, scale = 30, max_length = N_Pixel_Width / n_steps, - flipxy = false, + fliprc = false, reverser = false, reversec = false, ) @@ -20,11 +20,12 @@ function plot_as_quiver( v_rows = Float64[] v_cols = Float64[] - # Ensure that gradient arrows point reflect change of luminosity - # (outward flow = bigger cells = more luminosity) + # The gradient vectors reflect change of luminosity:outward flow = bigger cells = more luminosity + # Plots are cosmetically look better when showing the light focusing to a specific location. + # Those gradients are the opposite direction. ϕ = -mesh.corners.ϕ - mat_vr = (reverser ? 1 : -1) .* mesh.corners.vr .* scale + mat_vr = (reverser ? -1 : 1) .* mesh.corners.vr .* scale mat_vc = (reversec ? -1 : 1) .* mesh.corners.vc .* scale mat_vr = clamp.(mat_vr, -max_length, max_length) @@ -38,11 +39,11 @@ function plot_as_quiver( push!(v_cols, mat_vc[row, col]) end - q = - flipxy ? quiver(col_s, row_s, quiver = (v_cols, v_rows)) : - quiver(row_s, col_s, quiver = (v_rows, v_cols)) - - display(q) + display( + fliprc ? quiver(row_s, col_s, quiver = (v_rows, v_cols)) : + quiver(col_s, row_s, quiver = (v_cols, v_rows)), + ) + return nothing end @@ -53,8 +54,8 @@ function plot_as_quiver( ϕ; n_steps = 20, scale = 300, - max_length = 2, - flipxy = false, + max_length = N_Pixel_Width / n_steps, + fliprc = false, reverser = false, reversec = false, ) @@ -68,32 +69,38 @@ function plot_as_quiver( Δcol = Float64[] for row = 1:stride:height, col = 1:stride:width - reverser ? push!(row_s, col) : push!(row_s, -col) - reversec ? push!(col_s, -row) : push!(col_s, row) - - p1 = ϕ[row, col] dr = (-(ϕ[row, col+1] - ϕ[row, col]) * scale) dc = (ϕ[row+1, col] - ϕ[row, col]) * scale + reverser ? push!(row_s, col) : push!(row_s, width + 1 - col) + reversec ? push!(col_s, height + 1 - row) : push!(col_s, row) reverser && (dr = -dr) reversec && (dc = -dc) - dr >= 0 ? push!(Δrow, min(dr, max_length)) : push!(Δrow, max(dr, -max_length)) - dc >= 0 ? push!(Δcol, min(dc, max_length)) : push!(Δcol, max(dc, -max_length)) + push!(Δrow, clamp(dr, -maxlength, max_length)) + push!(Δcol, clamp(dc, -maxlength, max_length)) end - q = - flipxy ? quiver(col_s, row_s, quiver = (Δcol, Δrow)) : - quiver(row_s, col_s, quiver = (Δrow, Δcol)) + # By default, we flip to match the original image. + display( + fliprc ? quiver(row_s, col_s, quiver = (Δrow, Δcol)) : + quiver(col_s, row_s, quiver = (Δcol, Δrow)), + ) - display(q) + return nothing end """ $(SIGNATURES) """ -function plot_velocities_as_quiver(vr, vc; n_steps = 20, scale = 300, max_length = 2) +function plot_velocities_as_quiver( + vr, + vc; + n_steps = 20, + scale = 300, + max_length = N_Pixel_Width / n_steps, +) height, width = size(vr) stride = Int64(ceil(max(height, width) / n_steps)) @@ -115,9 +122,7 @@ function plot_velocities_as_quiver(vr, vc; n_steps = 20, scale = 300, max_length end # readline() - q = quiver(row_s, col_s, quiver = (Δrow, Δcol), aspect_ratio = :equal) - display(q) - readline() + display(quiver(row_s, col_s, quiver = (Δrow, Δcol), aspect_ratio = :equal)) end @@ -125,13 +130,15 @@ end """ $(SIGNATURES) """ -function plot_scalar_field!(field, filename, img) - blue = zeros(size(field)) - red = zeros(size(field)) - green = zeros(size(field)) +function save_plot_scalar_field!(calculated_scalar_field, filename, img) + scalar_field = calculated_scalar_field' + + blue = zeros(size(scalar_field)) + red = zeros(size(scalar_field)) + green = zeros(size(scalar_field)) - blue[field.>0] = field[field.>0] - red[field.<0] = -field[field.<0] + blue[scalar_field.>0] = scalar_field[scalar_field.>0] + red[scalar_field.<0] = -scalar_field[scalar_field.<0] rgbImg = RGB.(red, green, blue)' save("./examples/$(filename).png", map(clamp01nan, rgbImg)) @@ -141,7 +148,8 @@ end """ $(SIGNATURES) """ -function plot_scalar_field(scalar_field, suffix, img) +function save_plot_scalar_field(calculated_scalar_field, prefix, img) + scalar_field = calculated_scalar_field' normalised_D_max = scalar_field ./ maximum(scalar_field) normalised_D_min = scalar_field ./ minimum(scalar_field) @@ -153,12 +161,12 @@ function plot_scalar_field(scalar_field, suffix, img) red[scalar_field.<0] = -normalised_D_min[scalar_field.<0] rgbImg = RGB.(red, green, blue)' - save("./examples/$(suffix)_loss.png", map(clamp01nan, rgbImg)) + save("./examples/$(prefix)_loss.png", map(clamp01nan, rgbImg)) println("Saving output image:") println(typeof(img)) E = Gray.(scalar_field) println(typeof(E)) outputImg = img - E - save("./examples/$(suffix)_actual.png", outputImg) + save("./examples/$(prefix)_actual.png", outputImg) end diff --git a/src/scratchpad.jl b/src/scratchpad.jl index 8cc7025..d5a7b98 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -8,31 +8,29 @@ image = Images.load("./examples/personal/caricature.jpg"); # Check current worki image = Images.load("./examples/personal/bilal.jpg"); # Check current working directory with pwd() image = Images.load("./examples/personal/image.jpg"); # Check current working directory with pwd() +using Plots; +gr(); mesh, imageBW = engineer_caustics(image); # Check a few values to make sure they make sense mesh.corners.r +mesh.corners.vr minimum(mesh.corners.vr) maximum(mesh.corners.vr) mesh.corners.c +mesh.corners.vc minimum(mesh.corners.vc) maximum(mesh.corners.vc) +mesh.corners.ϕ minimum(mesh.corners.ϕ) maximum(mesh.corners.ϕ) mean_ϕ = sum(mesh.corners.ϕ) / length(mesh.corners.ϕ) # Plot the last vector field -plot_as_quiver( - mesh, - stride = 20, - scale = 5.0, - max_length = 20, - flipxy = true, - reverser = false, - reversec = false, -) +p = plot_as_quiver(mesh, n_steps = 60, scale = 5.0, max_length = 20) + # Generate dictionaries and arrays containing the vertices and triangles. diff --git a/src/utilities.jl b/src/utilities.jl index fc57df1..bd7c529 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -130,6 +130,7 @@ function reset_border_values!(corners::FieldVertex3D) # Reset the border at the fixed values fixed coordinates. corners.r[1, :] .= corners.rows_numbers[1, :] corners.r[end, :] .= corners.rows_numbers[end, :] + corners.r[:, 1] .= corners.rows_numbers[:, 1] corners.r[:, end] .= corners.rows_numbers[:, end] From e0ad5e70405d7765642f7a867fc593a6a7c04544 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Mon, 13 Sep 2021 14:16:07 +0200 Subject: [PATCH 27/58] Halting criteria changes. 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zwawLgSQ;}pYKT}1?o^B~52?m$MI{i|PGqOyjCuL_D9=Br=I=YB7ZeNf#L(7@0GfSMSj$Ia*-+xRhbTGIJT={}wUMQ|JBwmw zD2_`HRp%T0d4<#ow7TH`d~=jGo*#IYGF z9$h1}=oL^esD4)H-lZsOsvZCuU1;zu5z`iu+c0%h;=R;d8w4{{XKO8e30v$d3+3gC z2+QO>g1X`E8IpFi7Bh`R87t$KH#}TK(sy#8!*MvUfNE;w_ln2doVtN@N}G0X9^rbJiF6~K z`K~l7xNyBqNCouL6K!nLt?Kx|&1{i)$RmA|lss)T05G+-wXRmPD#qi5s_H%usg6N< zIc?D7T1-2J>a=TMECWlsKowPAv^s+$SrHAmRdw8PTv~5ZS~}T3DqcKs>D2I0U@)1d zb0w*_{l1GQk8!ask&&ALv0hhuSrf&?kCOXoB3G`lU z`FXN|)2e>66nxOK761cuHtL+qLo5<;JWnvn!=k2*kEwmmjqaVMgh=q|ZsXZq(NGy) z(i>)uilo@Nc$lG~5@l#Sk>uKmm7?W{#@2r#@F@ znnWQWRYCzB}Bd0ULct{Q-ORQH0 zOPZCA9mv1TttgSvPFt{cp*CByp&4o^+~aOL*|tBNbOKs4_y$OqCQAT*K`d8lsyU}b?AiyK`9DTYoR)(S|KP(Q@*JV z$N{<%i0QHdJy0}5y^<1F8+?}_v;t6_(GR*pP 1e-2 && + abs(max_update) > 0.0 && + abs((error_luminosity - old_error_luminosity) / old_error_luminosity) > 0.01 && abs((max_update - old_max_update) / old_max_update) > 0.0 && iteration_count < 10_000 ) @@ -51,8 +55,12 @@ function engineer_caustics(source_image) ) old_max_update = max_update - max_update = solve_velocity_potential!(mesh, imageBW, "it$(iteration_count)") - print("Vertical move max update = $(max_update) \n") + old_error_luminosity = error_luminosity + max_update, error_luminosity = + solve_velocity_potential!(mesh, imageBW, "it$(iteration_count)") + print( + "Vertical move max update = $(max_update) -- Mean error luminosity = $(error_luminosity)\n", + ) end println("\nSTARTING HORIZONTAL ITERATION ---") @@ -198,7 +206,7 @@ function solve_velocity_potential!(mesh, image, prefix) plot_as_quiver(mesh, n_steps = 30, scale = 1.0, max_length = height / 20) - return max_update + return max_update, sum(abs.(error_luminosity)) / length(error_luminosity) end @@ -239,10 +247,10 @@ function move_horizontally(mesh::FaceMesh, image; f = Focal_Length) # We need to find the divergence of the Vector field described by Nx and Ny # div_row/div_col are _FENCES_SIZED_ - div_row = zeros(Float64, width, height) - div_col = zeros(Float64, width, height) - @. div_row[1:end, 1:end] = N_row[2:end, 1:end-1] - N_row[1:end-1, 1:end-1] - @. div_col[1:end, 1:end] = N_col[1:end-1, 2:end] - N_col[1:end-1, 1:end-1] + div_row = zeros(Float64, height, width) + div_col = zeros(Float64, height, width) + div_row[1:end, 1:end] = N_row[2:end, 1:end-1] .- N_row[1:end-1, 1:end-1] + div_col[1:end, 1:end] = N_col[1:end-1, 2:end] - N_col[1:end-1, 1:end-1] # divergence_direction = zeros(Float64, size(div_row)) # divergence_direction is _FENCES_SIZED_ diff --git a/src/scratchpad.jl b/src/scratchpad.jl index d5a7b98..1976b32 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -4,6 +4,9 @@ using Images using CausticsEngineering image = Images.load("./examples/cat_posing.jpg"); # Check current working directory with pwd() +image = Images.load("./examples/salvador_dali_2.jpg"); # Check current working directory with pwd() +image = Images.load("./examples/statue_of_liberty_2.jpg"); # Check current working directory with pwd() + image = Images.load("./examples/personal/caricature.jpg"); # Check current working directory with pwd() image = Images.load("./examples/personal/bilal.jpg"); # Check current working directory with pwd() image = Images.load("./examples/personal/image.jpg"); # Check current working directory with pwd() From ac3c1fde1524d4af444f4fa7668e45d48363104c Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Mon, 13 Sep 2021 16:52:38 +0200 Subject: [PATCH 28/58] Tracking area conservation bug --- examples/salvador_dali_1.jpeg | Bin 182216 -> 0 bytes examples/salvador_dali_2.jpg | Bin 245986 -> 0 bytes examples/statue_of_liberty_1.jpg | Bin 66127 -> 0 bytes examples/statue_of_liberty_2.jpg | Bin 237715 -> 0 bytes examples/statue_of_liberty_3.jpg | Bin 123033 -> 0 bytes src/create_mesh.jl | 50 +++++++++++++++++--------- src/math_utilities.jl | 13 ++++++- src/scratchpad.jl | 10 +++++- src/test_functions.jl | 59 +++++++++++++++++++++++++++++++ src/utilities.jl | 7 ++-- 10 files changed, 116 insertions(+), 23 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error_luminosity = $(maximum(error_luminosity)) / $(minimum(error_luminosity)) """ + @assert 1 - 1e-2 < sum(area_distorted_corners) < 1 + 1 + 1e-2 """ + + solve_velocity_potential: area_distorted_corners has more than 1% difference compared to 1.0 + Total luminosity through lens: $(sum(area_distorted_corners)) + Total luminosity caustics: $(sum(image)) + Total luminosity error: $(sum(error_luminosity)) + Maximum error: $(maximum(error_luminosity))") + Minimum error: $(minimum(error_luminosity))") + Iteration prefix: $(prefix) + + """ + + + # Save the loss image as a png println("Loss:") println("\tMinimum loss: $(minimum(error_luminosity))") @@ -155,7 +169,7 @@ function solve_velocity_potential!(mesh, image, prefix) ϕ, max_update = propagate_poisson(mesh.corners.ϕ, error_luminosity) mesh.corners.ϕ[:, :] .= ϕ[:, :] - @assert average_absolute(mesh.corners.ϕ) """ + @assert test_average_absolute(mesh.corners.ϕ) """ solve_velocity_potential: ϕ values seem too large iteration count = $(iteration_count) @@ -190,8 +204,7 @@ function solve_velocity_potential!(mesh, image, prefix) """ Convergence stopped at step $(iteration_count) with max_update = $(max_update) - max/min area_distorted_corners = $(maximum(area_distorted_corners)) / $(minimum(area_distorted_corners)) - max error_luminosity = $(maximum(abs.(error_luminosity))) + max / min error_luminosity = $(maximum(abs.(error_luminosity))) / $(minimum(abs.(error_luminosity))) Average mesh changes on ϕ = $(sum(abs.(mesh.corners.ϕ - mesh_ϕ)) / (height * width)) max ϕ divergence = $(maximum(abs.(mesh.corners.ϕ[begin+1:end, begin:end-1] .- mesh_ϕ[begin:end-1, begin:end-1] .+ mesh.corners.ϕ[begin:end-1, begin+1:end] .- mesh_ϕ[begin:end-1, begin:end-1]))) @@ -255,7 +268,7 @@ function move_horizontally(mesh::FaceMesh, image; f = Focal_Length) # divergence_direction = zeros(Float64, size(div_row)) # divergence_direction is _FENCES_SIZED_ divergence_direction = div_row + div_col - @assert average_absolute(divergence_direction) """ + @assert test_average_absolute(divergence_direction) """ ALERT: horiz. Δ divergence_direction seem too large max/min = $(maximum(divergence_direction)) / $(minimum(divergence_direction)) @@ -263,7 +276,7 @@ function move_horizontally(mesh::FaceMesh, image; f = Focal_Length) true_H, max_update = propagate_poisson(true_H, -divergence_direction; clamp_correction = false) - @assert average_absolute(true_H) """ + @assert test_average_absolute(true_H) """ ALERT: horiz. Δ corner_heights is too large max/min corner_heights = $(maximum(true_H)) / $(minimum(true_H)) @@ -306,7 +319,7 @@ function propagate_poisson( # Ensure that border conditions are as they should fill_borders!(∇²ϕ, 0.0) - @assert average_absolute(ϕ) """ + @assert test_average_absolute(ϕ) """ Relaxation: ϕ values seem too large max/min ∇ϕ = $(maximum(∇²ϕ)) / $(minimum(∇²ϕ)) @@ -314,7 +327,7 @@ function propagate_poisson( """ - @assert average_absolute(∇²ϕ) """ + @assert test_average_absolute(∇²ϕ) """ Relaxation: ∇²ϕ values seem too large max/min ∇²ϕ = $(maximum(∇²ϕ)) / $(minimum(∇²ϕ)) @@ -351,7 +364,7 @@ function propagate_poisson( # High intensity loss ∇²ϕ means that the triangles are too bright, too large. # This has to converge towards the ∇²ϕ. Difference to calculate speed of the descent. δ = Lϕ - ∇²ϕ - @assert average_absolute(δ) """ + @assert test_average_absolute(δ) """ Relaxation: difference between intensity loss and estimated Laplacian seem too large max/min δ = $(maximum(δ)) / $(minimum(δ)) @@ -428,14 +441,9 @@ function march_mesh!(mesh::FaceMesh) # Basically infinity time to shrink a triangle to nothing. min_positive_t = Inf - list_min_pos_t = zeros(Float64, (height - 2) * (width - 2)) - - t1 = zeros(Float64, size(mesh)) - t2 = zeros(Float64, size(mesh)) mesh_r = copy(mesh.corners.r) mesh_c = copy(mesh.corners.c) - mesh_ϕ = copy(mesh.corners.ϕ) # Get the time, at that velocity, for the area of the triangle to be nil. # We are only interested by positive values to only move in the direction of the gradient @@ -478,6 +486,14 @@ function march_mesh!(mesh::FaceMesh) """, ) + + @assert 1 - 1e-4 < get_area_corners(mesh) < 1 + 1 + 1e-4 """ + + march_meshl: area_distorted_corners is too difference from 1.0 + Total energy area: $(area_distorted_corners) + + """ + return end diff --git a/src/math_utilities.jl b/src/math_utilities.jl index 3271353..9224060 100644 --- a/src/math_utilities.jl +++ b/src/math_utilities.jl @@ -1,7 +1,18 @@ """ $(SIGNATURES) """ -average_absolute(m::AbstractMatrix) = (sum(abs.(m)) / length(m)) < 1e10 +average_absolute(m::AbstractMatrix) = (sum(abs.(m)) / length(m)) + +""" +$(SIGNATURES) +""" +average(m::AbstractMatrix) = (sum(m) / length(m)) + + +""" +$(SIGNATURES) +""" +test_average_absolute(m::AbstractMatrix) = (average_absolute(m)) < 1e10 """ diff --git a/src/scratchpad.jl b/src/scratchpad.jl index 1976b32..16310e4 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -4,17 +4,25 @@ using Images using CausticsEngineering image = Images.load("./examples/cat_posing.jpg"); # Check current working directory with pwd() + +image = Images.load("./examples/salvador_dali_1.jpg"); # Check current working directory with pwd() image = Images.load("./examples/salvador_dali_2.jpg"); # Check current working directory with pwd() image = Images.load("./examples/statue_of_liberty_2.jpg"); # Check current working directory with pwd() image = Images.load("./examples/personal/caricature.jpg"); # Check current working directory with pwd() -image = Images.load("./examples/personal/bilal.jpg"); # Check current working directory with pwd() image = Images.load("./examples/personal/image.jpg"); # Check current working directory with pwd() +image = Images.load("./examples/personal/bilal.jpg"); # Check current working directory with pwd() using Plots; gr(); mesh, imageBW = engineer_caustics(image); + +imageBW = Float64.(Gray.(image)); +total_energy_caustics = sum(imageBW) +imageBW = imageBW ./ total_energy_caustics; + + # Check a few values to make sure they make sense mesh.corners.r mesh.corners.vr diff --git a/src/test_functions.jl b/src/test_functions.jl index 2003bbd..e90e4d2 100644 --- a/src/test_functions.jl +++ b/src/test_functions.jl @@ -1,3 +1,5 @@ +using Test + """ $(SIGNATURES) @@ -40,3 +42,60 @@ function testSolidify!() solidMesh = solidify(origMesh, 0) save_stl!(solidMesh, "./examples/testSolidify2.obj") end + + + +function testAreaTriangle(x1, y1, x2, y2, x3, y3) + a = sqrt((x2 - x1)^2 + (y2 - y1)^2) + b = sqrt((x3 - x2)^2 + (y3 - y2)^2) + c = sqrt((x1 - x3)^2 + (y1 - y3)^2) + s = (a + b + c) / 2.0 + + surface_sq = (a + b + c) * (-a + b + c) * (a - b + c) * (a + b - c) / 16.0 + return surface_sq <= 1e-100 ? 1e-100 : surface_sq +end + +function doTestAreaTriangle(N = 10_000) + X1 = 10_000 .* rand(N) + Y1 = 10_000 .* rand(N) + X2 = 10_000 .* rand(N) + Y2 = 10_000 .* rand(N) + X3 = 10_000 .* rand(N) + Y3 = 10_000 .* rand(N) + + for x1 ∈ X1, y1 ∈ Y1, x2 ∈ X2, y2 ∈ Y2, x3 ∈ X3, y3 ∈ Y3 + + _ = testAreaTriangle(x1, y1, x2, y2, x3, y3) > 0.0 + end +end + +@testset "triangle area" begin + for x1 ∈ 10_000 .* rand(10_000), + y1 ∈ 10_000 .* rand(10_000), + x2 ∈ 10_000 .* rand(10_000), + y2 ∈ 10_000 .* rand(10_000), + x3 ∈ 10_000 .* rand(10_000), + y3 ∈ 10_000 .* rand(10_000) + + @test testAreaTriangle(x1, y1, x2, y2, x3, y3) > 0.0 + end +end + + + +v1 = [7250.768146661309, 4849.994680605491] +v2 = [1725.2665442814496, 8169.783790398901] +v3 = [6560.1725812433, 5264.912964907599] + +a = sqrt(sum((v2 - v1) .^ 2)) +b = sqrt(sum((v3 - v2) .^ 2)) +c = sqrt(sum((v1 - v3) .^ 2)) +s = (a + b + c) / 2.0 + +s * (s - a) * (s - b) * (s - c) +(a + b + c) * (-a + b + c) * (a - b + c) * (a + b - c) / 16.0 + +b + c +a + +10^8 * (b + c - a) diff --git a/src/utilities.jl b/src/utilities.jl index bd7c529..b486b94 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -45,10 +45,9 @@ function area(v1::Vertex3D, v2::Vertex3D, v3::Vertex3D) c = dist(v3, v1) s = (a + b + c) / 2.0 - surface = max(s * (s - a) * (s - b) * (s - c), 1 / 100.0) - @assert surface >= 0.0 "Negative surface for $(v1), $(v2), $(v3)" - - return sqrt(surface) + # surface_sq = (a + b + c) * (- a + b + c) * (a - b + c) * (a + b - c) / 16.0 + surface_sq = s * (s - a) * (s - b) * (s - c) + return surface_sq <= 1e-100 ? 1e-100 : sqrt(surface_sq) end From 8abc24c7b832f0bfb6b1663cb25ac2e28c8db09b Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Tue, 14 Sep 2021 14:50:40 +0200 Subject: [PATCH 29/58] Tracking area convergence bug --- .gitignore | 7 +- src/create_mesh.jl | 344 ++++++++++++++++++++++-------------------- src/math_utilities.jl | 15 +- src/parameters.jl | 2 +- src/scratchpad.jl | 22 +-- src/utilities.jl | 19 ++- 6 files changed, 224 insertions(+), 185 deletions(-) diff --git a/.gitignore b/.gitignore index 7607609..4d09190 100644 --- a/.gitignore +++ b/.gitignore @@ -35,8 +35,7 @@ Manifest.toml *.tmp *.temp - - - +*sync-conflict* src/debug_script.jl -examples/personal \ No newline at end of file +examples/personal + diff --git a/src/create_mesh.jl b/src/create_mesh.jl index bb9e7fa..780dcff 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -3,33 +3,30 @@ $(SIGNATURES) """ -function engineer_caustics(source_image) +function engineer_caustics(source_image; clamp_correction = true) imageBW = Float64.(Gray.(source_image)) - height, width = size(imageBW) - println("Image size: $((height, width))") - # Set some global size parameters + # Set global size parameters + height, width = size(imageBW) global N_Pixel_Height = height global N_Pixel_Width = width + global Meters_Per_Pixel = Caustics_Long_Side / N_Pixel_Height + println("Image size: $(N_Pixel_Height) x $(N_Pixel_Width)") - global Caustics_Height = Caustics_Long_Side - global Caustics_Width = Caustics_Height * N_Pixel_Width / N_Pixel_Height - - global Meters_Per_Pixel = Caustics_Height / N_Pixel_Height # mesh is the same size as the image with an extra row/column to have coordinates to # cover each image corner with a triangle. - mesh = FaceMesh(height, width) + mesh = FaceMesh(N_Pixel_Height, N_Pixel_Width) # The total energy going through the lens is equal to the amount of energy on the caustics - total_energy_lens = height * width * 1 # 1 unit of energy per pixel + total_energy_lens = N_Pixel_Height * N_Pixel_Width * 1 # 1 unit of energy per pixel total_energy_caustics = sum(imageBW) - correction_ratio = average(imageBW) + average_energy_per_pixel = average(imageBW) # imageBW is normalised to the same (sort of) _energy_ as the original image. - imageBW = imageBW ./ total_energy_caustics + imageBW = imageBW / average_energy_per_pixel # start_max_update has no particular meing. # It is basically the initial max_update. But then is used to initialise other variables so that @@ -38,13 +35,14 @@ function engineer_caustics(source_image) max_update = start_max_update old_max_update = 2 * start_max_update - error_luminosity = 1e9 + error_luminosity = 1e6 * N_Pixel_Height * N_Pixel_Width old_error_luminosity = 2 * error_luminosity iteration_count = 0 while ( - abs(max_update) > 0.0 && - abs((error_luminosity - old_error_luminosity) / old_error_luminosity) > 0.01 && + abs(max_update) > 1e-5 && + error_luminosity > 1e-2 && + abs((error_luminosity - old_error_luminosity) / old_error_luminosity) > 0.0 && abs((max_update - old_max_update) / old_max_update) > 0.0 && iteration_count < 10_000 ) @@ -56,8 +54,12 @@ function engineer_caustics(source_image) old_max_update = max_update old_error_luminosity = error_luminosity - max_update, error_luminosity = - solve_velocity_potential!(mesh, imageBW, "it$(iteration_count)") + max_update, error_luminosity = solve_velocity_potential!( + mesh, + imageBW, + "it$(iteration_count)"; + clamp_correction = clamp_correction, + ) print( "Vertical move max update = $(max_update) -- Mean error luminosity = $(error_luminosity)\n", ) @@ -65,12 +67,13 @@ function engineer_caustics(source_image) println("\nSTARTING HORIZONTAL ITERATION ---") - ϕ, max_update = move_horizontally(mesh, imageBW; f = 1.0) + ϕ, max_update = + move_horizontally(mesh, imageBW; f = Focal_Length, clamp_correction = true) mesh.corners.ϕ .= ϕ println("\t Horizontal max update = $(max_update)") # Move the around a nil average. - mean_ϕ = sum(mesh.corners.ϕ) / length(mesh.corners.ϕ) + mean_ϕ = average(mesh.corners.ϕ) mesh.corners.ϕ = mesh.corners.ϕ .- mean_ϕ return mesh, imageBW @@ -84,20 +87,20 @@ $(SIGNATURES) ϕ is the _velocity potential_. The velocity represents the direction towards which the mesh vertices should move. Zones of high luminosity should be covered with more triangles and should attract more vertices. """ -function solve_velocity_potential!(mesh, image, prefix) - # Remember mesh is (will be) `grid_definition x grid_definition` just like the image - # `grid_definition x grid_definition`, so LJ is `grid_definition x grid_definition`. - - area_distorted_corners = get_area_corners(mesh) - @assert test_average_absolute(area_distorted_corners) """ +function solve_velocity_potential!(mesh, image, prefix; clamp_correction = true) + # Get the area of each individual pixel as stretch/shrunk on the lens. Area = energy. + # _FENCES_SIZED_ + lens_pixels_area = get_lens_pixels_area(mesh) + @assert test_average_absolute(lens_pixels_area) """ - solve_velocity_potential: area_distorted_corners values seem too large - $(maximum(area_distorted_corners)) / $(minimum(area_distorted_corners)) + solve_velocity_potential: + area_distorted_corners values seem too large + $(maximum(lens_pixels_area)) / $(minimum(lens_pixels_area)) - """ + """ # Positive error => the triangle needs to shrink (less light) - error_luminosity = Float64.(area_distorted_corners - image) + error_luminosity = Float64.(lens_pixels_area - image) @assert test_average_absolute(error_luminosity) """ solve_velocity_potential: error_luminosity values seem too large @@ -105,32 +108,20 @@ function solve_velocity_potential!(mesh, image, prefix) """ - @assert 1 - 1e-2 < sum(area_distorted_corners) < 1 + 1 + 1e-2 """ - - solve_velocity_potential: area_distorted_corners has more than 1% difference compared to 1.0 - Total luminosity through lens: $(sum(area_distorted_corners)) - Total luminosity caustics: $(sum(image)) - Total luminosity error: $(sum(error_luminosity)) - Maximum error: $(maximum(error_luminosity))") - Minimum error: $(minimum(error_luminosity))") - Iteration prefix: $(prefix) - - """ - - # Save the loss image as a png - println("Loss:") - println("\tMinimum loss: $(minimum(error_luminosity))") - println("\tMaximum loss: $(maximum(error_luminosity))") + println(""" + Loss: + Maximum loss: $(maximum(error_luminosity)) + Minimum loss: $(minimum(error_luminosity)) + Average abs loss: $(average_absolute(error_luminosity)) + Average loss: $(average(error_luminosity)) + """) save_plot_scalar_field!(error_luminosity, prefix * "_loss", image) # For the purpose of Poisson, we need to divergence to increase towards the inside: negative divergence for high luminosity # error_luminosity = -error_luminosity - mesh_r = copy(mesh.corners.r) - mesh_c = copy(mesh.corners.c) mesh_ϕ = copy(mesh.corners.ϕ) - height, width = size(mesh.corners.ϕ) # start_max_update has no particular meeting. # It is basically the initial max_update. But then is used to initialise other variables so that @@ -143,22 +134,24 @@ function solve_velocity_potential!(mesh, image, prefix) new_divergence_mean = 1_000.0 while ( - abs(max_update) > 0.0 && - abs((max_update - old_max_update) / old_max_update) >= 0.01 && + abs(max_update) > 1e-5 && + abs((max_update - old_max_update) / old_max_update) >= 0.00 && new_divergence_max >= 0.0 ) iteration_count += 1 iteration_count % 100 == 0 && println("Converging for intensity: $(max_update)") - mesh.corners.ϕ[:, :] .-= sum(mesh.corners.ϕ) / (height * width) + mesh.corners.ϕ[:, :] .-= average(mesh.corners.ϕ) old_max_update = max_update println( """ + solve_velocity_potential: max/min mesh.corners.ϕ = $(maximum(mesh.corners.ϕ)) / $(minimum(mesh.corners.ϕ)) - iteration count = $(iteration_count), max_update = $(max_update) + iteration count = $(iteration_count) + max_update = $(max_update) new mean divergence = $(new_divergence_mean) new maximum divergence = $(new_divergence_max) """, @@ -166,7 +159,11 @@ function solve_velocity_potential!(mesh, image, prefix) # Solve the Poisson equation where the divergence of the gradient of ϕ is equal to the luminosity error. # High error => Too much luminosity. - ϕ, max_update = propagate_poisson(mesh.corners.ϕ, error_luminosity) + ϕ, max_update = propagate_poisson( + mesh.corners.ϕ, + error_luminosity; + clamp_correction = clamp_correction, + ) mesh.corners.ϕ[:, :] .= ϕ[:, :] @assert test_average_absolute(mesh.corners.ϕ) """ @@ -191,47 +188,44 @@ function solve_velocity_potential!(mesh, image, prefix) ) new_divergence_max = maximum(new_divergence) - new_divergence_mean = sum(new_divergence) / length(new_divergence) + new_divergence_mean = average(new_divergence) end # Relevel ϕ around its average. It doesn't matter for potential fields - mean_ϕ = sum(mesh.corners.ϕ) / length(mesh.corners.ϕ) + mean_ϕ = average(mesh.corners.ϕ) mesh.corners.ϕ .-= mean_ϕ println( """ - Convergence stopped at step $(iteration_count) with + + Luminosity convergence stopped at step $(iteration_count) with max_update = $(max_update) max / min error_luminosity = $(maximum(abs.(error_luminosity))) / $(minimum(abs.(error_luminosity))) - Average mesh changes on ϕ = $(sum(abs.(mesh.corners.ϕ - mesh_ϕ)) / (height * width)) + Average mesh changes on ϕ = $(average_absolute(mesh.corners.ϕ - mesh_ϕ)) max ϕ divergence = $(maximum(abs.(mesh.corners.ϕ[begin+1:end, begin:end-1] .- mesh_ϕ[begin:end-1, begin:end-1] .+ mesh.corners.ϕ[begin:end-1, begin+1:end] .- mesh_ϕ[begin:end-1, begin:end-1]))) """, ) - # Now we need to march the x,y locations in our mesh according to this gradient! - # Tasks are a control flow feature that allows computations to be suspended and resumed in a flexible manner. - # We mention them here only for completeness; for a full discussion see Asynchronous Programming. + # Now we need to march the mesh row,col corner locations according to this gradient. march_mesh!(mesh) + plot_as_quiver(mesh, n_steps = 30, scale = 1.0, max_length = N_Pixel_Height / 20) - plot_as_quiver(mesh, n_steps = 30, scale = 1.0, max_length = height / 20) - - return max_update, sum(abs.(error_luminosity)) / length(error_luminosity) + return max_update, average_absolute(error_luminosity) end """ $(SIGNATURES) """ -function move_horizontally(mesh::FaceMesh, image; f = Focal_Length) +function move_horizontally(mesh::FaceMesh, image; f = Focal_Length, clamp_correction = true) # height indexes rows, width indexes columns height, width = size(mesh) - # Coordinates difference # Coordinates on the caustics = simple rectangular values in corners. # Coordinates on the lens face comes from corner field. # d_row/d_col are _POSTS-SIZED_ @@ -247,40 +241,56 @@ function move_horizontally(mesh::FaceMesh, image; f = Focal_Length) # Note: Higher location means closer to the caustics => negative sign # true_H is _POSTS_SIZED_ true_H = zeros(Float64, size(mesh.corners.ϕ)) - @. true_H[:] = -mesh.corners.ϕ[:] + H + true_H = -mesh.corners.ϕ .+ H # Normals. # N_row/N_col are _POSTS_SIZED_ N_row = zeros(Float64, size(true_H)) N_col = zeros(Float64, size(true_H)) - @. N_row[1:end, 1:end] = - tan(atan(d_row[1:end, 1:end] / true_H[1:end, 1:end]) / (n₁ - n₂)) - @. N_col[1:end, 1:end] = - tan(atan(d_col[1:end, 1:end] / true_H[1:end, 1:end]) / (n₁ - n₂)) + N_row = tan.(atan.(d_row ./ true_H) / (n₁ - n₂)) + N_col = tan.(atan.(d_col ./ true_H) / (n₁ - n₂)) + + # @. N_row[1:end, 1:end] = + # tan(atan(d_row[1:end, 1:end] / true_H[1:end, 1:end]) / (n₁ - n₂)) + # @. N_col[1:end, 1:end] = + # tan(atan(d_col[1:end, 1:end] / true_H[1:end, 1:end]) / (n₁ - n₂)) # We need to find the divergence of the Vector field described by Nx and Ny # div_row/div_col are _FENCES_SIZED_ div_row = zeros(Float64, height, width) div_col = zeros(Float64, height, width) div_row[1:end, 1:end] = N_row[2:end, 1:end-1] .- N_row[1:end-1, 1:end-1] - div_col[1:end, 1:end] = N_col[1:end-1, 2:end] - N_col[1:end-1, 1:end-1] + div_col[1:end, 1:end] = N_col[1:end-1, 2:end] .- N_col[1:end-1, 1:end-1] # divergence_direction = zeros(Float64, size(div_row)) # divergence_direction is _FENCES_SIZED_ divergence_direction = div_row + div_col @assert test_average_absolute(divergence_direction) """ - ALERT: horiz. Δ divergence_direction seem too large - max/min = $(maximum(divergence_direction)) / $(minimum(divergence_direction)) - """ + ALERT: horiz. + Δ divergence_direction seem too large + max/min = $(maximum(divergence_direction)) / $(minimum(divergence_direction)) + + """ - true_H, max_update = - propagate_poisson(true_H, -divergence_direction; clamp_correction = false) + ## + ## CHECK SIGN!!! + ## + max_update = Inf + while max_update >= 1e-5 + true_H, max_update = propagate_poisson( + true_H, + divergence_direction; + clamp_correction = clamp_correction, + ) + end @assert test_average_absolute(true_H) """ - ALERT: horiz. Δ corner_heights is too large - max/min corner_heights = $(maximum(true_H)) / $(minimum(true_H)) - """ + ALERT: + horiz. Δ corner_heights is too large + max/min corner_heights = $(maximum(true_H)) / $(minimum(true_H)) + + """ println("Convergence horiz. Δ stopped with max_update of $(max_update)") @@ -317,11 +327,12 @@ function propagate_poisson( clamp_correction = true, ) - # Ensure that border conditions are as they should + # Ensure that border conditions are as they should (= 0.0) fill_borders!(∇²ϕ, 0.0) @assert test_average_absolute(ϕ) """ - Relaxation: ϕ values seem too large + Relaxation: + ϕ values seem too large max/min ∇ϕ = $(maximum(∇²ϕ)) / $(minimum(∇²ϕ)) max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) @@ -329,7 +340,8 @@ function propagate_poisson( @assert test_average_absolute(∇²ϕ) """ - Relaxation: ∇²ϕ values seem too large + Relaxation: + ∇²ϕ values seem too large max/min ∇²ϕ = $(maximum(∇²ϕ)) / $(minimum(∇²ϕ)) max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) @@ -338,76 +350,81 @@ function propagate_poisson( @assert any(isnan.(ϕ)) == false "Relaxation: calling with a ϕ that contains NaN!!" @assert any(isnan.(∇²ϕ)) == false "Relaxation: calling with a ∇²ϕ that contains NaN!!" - # ϕ is of the same size as corners = number of corners + 1 - height_corners, width_corners = size(ϕ) - height_pixels, width_pixels = size(∇²ϕ) + ################################################################################################################## # From the velocity potential field ϕ, we calculate its gradient (the velocity), then its divergence. # This is then compared to the intensity loss # Laplacian - # Those values are all of ϕ's size and represent the second order approximation of the - # Laplacian of ϕ. + # Lϕ represent the approximation of the Laplacian of ϕ (second-order value) Lϕ = laplacian(ϕ) - # @assert average_absolute(Lϕ) """ - # Relaxation: Laplacian of ϕ a seem too large - # max/min target Lϕ = $(maximum(Lϕ)) / $(minimum(Lϕ)) - # max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) - # """ + # In the case of the velocity potential, δ is the difference between the divergence of the luminosity error + # and the current one for the current field ϕ (divergence of its gradient). - # δ is the difference between the divergence of the intensity loss (in the case of the velocity potential) - # and the current one for the current field ϕ (divergence of its gradient). - # - # High intensity loss ∇²ϕ means that the triangles are too bright, too large. - # This has to converge towards the ∇²ϕ. Difference to calculate speed of the descent. + # High luminosity error ∇²ϕ means that the triangles are too bright = too large. + # The Laplacian Lϕ has to converge towards the ∇²ϕ. Difference to calculate speed of the descent. δ = Lϕ - ∇²ϕ @assert test_average_absolute(δ) """ - Relaxation: difference between intensity loss and estimated Laplacian seem too large + Relaxation: + difference between luminosity error and estimated Laplacian seem too large max/min δ = $(maximum(δ)) / $(minimum(δ)) max/min target Lϕ = $(maximum(Lϕ)) / $(minimum(Lϕ)) max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) """ - # Default correction ratio to adjust δ is 1.94/ 4.0 - correction_ratio = 1.94 / 4.0 + # Default correction ratio to adjust δ is ω / 4.0 + ω_clamped = ω / 4.0 + # We limit the changes of the potential to a maximum + max_correction_max = 20.0 + max_correction_μ = 7.0 - # Calculate the average δ that will be used to limit average changes to 5 pixels - if clamp_correction - abs_δ = abs.(δ) - maximum_δ = maximum(abs_δ) - μ_δ = sum(abs_δ) / length(abs_δ) + abs_δ = abs.(δ) + maximum_δ = maximum(abs_δ) - # We limit the changes of the potential to a maximum - max_correction_max = 20.0 - max_correction_μ = 5.0 - max_correction_in_between = 10.0 + # A correction factor is calculated to limit too wide changes on the field ϕ. + if clamp_correction + μ_δ = average(abs_δ) if maximum_δ > max_correction_max - correction_ratio = min(correction_ratio, max_correction_max / maximum_δ) + ω_clamped = min(ω_clamped, max_correction_max / maximum_δ) + println( + "Propagation clamped for maximum_δ. $(maximum_δ) > $(max_correction_max)", + ) elseif μ_δ > max_correction_μ - correction_ratio = min(correction_ratio, max_correction_μ / μ_δ) - elseif (μ_δ + maximum_δ) / 2 > max_correction_in_between - correction_ratio = - min(correction_ratio, max_correction_in_between / ((μ_δ + maximum_δ) / 2)) + ω_clamped = min(ω_clamped, max_correction_μ / μ_δ) + println("Propagation clamped for average δ. $(μ_δ) > $(max_correction_μ)") end end - # if δ > 0, the intensity loss is too high, or the Laplacian is too high at that point. - # => increase flow towards outside - # => decrease the flow towards the inside. - # => increase divergence of the flow - # => increase the height of the potential there so that gradient are locally increasing - # => correction has to be of the same sign as δ. - @. ϕ[1:height_pixels, 1:width_pixels] += - correction_ratio * δ[1:height_pixels, 1:width_pixels] - @assert !any(isnan.(ϕ)) "Relaxation: Updated ϕ contains NaN!!" + # In the case of the velocity potential, + # if δ > 0, the Laplacian is too high at that point (∇²ϕ is too low). + + # To decrease the Laplacian ∇²ϕ, note that ∇² is a divergence (of a gradient) that represents net flow going outside. + # + # Decrease the Laplacian + # => decrease a divergence + # => decrease flow towards outside + # + # The flow is a gradient of the potential ϕ. + # => decrease flow towards outside + # => either decrease the values of the potential around that point, or increase the value of the potential at that point. + # => Increase the value of ϕ at that point means a positive change when δ > 0. + # δ > 0 => correction of the SAME sign. + @. ϕ[1:N_Pixel_Height, 1:N_Pixel_Width] += + ω_clamped * δ[1:N_Pixel_Height, 1:N_Pixel_Width] + @assert !any(isnan.(ϕ)) """ + + Relaxation: + Updated ϕ contains NaN!! + + """ - max_update = correction_ratio * maximum(abs.(δ)) + max_update = ω_clamped * maximum_δ return ϕ, max_update end @@ -423,11 +440,9 @@ $(SIGNATURES) """ function march_mesh!(mesh::FaceMesh) - height, width = size(mesh.corners.ϕ) - + # Calculate the gradient of the velocity potential. ∇ϕᵤ, ∇ϕᵥ = ∇(mesh.corners.ϕ) - # For each point in the mesh we need to figure out its velocity # However all the nodes located at a border will never move # I.e. velocity (Vx, Vy) = (0, 0) and the square of acrylate will remain @@ -447,53 +462,56 @@ function march_mesh!(mesh::FaceMesh) # Get the time, at that velocity, for the area of the triangle to be nil. # We are only interested by positive values to only move in the direction of the gradient - for row ∈ 1:height-1, col ∈ 1:width-1 - list_triangles = - [triangle3D(mesh, row, col, :top), triangle3D(mesh, row, col, :bottom)] - list_maximum_t = [ - time for time ∈ find_maximum_t.(list_triangles) if - !isnan(time) && time > 0.0 && time < 1e6 - ] + list_triangles = vcat( + [ + triangle3D(mesh, row, col, :top) for row ∈ 1:N_Pixel_Height, + col ∈ 1:N_Pixel_Width + ], + [ + triangle3D(mesh, row, col, :bottom) for row ∈ 1:N_Pixel_Height, + col ∈ 1:N_Pixel_Width + ], + ) - if !isempty(list_maximum_t) - min_positive_t = minimum(list_maximum_t) + list_maximum_t = [ + time for time ∈ find_maximum_t.(list_triangles) if + !isnan(time) && time > 0.0 && time < 1e6 + ] - max_shift = max(abs(∇ϕᵤ[row, col]), abs(∇ϕᵥ[row, col])) + if !isempty(list_maximum_t) + min_positive_t = minimum(list_maximum_t) - # No shift more than 100 pixels - max_pixel_move = 100.0 + # Maximum movement along either coordinate + max_shift = max(maximum(abs.(∇ϕᵤ)), maximum(abs.(∇ϕᵥ))) - δ = min(min_positive_t / 2.0, max_pixel_move / max_shift) - δ_row = clamp.(δ * ∇ϕᵤ[row, col], -max_pixel_move, max_pixel_move) - δ_col = clamp.(δ * ∇ϕᵥ[row, col], -max_pixel_move, max_pixel_move) + # # No shift more than 10 pixels + # max_pixel_move = 10.0 + # δ = min(min_positive_t / 2.0, max_pixel_move / max_shift) - mesh.corners.r[row, col] = clamp(mesh.corners.r[row, col] + δ_row, 1, height) - mesh.corners.c[row, col] = clamp(mesh.corners.c[row, col] + δ_col, 1, width) - end + δ = min_positive_t / 2.0 + mesh.corners.r += δ * ∇ϕᵤ + mesh.corners.c += δ * ∇ϕᵥ end - # Reset the border at the fixed values fixed coordinates. reset_border_values!(mesh.corners) - println( - """ - March mesh: - max/min Vu = $(maximum(abs.(∇ϕᵤ))) / $(minimum(abs.(∇ϕᵤ))) - max/min Vv = $(maximum(abs.(∇ϕᵥ))) / $(minimum(abs.(∇ϕᵥ))) - Average mesh changes on row = $(sum(abs.(mesh.corners.r - mesh_r)) / (height * width)) - Average mesh changes on col = $(sum(abs.(mesh.corners.c - mesh_c)) / (height * width)) + println(""" + March mesh: + max/min Vu = $(maximum(abs.(∇ϕᵤ))) / $(minimum(abs.(∇ϕᵤ))) + max/min Vv = $(maximum(abs.(∇ϕᵥ))) / $(minimum(abs.(∇ϕᵥ))) + Average mesh changes on row = $(average_absolute(mesh.corners.r - mesh_r)) + Average mesh changes on col = $(average_absolute(mesh.corners.c - mesh_c)) - """, - ) + """) - @assert 1 - 1e-4 < get_area_corners(mesh) < 1 + 1 + 1e-4 """ + @assert 1 - 1e-4 < average(get_lens_pixels_area(mesh)) < 1 + 1e-4 """ - march_meshl: area_distorted_corners is too difference from 1.0 - Total energy area: $(area_distorted_corners) + march_mesh!: average energy per pixel is too different from 1.0 + Total energy per pixel: $(average(get_lens_pixels_area(mesh))) - """ - return + """ + return nothing end @@ -504,8 +522,10 @@ function ∇(ϕ::Matrix{Float64}) ∇ϕᵤ = zeros(Float64, size(ϕ)) # divergence on the right edge will be filled with zeros ∇ϕᵥ = zeros(Float64, size(ϕ)) # divergence on bottom edge will be filled with zeros - @. ∇ϕᵤ[begin:end-1, :] = ϕ[begin+1:end, :] - ϕ[begin:end-1, :] - @. ∇ϕᵥ[:, begin:end-1] = ϕ[:, begin+1:end] - ϕ[:, begin:end-1] + ∇ϕᵤ[begin:end-1, begin:end-1] = + ϕ[begin+1:end, begin:end-1] .- ϕ[begin:end-1, begin:end-1] + ∇ϕᵥ[begin:end-1, begin:end-1] = + ϕ[begin:end-1, begin+1:end] .- ϕ[begin:end-1, begin:end-1] fill_borders!(∇ϕᵤ, 0.0) fill_borders!(∇ϕᵥ, 0.0) diff --git a/src/math_utilities.jl b/src/math_utilities.jl index 9224060..29a61f5 100644 --- a/src/math_utilities.jl +++ b/src/math_utilities.jl @@ -1,28 +1,29 @@ + """ $(SIGNATURES) """ -average_absolute(m::AbstractMatrix) = (sum(abs.(m)) / length(m)) +average(m::AbstractMatrix) = (sum(m) / length(m)) + """ $(SIGNATURES) """ -average(m::AbstractMatrix) = (sum(m) / length(m)) +average_absolute(m::AbstractMatrix) = (sum(abs.(m)) / length(m)) """ $(SIGNATURES) """ -test_average_absolute(m::AbstractMatrix) = (average_absolute(m)) < 1e10 +test_average_absolute(m::AbstractMatrix) = (average_absolute(m)) < 1e6 """ $(SIGNATURES) """ function smallest_positive(x1::Float64, x2::Float64) - x1 < 0.0 && x2 < 0.0 && return -1.0 - x1 >= 0.0 && x2 < 0.0 && return x1 - x1 < 0.0 && x2 >= 0.0 && return x2 - x1 >= 0.0 && x2 >= 0.0 && return min(x1, x2) + (x1 >= 0.0 && x2 < 0.0) && return x1 + (x1 < 0.0 && x2 >= 0.0) && return x2 + (x1 >= 0.0 && x2 >= 0.0) && return min(x1, x2) return -1.0 end diff --git a/src/parameters.jl b/src/parameters.jl index d99b17a..da60a3b 100644 --- a/src/parameters.jl +++ b/src/parameters.jl @@ -32,7 +32,7 @@ global Meters_Per_Pixel = Caustics_Height / N_Pixel_Height # calculation -const ω = 1.94 +const ω = 1.99 # const ω = 2 / (1 + π / sqrt(N_Pixel_Height * N_Pixel_Width)) const N_Iterations_Convergence = 10_000 # CHECK: What is a reasonable number of iterations? diff --git a/src/scratchpad.jl b/src/scratchpad.jl index 16310e4..4e40bbc 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -1,26 +1,30 @@ using Revise, Debugger -using Images +using Images, Plots; +gr(); using CausticsEngineering image = Images.load("./examples/cat_posing.jpg"); # Check current working directory with pwd() -image = Images.load("./examples/salvador_dali_1.jpg"); # Check current working directory with pwd() -image = Images.load("./examples/salvador_dali_2.jpg"); # Check current working directory with pwd() -image = Images.load("./examples/statue_of_liberty_2.jpg"); # Check current working directory with pwd() +image = Images.load("./examples/personal/salvador_dali_1.jpg"); # Check current working directory with pwd() +image = Images.load("./examples/personal/salvador_dali_2.jpg"); # Check current working directory with pwd() + +image = Images.load("./examples/personal/statue_of_liberty_1.jpg"); # Check current working directory with pwd() +image = Images.load("./examples/personal/statue_of_liberty_2.jpg"); # Check current working directory with pwd() +image = Images.load("./examples/personal/statue_of_liberty_3.jpg"); # Check current working directory with pwd() image = Images.load("./examples/personal/caricature.jpg"); # Check current working directory with pwd() image = Images.load("./examples/personal/image.jpg"); # Check current working directory with pwd() image = Images.load("./examples/personal/bilal.jpg"); # Check current working directory with pwd() -using Plots; -gr(); -mesh, imageBW = engineer_caustics(image); +mesh, imageBW = engineer_caustics(image; clamp_correction = true); imageBW = Float64.(Gray.(image)); -total_energy_caustics = sum(imageBW) -imageBW = imageBW ./ total_energy_caustics; +average_energy_caustics = CausticsEngineering.average(imageBW) +imageBW = imageBW / average_energy_caustics; + +(sum(imageBW) / length(imageBW) - 1.0) * 1e12 # Check a few values to make sure they make sense diff --git a/src/utilities.jl b/src/utilities.jl index b486b94..e18b714 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -364,7 +364,7 @@ area in the r, r plane. h is ignored. The function returns a matrix with the quantity of light coming from each 'rectangle' around a corner. That 'rectangle' has been shifted and flexed around. """ -function get_area_corners(mesh::FaceMesh) +function get_lens_pixels_area(mesh::FaceMesh) height, width = size(mesh) top_tri_area = @@ -375,5 +375,20 @@ function get_area_corners(mesh::FaceMesh) [area(triangle3D(mesh, row, col, :bottom)...) for row ∈ 1:height, col ∈ 1:width] @assert !any(isnan.(top_tri_area)) "get_area_corners: NaN area in bottom triangles." - return top_tri_area + bot_tri_area + + total_area = top_tri_area + bot_tri_area + @assert 1.0 - 1e-4 < average(total_area) < 1.0 + 1e-4 """ + + solve_velocity_potential: + The total energy through the lens has more than 1% difference compared to 1.0 energy per pixel. + Total luminosity through lens: $(sum(lens_pixels_area)) + Average luminosity through lens: $(average(lens_pixels_area)) + Total luminosity caustics: $(sum(image)) + Total luminosity error: $(sum(error_luminosity)) + Maximum error: $(maximum(error_luminosity))") + Minimum error: $(minimum(error_luminosity))") + Iteration prefix: $(prefix) + + """ + return total_area end From 891c1f5a8e5920ff192b46a6d8efd73be10b0ee5 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Tue, 14 Sep 2021 18:54:26 +0200 Subject: [PATCH 30/58] Move divergence function to maths utilities. --- src/create_mesh.jl | 91 ++++++++++++------------------------------- src/math_utilities.jl | 24 ++++++++++++ src/scratchpad.jl | 2 +- 3 files changed, 50 insertions(+), 67 deletions(-) diff --git a/src/create_mesh.jl b/src/create_mesh.jl index 780dcff..229bef0 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -21,7 +21,7 @@ function engineer_caustics(source_image; clamp_correction = true) mesh = FaceMesh(N_Pixel_Height, N_Pixel_Width) # The total energy going through the lens is equal to the amount of energy on the caustics - total_energy_lens = N_Pixel_Height * N_Pixel_Width * 1 # 1 unit of energy per pixel + total_energy_lens = N_Pixel_Height * N_Pixel_Width * 1.0 # 1 unit of energy per pixel total_energy_caustics = sum(imageBW) average_energy_per_pixel = average(imageBW) @@ -39,13 +39,8 @@ function engineer_caustics(source_image; clamp_correction = true) old_error_luminosity = 2 * error_luminosity iteration_count = 0 - while ( - abs(max_update) > 1e-5 && - error_luminosity > 1e-2 && - abs((error_luminosity - old_error_luminosity) / old_error_luminosity) > 0.0 && - abs((max_update - old_max_update) / old_max_update) > 0.0 && - iteration_count < 10_000 - ) + while (abs(max_update) > 1e-5 && error_luminosity > 1e-5 && # abs((error_luminosity - old_error_luminosity) / old_error_luminosity) > 0.0 && # abs((max_update - old_max_update) / old_max_update) > 0.0 && + iteration_count < 10_000) iteration_count += 1 println( @@ -88,6 +83,9 @@ $(SIGNATURES) Zones of high luminosity should be covered with more triangles and should attract more vertices. """ function solve_velocity_potential!(mesh, image, prefix; clamp_correction = true) + # Keep that to track how much progress is made + mesh_ϕ = copy(mesh.corners.ϕ) + # Get the area of each individual pixel as stretch/shrunk on the lens. Area = energy. # _FENCES_SIZED_ lens_pixels_area = get_lens_pixels_area(mesh) @@ -106,22 +104,20 @@ function solve_velocity_potential!(mesh, image, prefix; clamp_correction = true) solve_velocity_potential: error_luminosity values seem too large max/min error_luminosity = $(maximum(error_luminosity)) / $(minimum(error_luminosity)) - """ + """ # Save the loss image as a png - println(""" - Loss: - Maximum loss: $(maximum(error_luminosity)) - Minimum loss: $(minimum(error_luminosity)) - Average abs loss: $(average_absolute(error_luminosity)) - Average loss: $(average(error_luminosity)) - """) + println( + """ + Luminosity error: + Max/min luminosity error: $(maximum(error_luminosity)) / $(minimum(error_luminosity)) + Average abs loss: $(average_absolute(error_luminosity)) + Average loss: $(average(error_luminosity)) + """, + ) save_plot_scalar_field!(error_luminosity, prefix * "_loss", image) - # For the purpose of Poisson, we need to divergence to increase towards the inside: negative divergence for high luminosity - # error_luminosity = -error_luminosity - mesh_ϕ = copy(mesh.corners.ϕ) # start_max_update has no particular meeting. # It is basically the initial max_update. But then is used to initialise other variables so that @@ -130,20 +126,15 @@ function solve_velocity_potential!(mesh, image, prefix; clamp_correction = true) max_update = start_max_update old_max_update = 2 * start_max_update iteration_count = 0 - new_divergence_max = 1_000.0 - new_divergence_mean = 1_000.0 while ( abs(max_update) > 1e-5 && - abs((max_update - old_max_update) / old_max_update) >= 0.00 && - new_divergence_max >= 0.0 + abs((max_update - old_max_update) / old_max_update) >= 0.00 ) iteration_count += 1 iteration_count % 100 == 0 && println("Converging for intensity: $(max_update)") - mesh.corners.ϕ[:, :] .-= average(mesh.corners.ϕ) - old_max_update = max_update println( """ @@ -164,8 +155,8 @@ function solve_velocity_potential!(mesh, image, prefix; clamp_correction = true) error_luminosity; clamp_correction = clamp_correction, ) - mesh.corners.ϕ[:, :] .= ϕ[:, :] + mesh.corners.ϕ[:, :] .= ϕ[:, :] @assert test_average_absolute(mesh.corners.ϕ) """ solve_velocity_potential: ϕ values seem too large @@ -176,22 +167,9 @@ function solve_velocity_potential!(mesh, image, prefix; clamp_correction = true) max_update = $(max_update) """ - new_divergence = - abs.( - ( - mesh.corners.ϕ[begin+1:end, begin:end-1] .- - mesh_ϕ[begin:end-1, begin:end-1] - ) .+ ( - mesh.corners.ϕ[begin:end-1, begin+1:end] .- - mesh_ϕ[begin:end-1, begin:end-1] - ), - ) - - new_divergence_max = maximum(new_divergence) - new_divergence_mean = average(new_divergence) - end + mesh.corners.ϕ[:, :] .-= average(mesh.corners.ϕ) # Relevel ϕ around its average. It doesn't matter for potential fields mean_ϕ = average(mesh.corners.ϕ) @@ -212,7 +190,7 @@ function solve_velocity_potential!(mesh, image, prefix; clamp_correction = true) # Now we need to march the mesh row,col corner locations according to this gradient. march_mesh!(mesh) - plot_as_quiver(mesh, n_steps = 30, scale = 1.0, max_length = N_Pixel_Height / 20) + plot_as_quiver(mesh, n_steps = 50, scale = 1.0, max_length = N_Pixel_Height / 20) return max_update, average_absolute(error_luminosity) end @@ -380,7 +358,7 @@ function propagate_poisson( # Default correction ratio to adjust δ is ω / 4.0 ω_clamped = ω / 4.0 # We limit the changes of the potential to a maximum - max_correction_max = 20.0 + max_correction_max = 50.0 max_correction_μ = 7.0 abs_δ = abs.(δ) @@ -447,7 +425,9 @@ function march_mesh!(mesh::FaceMesh) # However all the nodes located at a border will never move # I.e. velocity (Vx, Vy) = (0, 0) and the square of acrylate will remain # of the same size. - # Warning: The indices are necessary because corner and ∇ϕ are of different sizes + # + # CHECK - SIGN? + # mesh.corners.vr .= -∇ϕᵤ mesh.corners.vc .= -∇ϕᵥ @@ -473,10 +453,8 @@ function march_mesh!(mesh::FaceMesh) ], ) - list_maximum_t = [ - time for time ∈ find_maximum_t.(list_triangles) if - !isnan(time) && time > 0.0 && time < 1e6 - ] + list_maximum_t = + [time for time ∈ find_maximum_t.(list_triangles) if !isnan(time) && time > 0.0] if !isempty(list_maximum_t) min_positive_t = minimum(list_maximum_t) @@ -513,22 +491,3 @@ function march_mesh!(mesh::FaceMesh) """ return nothing end - - -""" -$(SIGNATURES) -""" -function ∇(ϕ::Matrix{Float64}) - ∇ϕᵤ = zeros(Float64, size(ϕ)) # divergence on the right edge will be filled with zeros - ∇ϕᵥ = zeros(Float64, size(ϕ)) # divergence on bottom edge will be filled with zeros - - ∇ϕᵤ[begin:end-1, begin:end-1] = - ϕ[begin+1:end, begin:end-1] .- ϕ[begin:end-1, begin:end-1] - ∇ϕᵥ[begin:end-1, begin:end-1] = - ϕ[begin:end-1, begin+1:end] .- ϕ[begin:end-1, begin:end-1] - - fill_borders!(∇ϕᵤ, 0.0) - fill_borders!(∇ϕᵥ, 0.0) - - return ∇ϕᵤ, ∇ϕᵥ -end diff --git a/src/math_utilities.jl b/src/math_utilities.jl index 29a61f5..17aa428 100644 --- a/src/math_utilities.jl +++ b/src/math_utilities.jl @@ -28,6 +28,30 @@ function smallest_positive(x1::Float64, x2::Float64) end +""" +$(SIGNATURES) + +Approximates the gradient of a scalar field. +""" +function ∇(ϕ::Matrix{Float64}) + # x, y only represents the first and the second variables. No reference to graphical representations. + + ∇ϕx = zeros(Float64, size(ϕ)) # divergence on the right edge will be filled with zeros + ∇ϕy = zeros(Float64, size(ϕ)) # divergence on bottom edge will be filled with zeros + + ∇ϕx[begin:end-1, begin:end-1] = + ϕ[begin+1:end, begin:end-1] .- ϕ[begin:end-1, begin:end-1] + ∇ϕy[begin:end-1, begin:end-1] = + ϕ[begin:end-1, begin+1:end] .- ϕ[begin:end-1, begin:end-1] + + fill_borders!(∇ϕx, 0.0) + fill_borders!(∇ϕy, 0.0) + + return ∇ϕx, ∇ϕy +end + + + """ $(SIGNATURES) diff --git a/src/scratchpad.jl b/src/scratchpad.jl index 4e40bbc..a662810 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -1,7 +1,7 @@ using Revise, Debugger - using Images, Plots; gr(); + using CausticsEngineering image = Images.load("./examples/cat_posing.jpg"); # Check current working directory with pwd() From 5e4dbbc0f9499114432f4ab29191f8c81dec2c03 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Wed, 15 Sep 2021 17:40:54 +0200 Subject: [PATCH 31/58] Minor. --- src/create_mesh.jl | 6 ++---- 1 file changed, 2 insertions(+), 4 deletions(-) diff --git a/src/create_mesh.jl b/src/create_mesh.jl index 229bef0..b085305 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -143,8 +143,6 @@ function solve_velocity_potential!(mesh, image, prefix; clamp_correction = true) max/min mesh.corners.ϕ = $(maximum(mesh.corners.ϕ)) / $(minimum(mesh.corners.ϕ)) iteration count = $(iteration_count) max_update = $(max_update) - new mean divergence = $(new_divergence_mean) - new maximum divergence = $(new_divergence_max) """, ) @@ -358,8 +356,8 @@ function propagate_poisson( # Default correction ratio to adjust δ is ω / 4.0 ω_clamped = ω / 4.0 # We limit the changes of the potential to a maximum - max_correction_max = 50.0 - max_correction_μ = 7.0 + max_correction_max = 1e12 + max_correction_μ = 100.0 abs_δ = abs.(δ) maximum_δ = maximum(abs_δ) From 8be5b20bcbbc8c9ece8226dd412b1b2f9a1e6420 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Thu, 16 Sep 2021 08:58:06 +0200 Subject: [PATCH 32/58] Tracking converging bug. --- src/create_mesh.jl | 145 +++++++++++++++++++++++++++++---------------- 1 file changed, 94 insertions(+), 51 deletions(-) diff --git a/src/create_mesh.jl b/src/create_mesh.jl index b085305..76f6e74 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -28,7 +28,7 @@ function engineer_caustics(source_image; clamp_correction = true) # imageBW is normalised to the same (sort of) _energy_ as the original image. imageBW = imageBW / average_energy_per_pixel - # start_max_update has no particular meing. + # start_max_update has no particular meaning. # It is basically the initial max_update. But then is used to initialise other variables so that # not to stop the `while` loop on the first iteration start_max_update = 1_000.0 @@ -39,8 +39,14 @@ function engineer_caustics(source_image; clamp_correction = true) old_error_luminosity = 2 * error_luminosity iteration_count = 0 - while (abs(max_update) > 1e-5 && error_luminosity > 1e-5 && # abs((error_luminosity - old_error_luminosity) / old_error_luminosity) > 0.0 && # abs((max_update - old_max_update) / old_max_update) > 0.0 && - iteration_count < 10_000) + # OLD + # while (abs(max_update) > 1e-5 && error_luminosity > 1e-5 && # abs((error_luminosity - old_error_luminosity) / old_error_luminosity) > 0.0 && # abs((max_update - old_max_update) / old_max_update) > 0.0 && + # OLD + while ( + 1e-8 < abs(max_update) < 10 * start_max_update && + 1e-6 < abs((max_update - old_max_update) / old_max_update) && + iteration_count < 10_000 + ) iteration_count += 1 println( @@ -126,10 +132,12 @@ function solve_velocity_potential!(mesh, image, prefix; clamp_correction = true) max_update = start_max_update old_max_update = 2 * start_max_update iteration_count = 0 + new_divergence = 0.0 while ( - abs(max_update) > 1e-5 && - abs((max_update - old_max_update) / old_max_update) >= 0.00 + 1e-5 < abs(max_update) < 10 * start_max_update && + 1e06 < abs((max_update - old_max_update) / old_max_update) && + new_divergence < 100.0 ) iteration_count += 1 @@ -169,6 +177,15 @@ function solve_velocity_potential!(mesh, image, prefix; clamp_correction = true) mesh.corners.ϕ[:, :] .-= average(mesh.corners.ϕ) + new_divergence = maximum( + abs.( + mesh.corners.ϕ[begin+1:end, begin:end-1] .- + mesh.corners.ϕ[begin:end-1, begin:end-1] .+ + mesh.corners.ϕ[begin:end-1, begin+1:end] .- + mesh.corners.ϕ[begin:end-1, begin:end-1], + ), + ) + # Relevel ϕ around its average. It doesn't matter for potential fields mean_ϕ = average(mesh.corners.ϕ) mesh.corners.ϕ .-= mean_ϕ @@ -223,13 +240,13 @@ function move_horizontally(mesh::FaceMesh, image; f = Focal_Length, clamp_correc # N_row/N_col are _POSTS_SIZED_ N_row = zeros(Float64, size(true_H)) N_col = zeros(Float64, size(true_H)) - N_row = tan.(atan.(d_row ./ true_H) / (n₁ - n₂)) - N_col = tan.(atan.(d_col ./ true_H) / (n₁ - n₂)) + # N_row = tan.(atan.(d_row ./ true_H) / (n₁ - n₂)) + # N_col = tan.(atan.(d_col ./ true_H) / (n₁ - n₂)) - # @. N_row[1:end, 1:end] = - # tan(atan(d_row[1:end, 1:end] / true_H[1:end, 1:end]) / (n₁ - n₂)) - # @. N_col[1:end, 1:end] = - # tan(atan(d_col[1:end, 1:end] / true_H[1:end, 1:end]) / (n₁ - n₂)) + @. N_row[1:end, 1:end] = + tan(atan(d_row[1:end, 1:end] / true_H[1:end, 1:end]) / (n₁ - n₂)) + @. N_col[1:end, 1:end] = + tan(atan(d_col[1:end, 1:end] / true_H[1:end, 1:end]) / (n₁ - n₂)) # We need to find the divergence of the Vector field described by Nx and Ny # div_row/div_col are _FENCES_SIZED_ @@ -253,13 +270,13 @@ function move_horizontally(mesh::FaceMesh, image; f = Focal_Length, clamp_correc ## CHECK SIGN!!! ## max_update = Inf - while max_update >= 1e-5 - true_H, max_update = propagate_poisson( - true_H, - divergence_direction; - clamp_correction = clamp_correction, - ) - end + # while max_update >= 1e-5 + true_H, max_update = propagate_poisson( + true_H, + -divergence_direction; + clamp_correction = clamp_correction, + ) + # end @assert test_average_absolute(true_H) """ ALERT: @@ -355,9 +372,10 @@ function propagate_poisson( # Default correction ratio to adjust δ is ω / 4.0 ω_clamped = ω / 4.0 + # We limit the changes of the potential to a maximum - max_correction_max = 1e12 - max_correction_μ = 100.0 + max_correction_max = 5.0 + max_correction_μ = 1e5 abs_δ = abs.(δ) maximum_δ = maximum(abs_δ) @@ -375,6 +393,12 @@ function propagate_poisson( ω_clamped = min(ω_clamped, max_correction_μ / μ_δ) println("Propagation clamped for average δ. $(μ_δ) > $(max_correction_μ)") end + + if ω / 4.0 * maximum_δ < max_correction_max + ω_clamped = ω / 4.0 + else + ω_clamped = max_correction_max / maximum_δ + end end # In the case of the velocity potential, @@ -417,8 +441,29 @@ $(SIGNATURES) function march_mesh!(mesh::FaceMesh) # Calculate the gradient of the velocity potential. + # _POSTS_SIZED_ ∇ϕᵤ, ∇ϕᵥ = ∇(mesh.corners.ϕ) + # Normalize the vectors + vector_length = zeros(Float64, N_Pixel_Height + 1, N_Pixel_Width + 1) + @. vector_length = max.(sqrt(∇ϕᵤ^2 + ∇ϕᵥ^2), 1e-12) + ∇ϕᵤ ./= vector_length + ∇ϕᵥ ./= vector_length + + @assert !any(isnan.(∇ϕᵤ)) """ + + march_mesh!: + ∇ϕᵤ contains NaN!! + + """ + + @assert !any(isnan.(∇ϕᵥ)) """ + + march_mesh!: + ∇ϕᵥ contains NaN!! + + """ + # For each point in the mesh we need to figure out its velocity # However all the nodes located at a border will never move # I.e. velocity (Vx, Vy) = (0, 0) and the square of acrylate will remain @@ -426,48 +471,46 @@ function march_mesh!(mesh::FaceMesh) # # CHECK - SIGN? # + # _POSTS_SIZED_ mesh.corners.vr .= -∇ϕᵤ mesh.corners.vc .= -∇ϕᵥ # Just in case... reset_border_values!(mesh.corners) - # Basically infinity time to shrink a triangle to nothing. - min_positive_t = Inf - mesh_r = copy(mesh.corners.r) mesh_c = copy(mesh.corners.c) # Get the time, at that velocity, for the area of the triangle to be nil. - # We are only interested by positive values to only move in the direction of the gradient - list_triangles = vcat( - [ - triangle3D(mesh, row, col, :top) for row ∈ 1:N_Pixel_Height, - col ∈ 1:N_Pixel_Width - ], - [ - triangle3D(mesh, row, col, :bottom) for row ∈ 1:N_Pixel_Height, - col ∈ 1:N_Pixel_Width - ], - ) + # _FENCES_SIZED_ + top_triangles = + [triangle3D(mesh, row, col, :top) for row ∈ 1:N_Pixel_Height, col ∈ 1:N_Pixel_Width] - list_maximum_t = - [time for time ∈ find_maximum_t.(list_triangles) if !isnan(time) && time > 0.0] + # Get the maximum moximum move along the distance of the gradient + # _POSTS_SIZED_ + max_move_length = zeros(Float64, N_Pixel_Height + 1, N_Pixel_Width + 1) + max_move_length[1:N_Pixel_Height, 1:N_Pixel_Width] .= find_maximum_t.(top_triangles) + @assert !any(isnan.(max_move_length)) """ - if !isempty(list_maximum_t) - min_positive_t = minimum(list_maximum_t) + march_mesh!: + max_move_length contains NaN!! - # Maximum movement along either coordinate - max_shift = max(maximum(abs.(∇ϕᵤ)), maximum(abs.(∇ϕᵥ))) + """ - # # No shift more than 10 pixels - # max_pixel_move = 10.0 - # δ = min(min_positive_t / 2.0, max_pixel_move / max_shift) - δ = min_positive_t / 2.0 - mesh.corners.r += δ * ∇ϕᵤ - mesh.corners.c += δ * ∇ϕᵥ - end + # Maximum movement along either coordinate + max_pixel_move = 20.0 + + δ = min.(max_move_length / 2.0, max_pixel_move) + @assert !any(isnan.(δ)) """ + + march_mesh!: + δ contains NaN!! + + """ + + @. mesh.corners.r += δ * ∇ϕᵤ + @. mesh.corners.c += δ * ∇ϕᵥ # Reset the border at the fixed values fixed coordinates. reset_border_values!(mesh.corners) @@ -481,11 +524,11 @@ function march_mesh!(mesh::FaceMesh) """) - @assert 1 - 1e-4 < average(get_lens_pixels_area(mesh)) < 1 + 1e-4 """ + # @assert 1 - 1e-4 < average(get_lens_pixels_area(mesh)) < 1 + 1e-4 """ - march_mesh!: average energy per pixel is too different from 1.0 - Total energy per pixel: $(average(get_lens_pixels_area(mesh))) + # march_mesh!: average energy per pixel is too different from 1.0 + # Total energy per pixel: $(average(get_lens_pixels_area(mesh))) - """ + # """ return nothing end From ca33de31965726466f634b95d0a489aec6a80447 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Thu, 16 Sep 2021 13:49:23 +0200 Subject: [PATCH 33/58] Tracking area convergence bug --- src/create_mesh.jl | 207 +++++++++++++++++++++--------------------- src/math_utilities.jl | 12 +-- src/mesh.jl | 12 ++- src/scratchpad.jl | 1 + src/test_functions.jl | 31 ++++++- src/utilities.jl | 58 +++--------- 6 files changed, 160 insertions(+), 161 deletions(-) diff --git a/src/create_mesh.jl b/src/create_mesh.jl index 76f6e74..079f28c 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -15,18 +15,13 @@ function engineer_caustics(source_image; clamp_correction = true) println("Image size: $(N_Pixel_Height) x $(N_Pixel_Width)") - # mesh is the same size as the image with an extra row/column to have coordinates to # cover each image corner with a triangle. mesh = FaceMesh(N_Pixel_Height, N_Pixel_Width) # The total energy going through the lens is equal to the amount of energy on the caustics - total_energy_lens = N_Pixel_Height * N_Pixel_Width * 1.0 # 1 unit of energy per pixel - total_energy_caustics = sum(imageBW) - average_energy_per_pixel = average(imageBW) - # imageBW is normalised to the same (sort of) _energy_ as the original image. - imageBW = imageBW / average_energy_per_pixel + imageBW = imageBW / average(imageBW) # start_max_update has no particular meaning. # It is basically the initial max_update. But then is used to initialise other variables so that @@ -43,14 +38,17 @@ function engineer_caustics(source_image; clamp_correction = true) # while (abs(max_update) > 1e-5 && error_luminosity > 1e-5 && # abs((error_luminosity - old_error_luminosity) / old_error_luminosity) > 0.0 && # abs((max_update - old_max_update) / old_max_update) > 0.0 && # OLD while ( - 1e-8 < abs(max_update) < 10 * start_max_update && - 1e-6 < abs((max_update - old_max_update) / old_max_update) && - iteration_count < 10_000 + # 1e-8 < abs(max_update) < 10 * start_max_update && + # 1e-6 < abs((max_update - old_max_update) / old_max_update) && + iteration_count < 10 ) iteration_count += 1 - println( - "\nSTARTING VERTICAL ITERATION $(iteration_count) --------------------------------------------", + println(""" + engineer_caustics: + STARTING VERTICAL ITERATION $(iteration_count) -------------------------------------------- + + """, ) old_max_update = max_update @@ -61,17 +59,26 @@ function engineer_caustics(source_image; clamp_correction = true) "it$(iteration_count)"; clamp_correction = clamp_correction, ) - print( - "Vertical move max update = $(max_update) -- Mean error luminosity = $(error_luminosity)\n", + print(""" + engineer_caustics: + Vertical move max update = $(max_update) -- Mean error luminosity = $(error_luminosity) + """, ) end - println("\nSTARTING HORIZONTAL ITERATION ---") + println("\nSTARTING HORIZONTAL ITERATION AFTER $(iteration_count) iterations ---\n") ϕ, max_update = move_horizontally(mesh, imageBW; f = Focal_Length, clamp_correction = true) - mesh.corners.ϕ .= ϕ - println("\t Horizontal max update = $(max_update)") + mesh.corners.ϕ = ϕ + + println(""" + engineer_caustics: + max/min ϕ = $(maximum(abs.(ϕ))) / $(minimum(abs.(ϕ))) + size ϕ = $(size(ϕ)) + average ϕ = $(average_absolute(ϕ)) + Horizontal max update = $(max_update) + """) # Move the around a nil average. mean_ϕ = average(mesh.corners.ϕ) @@ -95,33 +102,19 @@ function solve_velocity_potential!(mesh, image, prefix; clamp_correction = true) # Get the area of each individual pixel as stretch/shrunk on the lens. Area = energy. # _FENCES_SIZED_ lens_pixels_area = get_lens_pixels_area(mesh) - @assert test_average_absolute(lens_pixels_area) """ - - solve_velocity_potential: - area_distorted_corners values seem too large - $(maximum(lens_pixels_area)) / $(minimum(lens_pixels_area)) - - """ # Positive error => the triangle needs to shrink (less light) error_luminosity = Float64.(lens_pixels_area - image) + println(""" + solve_velocity_potential: + max/min error_luminosity: $(maximum(error_luminosity)) / $(minimum(error_luminosity)) + """) @assert test_average_absolute(error_luminosity) """ solve_velocity_potential: error_luminosity values seem too large max/min error_luminosity = $(maximum(error_luminosity)) / $(minimum(error_luminosity)) """ - - - # Save the loss image as a png - println( - """ - Luminosity error: - Max/min luminosity error: $(maximum(error_luminosity)) / $(minimum(error_luminosity)) - Average abs loss: $(average_absolute(error_luminosity)) - Average loss: $(average(error_luminosity)) - """, - ) save_plot_scalar_field!(error_luminosity, prefix * "_loss", image) @@ -136,7 +129,7 @@ function solve_velocity_potential!(mesh, image, prefix; clamp_correction = true) while ( 1e-5 < abs(max_update) < 10 * start_max_update && - 1e06 < abs((max_update - old_max_update) / old_max_update) && + 1e-6 < abs((max_update - old_max_update) / old_max_update) && new_divergence < 100.0 ) @@ -146,9 +139,8 @@ function solve_velocity_potential!(mesh, image, prefix; clamp_correction = true) old_max_update = max_update println( """ - - solve_velocity_potential: - max/min mesh.corners.ϕ = $(maximum(mesh.corners.ϕ)) / $(minimum(mesh.corners.ϕ)) + solve_velocity_potential: before propagation + max/min ϕ = $(maximum(mesh.corners.ϕ)) / $(minimum(mesh.corners.ϕ)) iteration count = $(iteration_count) max_update = $(max_update) """, @@ -162,9 +154,20 @@ function solve_velocity_potential!(mesh, image, prefix; clamp_correction = true) clamp_correction = clamp_correction, ) - mesh.corners.ϕ[:, :] .= ϕ[:, :] - @assert test_average_absolute(mesh.corners.ϕ) """ + mean_ϕ = sum(ϕ) / length(ϕ) + mesh.corners.ϕ = ϕ .- mean_ϕ + println( + """ + solve_velocity_potential: after propagation + max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) + + max/min mesh.corners.ϕ = $(maximum(mesh.corners.ϕ)) / $(minimum(mesh.corners.ϕ)) + iteration count = $(iteration_count) + max_update = $(max_update) + """, + ) + @assert test_average_absolute(mesh.corners.ϕ) """ solve_velocity_potential: ϕ values seem too large iteration count = $(iteration_count) max/min mesh.corners.ϕ = $(maximum(mesh.corners.ϕ)) / $(minimum(mesh.corners.ϕ)) @@ -173,22 +176,16 @@ function solve_velocity_potential!(mesh, image, prefix; clamp_correction = true) max_update = $(max_update) """ - end - - mesh.corners.ϕ[:, :] .-= average(mesh.corners.ϕ) - - new_divergence = maximum( - abs.( - mesh.corners.ϕ[begin+1:end, begin:end-1] .- - mesh.corners.ϕ[begin:end-1, begin:end-1] .+ - mesh.corners.ϕ[begin:end-1, begin+1:end] .- - mesh.corners.ϕ[begin:end-1, begin:end-1], - ), - ) + new_divergence = maximum( + abs.( + mesh.corners.ϕ[begin+1:end, begin:end-1] .- + mesh.corners.ϕ[begin:end-1, begin:end-1] .+ + mesh.corners.ϕ[begin:end-1, begin+1:end] .- + mesh.corners.ϕ[begin:end-1, begin:end-1], + ), + ) - # Relevel ϕ around its average. It doesn't matter for potential fields - mean_ϕ = average(mesh.corners.ϕ) - mesh.corners.ϕ .-= mean_ϕ + end println( """ @@ -240,9 +237,6 @@ function move_horizontally(mesh::FaceMesh, image; f = Focal_Length, clamp_correc # N_row/N_col are _POSTS_SIZED_ N_row = zeros(Float64, size(true_H)) N_col = zeros(Float64, size(true_H)) - # N_row = tan.(atan.(d_row ./ true_H) / (n₁ - n₂)) - # N_col = tan.(atan.(d_col ./ true_H) / (n₁ - n₂)) - @. N_row[1:end, 1:end] = tan(atan(d_row[1:end, 1:end] / true_H[1:end, 1:end]) / (n₁ - n₂)) @. N_col[1:end, 1:end] = @@ -269,14 +263,11 @@ function move_horizontally(mesh::FaceMesh, image; f = Focal_Length, clamp_correc ## ## CHECK SIGN!!! ## - max_update = Inf - # while max_update >= 1e-5 true_H, max_update = propagate_poisson( true_H, -divergence_direction; clamp_correction = clamp_correction, ) - # end @assert test_average_absolute(true_H) """ ALERT: @@ -374,8 +365,8 @@ function propagate_poisson( ω_clamped = ω / 4.0 # We limit the changes of the potential to a maximum - max_correction_max = 5.0 - max_correction_μ = 1e5 + max_correction_max = 2.0 + max_correction_μ = 5.0 abs_δ = abs.(δ) maximum_δ = maximum(abs_δ) @@ -415,9 +406,9 @@ function propagate_poisson( # => either decrease the values of the potential around that point, or increase the value of the potential at that point. # => Increase the value of ϕ at that point means a positive change when δ > 0. # δ > 0 => correction of the SAME sign. - @. ϕ[1:N_Pixel_Height, 1:N_Pixel_Width] += - ω_clamped * δ[1:N_Pixel_Height, 1:N_Pixel_Width] - @assert !any(isnan.(ϕ)) """ + ϕ2 = zeros(Float64, size(ϕ)) + @. ϕ2[1:N_Pixel_Height, 1:N_Pixel_Width] = ϕ[1:N_Pixel_Height, 1:N_Pixel_Width] + ω_clamped * δ[1:N_Pixel_Height, 1:N_Pixel_Width] + @assert !any(isnan.(ϕ2)) """ Relaxation: Updated ϕ contains NaN!! @@ -425,8 +416,7 @@ function propagate_poisson( """ max_update = ω_clamped * maximum_δ - - return ϕ, max_update + return ϕ2, max_update end @@ -440,15 +430,22 @@ $(SIGNATURES) """ function march_mesh!(mesh::FaceMesh) + println(""" + March mesh: + max/min ϕ = $(maximum(abs.(mesh.corners.ϕ))) / $(minimum(abs.(mesh.corners.ϕ))) + size ϕ = $(size(mesh.corners.ϕ)) + average ϕ = $(average_absolute(mesh.corners.ϕ)) + """) + # Calculate the gradient of the velocity potential. # _POSTS_SIZED_ ∇ϕᵤ, ∇ϕᵥ = ∇(mesh.corners.ϕ) # Normalize the vectors vector_length = zeros(Float64, N_Pixel_Height + 1, N_Pixel_Width + 1) - @. vector_length = max.(sqrt(∇ϕᵤ^2 + ∇ϕᵥ^2), 1e-12) - ∇ϕᵤ ./= vector_length - ∇ϕᵥ ./= vector_length + @. vector_length = sqrt(∇ϕᵤ^2 + ∇ϕᵥ^2) + ∇ϕᵤ[vector_length .!= 0.0] ./= vector_length[vector_length .!= 0.0] + ∇ϕᵥ[vector_length .!= 0.0] ./= vector_length[vector_length .!= 0.0] @assert !any(isnan.(∇ϕᵤ)) """ @@ -456,7 +453,6 @@ function march_mesh!(mesh::FaceMesh) ∇ϕᵤ contains NaN!! """ - @assert !any(isnan.(∇ϕᵥ)) """ march_mesh!: @@ -464,13 +460,20 @@ function march_mesh!(mesh::FaceMesh) """ + println(""" + march_mesh!: + max/min ∇ϕᵤ = $(maximum(abs.(∇ϕᵤ))) / $(minimum(abs.(∇ϕᵤ))) + size ∇ϕᵤ = $(size(∇ϕᵤ)) + average ∇ϕᵤ = $(average_absolute(∇ϕᵤ)) + max/min ∇ϕᵥ = $(maximum(abs.(∇ϕᵥ))) / $(minimum(abs.(∇ϕᵥ))) + size ∇ϕᵥ = $(size(∇ϕᵥ)) + average ∇ϕᵥ = $(average_absolute(∇ϕᵥ)) + """) + # For each point in the mesh we need to figure out its velocity # However all the nodes located at a border will never move # I.e. velocity (Vx, Vy) = (0, 0) and the square of acrylate will remain # of the same size. - # - # CHECK - SIGN? - # # _POSTS_SIZED_ mesh.corners.vr .= -∇ϕᵤ mesh.corners.vc .= -∇ϕᵥ @@ -481,33 +484,34 @@ function march_mesh!(mesh::FaceMesh) mesh_r = copy(mesh.corners.r) mesh_c = copy(mesh.corners.c) - # Get the time, at that velocity, for the area of the triangle to be nil. + # Get the time, at that velocity, for the area of the triangle to become nil. # _FENCES_SIZED_ - top_triangles = - [triangle3D(mesh, row, col, :top) for row ∈ 1:N_Pixel_Height, col ∈ 1:N_Pixel_Width] + top_triangles = [triangle3D(mesh, row, col, :top) for row ∈ 1:N_Pixel_Height, col ∈ 1:N_Pixel_Width] + bot_triangles = [triangle3D(mesh, row, col, :bottom) for row ∈ 1:N_Pixel_Height, col ∈ 1:N_Pixel_Width] # Get the maximum moximum move along the distance of the gradient # _POSTS_SIZED_ - max_move_length = zeros(Float64, N_Pixel_Height + 1, N_Pixel_Width + 1) - max_move_length[1:N_Pixel_Height, 1:N_Pixel_Width] .= find_maximum_t.(top_triangles) - @assert !any(isnan.(max_move_length)) """ + max_move = zeros(Float64, N_Pixel_Height + 1, N_Pixel_Width + 1) + max_move[1:N_Pixel_Height, 1:N_Pixel_Width] = min.(find_maximum_t.(top_triangles), find_maximum_t.(bot_triangles)) + @. max_move[isnan(max_move)] = 0.0 - march_mesh!: - max_move_length contains NaN!! - - """ + println(""" + march_mesh!: + max_move max/min t: $(maximum(max_move)) / $(minimum(max_move)) + TOP max/min t: $(maximum(find_maximum_t.(top_triangles))) / $(minimum(find_maximum_t.(top_triangles))) + BOT max/min t: $(maximum(find_maximum_t.(bot_triangles))) / $(minimum(find_maximum_t.(bot_triangles))) + """) - # Maximum movement along either coordinate - max_pixel_move = 20.0 - δ = min.(max_move_length / 2.0, max_pixel_move) - @assert !any(isnan.(δ)) """ - march_mesh!: - δ contains NaN!! + # Maximum movement along either coordinate + max_pixel_move = 10.0 - """ + # δ = zeros(Float64, N_Pixel_Height + 1, N_Pixel_Width + 1) + # δ = min.(max_move / 2.0, max_pixel_move) + δ = max_move / 2.0 + println("Size δ = $(size(δ))") @. mesh.corners.r += δ * ∇ϕᵤ @. mesh.corners.c += δ * ∇ϕᵥ @@ -516,19 +520,12 @@ function march_mesh!(mesh::FaceMesh) reset_border_values!(mesh.corners) println(""" - March mesh: - max/min Vu = $(maximum(abs.(∇ϕᵤ))) / $(minimum(abs.(∇ϕᵤ))) - max/min Vv = $(maximum(abs.(∇ϕᵥ))) / $(minimum(abs.(∇ϕᵥ))) - Average mesh changes on row = $(average_absolute(mesh.corners.r - mesh_r)) - Average mesh changes on col = $(average_absolute(mesh.corners.c - mesh_c)) - - """) - - # @assert 1 - 1e-4 < average(get_lens_pixels_area(mesh)) < 1 + 1e-4 """ - - # march_mesh!: average energy per pixel is too different from 1.0 - # Total energy per pixel: $(average(get_lens_pixels_area(mesh))) + march_mesh!: + Average mesh changes on row = $(average_absolute(mesh.corners.r - mesh_r)) + Average mesh changes on col = $(average_absolute(mesh.corners.c - mesh_c)) + Top left rows: $(mesh.corners.r[1:5, 1:5]) + Top right rows: $(mesh.corners.r[1:5, end-5:end]) + """) - # """ return nothing end diff --git a/src/math_utilities.jl b/src/math_utilities.jl index 17aa428..bdf252b 100644 --- a/src/math_utilities.jl +++ b/src/math_utilities.jl @@ -24,7 +24,7 @@ function smallest_positive(x1::Float64, x2::Float64) (x1 >= 0.0 && x2 < 0.0) && return x1 (x1 < 0.0 && x2 >= 0.0) && return x2 (x1 >= 0.0 && x2 >= 0.0) && return min(x1, x2) - return -1.0 + return 0.0 end @@ -33,16 +33,14 @@ $(SIGNATURES) Approximates the gradient of a scalar field. """ -function ∇(ϕ::Matrix{Float64}) +function ∇(ϕ::AbstractMatrix{Float64}) # x, y only represents the first and the second variables. No reference to graphical representations. ∇ϕx = zeros(Float64, size(ϕ)) # divergence on the right edge will be filled with zeros ∇ϕy = zeros(Float64, size(ϕ)) # divergence on bottom edge will be filled with zeros - ∇ϕx[begin:end-1, begin:end-1] = - ϕ[begin+1:end, begin:end-1] .- ϕ[begin:end-1, begin:end-1] - ∇ϕy[begin:end-1, begin:end-1] = - ϕ[begin:end-1, begin+1:end] .- ϕ[begin:end-1, begin:end-1] + @. ∇ϕx[begin:end-1, :] = ϕ[begin+1:end, :] - ϕ[begin:end-1, :] + @. ∇ϕy[:, begin:end-1] = ϕ[:, begin+1:end] - ϕ[:, begin:end-1] fill_borders!(∇ϕx, 0.0) fill_borders!(∇ϕy, 0.0) @@ -71,7 +69,7 @@ function laplacian(ϕ::AbstractMatrix{Float64}) # The Laplace operator can be calculated by convolving a kernel. # See https://www.wikiwand.com/en/Discrete_Laplace_operator for simple example in 2D - kernel = ([[0.0 1.0 0.0]; [1.0 -4.0 1.0]; [0.0 1.0 0.0]]) + kernel = [[0.0 1.0 0.0]; [1.0 -4.0 1.0]; [0.0 1.0 0.0]] # Convolution ∇²ϕ = zeros(Float64, height, width) diff --git a/src/mesh.jl b/src/mesh.jl index f295b42..cb9f0fa 100644 --- a/src/mesh.jl +++ b/src/mesh.jl @@ -4,6 +4,12 @@ $(SIGNATURES) Given 3 points and their velocities, calculate the time `t` required to bring the area of that triangle to zero """ function find_maximum_t(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) + # If a triangle is too small, no move + if area(p1, p2, p3) < 1e-3 + return 0.0 + end + + # Three points A, B and C, with coordinates (x, y) # The area of a triangle is 1/2 * [ Ax (By - Cy) + Bx (Cy - Ay) + Cx (Ay - By)] # where each point of the triangle is where it will be after time t @@ -32,21 +38,21 @@ function find_maximum_t(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) # if a = 0, this is just a linear equation. if a == 0 && b != 0 - return smallest_positive(-c / b, c / b) + return min(smallest_positive(-c / b, c / b), 2.0) else discriminant = b^2 - 4a * c # If there is a solution if discriminant >= 0 d = sqrt(discriminant) - return smallest_positive((-b - d) / 2a, (-b + d) / 2a) + return min(smallest_positive((-b - d) / 2a, (-b + d) / 2a), 2.0) end end # There can be no solution if, after translation, B abd C move in parallel direction. # C will never end up on the line AB. # Very unlikely with Float64. # Negative numbers are filtered out when calculating the minimum jiggle ratio - return -1.0 + return 0.0 end find_maximum_t(p::Tuple{Vertex3D,Vertex3D,Vertex3D}) = find_maximum_t(p[1], p[2], p[3]) diff --git a/src/scratchpad.jl b/src/scratchpad.jl index a662810..88f3742 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -15,6 +15,7 @@ image = Images.load("./examples/personal/statue_of_liberty_3.jpg"); # Check curr image = Images.load("./examples/personal/caricature.jpg"); # Check current working directory with pwd() image = Images.load("./examples/personal/image.jpg"); # Check current working directory with pwd() +image = Images.load("./examples/personal/portrait.jpg"); # Check current working directory with pwd() image = Images.load("./examples/personal/bilal.jpg"); # Check current working directory with pwd() mesh, imageBW = engineer_caustics(image; clamp_correction = true); diff --git a/src/test_functions.jl b/src/test_functions.jl index e90e4d2..931ce99 100644 --- a/src/test_functions.jl +++ b/src/test_functions.jl @@ -1,3 +1,4 @@ +using CausticsEngineering using Test """ @@ -45,6 +46,8 @@ end + + function testAreaTriangle(x1, y1, x2, y2, x3, y3) a = sqrt((x2 - x1)^2 + (y2 - y1)^2) b = sqrt((x3 - x2)^2 + (y3 - y2)^2) @@ -52,7 +55,7 @@ function testAreaTriangle(x1, y1, x2, y2, x3, y3) s = (a + b + c) / 2.0 surface_sq = (a + b + c) * (-a + b + c) * (a - b + c) * (a + b - c) / 16.0 - return surface_sq <= 1e-100 ? 1e-100 : surface_sq + return surface_sq <= 1e-100 ? 0.0 : surface_sq end function doTestAreaTriangle(N = 10_000) @@ -77,10 +80,34 @@ end x3 ∈ 10_000 .* rand(10_000), y3 ∈ 10_000 .* rand(10_000) - @test testAreaTriangle(x1, y1, x2, y2, x3, y3) > 0.0 + @test testAreaTriangle(x1, y1, x2, y2, x3, y3) >= 0.0 end end +@testset "More triangle area" begin + @test area(0, 1, 1 , 0, 0, 0) +end + + +v1 = CausticsEngineering.Vertex3D(0.0, 1.0, 0.0 , 0.0, 0.0) +v2 = CausticsEngineering.Vertex3D(1.0, 0.0, 0.0 , 0.0, 0.0) +v3 = CausticsEngineering.Vertex3D(0.0, 0.0, 0.0 , 0.0, 0.0) +CausticsEngineering.area(v1, v2, v3) + +v1 = CausticsEngineering.Vertex3D(0.0, 2.0, 0.0 , 0.0, 0.0) +v2 = CausticsEngineering.Vertex3D(2.0, 0.0, 0.0 , 0.0, 0.0) +v3 = CausticsEngineering.Vertex3D(0.0, 0.0, 0.0 , 0.0, 0.0) +CausticsEngineering.area(v1, v2, v3) + +fm = CausticsEngineering.FaceMesh(512, 512); +fm.toptriangles[1, 1] +CausticsEngineering.triangle3D(fm, 1, 1, :top) +CausticsEngineering.area(CausticsEngineering.triangle3D(fm, 1, 1, :top)...) +CausticsEngineering.area(CausticsEngineering.triangle3D(fm, 1, 1, :bottom)...) + +CausticsEngineering.area(CausticsEngineering.triangle3D(fm, 126, 13, :top)...) +CausticsEngineering.area(CausticsEngineering.triangle3D(fm, 126, 13, :bottom)...) + v1 = [7250.768146661309, 4849.994680605491] diff --git a/src/utilities.jl b/src/utilities.jl index e18b714..374ce8a 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -47,7 +47,7 @@ function area(v1::Vertex3D, v2::Vertex3D, v3::Vertex3D) # surface_sq = (a + b + c) * (- a + b + c) * (a - b + c) * (a + b - c) / 16.0 surface_sq = s * (s - a) * (s - b) * (s - c) - return surface_sq <= 1e-100 ? 1e-100 : sqrt(surface_sq) + return surface_sq <= 1e-100 ? 0.0 : sqrt(surface_sq) end @@ -226,23 +226,6 @@ Return the dimension of the mesh as the number of rectangles. It does not return Base.size(mesh::FaceMesh) = mesh.size -""" -$(TYPEDEF) -""" -struct Triangle - mesh::FaceMesh - points::Tuple{Int,Int,Int} - - function Triangle(mesh::FaceMesh) - return Triangle( - mesh, - Tuple(mesh.as_index(1, 1), mesh.as_index(2, 1), mesh.as_index(1, 2)), - ) - end -end - - - """ $(SIGNATURES) @@ -250,7 +233,7 @@ Converts a triangle as a triplet of references to mesh vertices to a triplet of """ function triangle3D(mesh::FaceMesh, row::Int, col::Int, side = Union{:top,:bottom}) height, width = size(mesh) - max_distance_sq = ((height + 1) * (width + 1))^2 + max_distance_squared = (height + 1)^2 + (width + 1)^2 if 1 <= row <= height && 1 <= col <= width if side == :top @@ -268,21 +251,21 @@ function triangle3D(mesh::FaceMesh, row::Int, col::Int, side = Union{:top,:botto ϕ1 = mesh.corners.ϕ[t1_row, t1_col] vr1 = mesh.corners.vr[t1_row, t1_col] vc1 = mesh.corners.vc[t1_row, t1_col] - @assert r1^2 + c1^2 <= max_distance_sq "Coordinate $(r1), $(c1), $(ϕ1) of point #1 at $(row), $(col), side = $(side) makes no sense " + @assert r1^2 + c1^2 <= max_distance_squared "Coordinate $(r1), $(c1), $(ϕ1) of point #1 at $(row), $(col), side = $(side) makes no sense " r2 = mesh.corners.r[t2_row, t2_col] c2 = mesh.corners.c[t2_row, t2_col] ϕ2 = mesh.corners.ϕ[t2_row, t2_col] vr2 = mesh.corners.vr[t2_row, t2_col] vc2 = mesh.corners.vc[t2_row, t2_col] - @assert r2^2 + c2^2 <= max_distance_sq "Coordinate $(r2), $(c2), $(ϕ2) of point #2 at $(row), $(col), side = $(side) makes no sense " + @assert r2^2 + c2^2 <= max_distance_squared "Coordinate $(r2), $(c2), $(ϕ2) of point #2 at $(row), $(col), side = $(side) makes no sense " r3 = mesh.corners.r[t3_row, t3_col] c3 = mesh.corners.c[t3_row, t3_col] ϕ3 = mesh.corners.ϕ[t3_row, t3_col] vr3 = mesh.corners.vr[t3_row, t3_col] vc3 = mesh.corners.vc[t3_row, t3_col] - @assert r3^2 + c3^2 <= max_distance_sq "Coordinate $(r3), $(c3), $(ϕ3) of point #3 at $(row), $(col), side = $(side) makes no sense " + @assert r3^2 + c3^2 <= max_distance_squared "Coordinate $(r3), $(c3), $(ϕ3) of point #3 at $(row), $(col), side = $(side) makes no sense " p1 = Vertex3D(r1, c1, ϕ1, vr1, vc1) p2 = Vertex3D(r2, c2, ϕ2, vr2, vc2) @@ -354,6 +337,10 @@ function area(mesh::FaceMesh, row::Int, col::Int; side = Union{:top,:bottom}) end end +""" +$(SIGNATURES) +""" +area(t::Tuple{Vertex3D, Vertex3D, Vertex3D}) = area(t...) """ $(SIGNATURES) @@ -367,28 +354,11 @@ has been shifted and flexed around. function get_lens_pixels_area(mesh::FaceMesh) height, width = size(mesh) - top_tri_area = - [area(triangle3D(mesh, row, col, :top)...) for row ∈ 1:height, col ∈ 1:width] - @assert !any(isnan.(top_tri_area)) "get_area_corners: NaN area in top triangles." - - bot_tri_area = - [area(triangle3D(mesh, row, col, :bottom)...) for row ∈ 1:height, col ∈ 1:width] - @assert !any(isnan.(top_tri_area)) "get_area_corners: NaN area in bottom triangles." - + top_tri_area = area.([triangle3D(mesh, row, col, :bottom) for row ∈ 1:height, col ∈ 1:width]) + bot_tri_area = area.([triangle3D(mesh, row, col, :bottom) for row ∈ 1:height, col ∈ 1:width]) total_area = top_tri_area + bot_tri_area - @assert 1.0 - 1e-4 < average(total_area) < 1.0 + 1e-4 """ - - solve_velocity_potential: - The total energy through the lens has more than 1% difference compared to 1.0 energy per pixel. - Total luminosity through lens: $(sum(lens_pixels_area)) - Average luminosity through lens: $(average(lens_pixels_area)) - Total luminosity caustics: $(sum(image)) - Total luminosity error: $(sum(error_luminosity)) - Maximum error: $(maximum(error_luminosity))") - Minimum error: $(minimum(error_luminosity))") - Iteration prefix: $(prefix) - - """ - return total_area + + average_energy_per_pixel = average(total_area) + return total_area / average_energy_per_pixel end From cadba11d458cfb53a01eee14959bfabd272d8fa0 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Thu, 16 Sep 2021 15:08:43 +0200 Subject: [PATCH 34/58] Tracking convergence bug --- src/create_mesh.jl | 228 +++++++++++++++++++++++++----------------- src/math_utilities.jl | 1 - src/test_functions.jl | 14 +-- src/utilities.jl | 8 +- 4 files changed, 147 insertions(+), 104 deletions(-) diff --git a/src/create_mesh.jl b/src/create_mesh.jl index 079f28c..7a4ca2b 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -34,21 +34,17 @@ function engineer_caustics(source_image; clamp_correction = true) old_error_luminosity = 2 * error_luminosity iteration_count = 0 - # OLD - # while (abs(max_update) > 1e-5 && error_luminosity > 1e-5 && # abs((error_luminosity - old_error_luminosity) / old_error_luminosity) > 0.0 && # abs((max_update - old_max_update) / old_max_update) > 0.0 && - # OLD - while ( - # 1e-8 < abs(max_update) < 10 * start_max_update && - # 1e-6 < abs((max_update - old_max_update) / old_max_update) && - iteration_count < 10 - ) + while (1e-6 < abs(max_update) < 10 * start_max_update && + # 1e-4 < abs((max_update - old_max_update) / old_max_update) && + iteration_count < 1_024) iteration_count += 1 - println(""" - engineer_caustics: - STARTING VERTICAL ITERATION $(iteration_count) -------------------------------------------- + println( + """ + engineer_caustics: + STARTING VERTICAL ITERATION $(iteration_count) -------------------------------------------- - """, + """, ) old_max_update = max_update @@ -56,13 +52,14 @@ function engineer_caustics(source_image; clamp_correction = true) max_update, error_luminosity = solve_velocity_potential!( mesh, imageBW, - "it$(iteration_count)"; + "loss_it$(iteration_count)"; clamp_correction = clamp_correction, ) - print(""" - engineer_caustics: - Vertical move max update = $(max_update) -- Mean error luminosity = $(error_luminosity) - """, + print( + """ + engineer_caustics: + Vertical move max update = $(max_update) -- Mean error luminosity = $(error_luminosity) + """, ) end @@ -70,7 +67,7 @@ function engineer_caustics(source_image; clamp_correction = true) ϕ, max_update = move_horizontally(mesh, imageBW; f = Focal_Length, clamp_correction = true) - mesh.corners.ϕ = ϕ + mesh.corners.ϕ .= ϕ println(""" engineer_caustics: @@ -105,10 +102,12 @@ function solve_velocity_potential!(mesh, image, prefix; clamp_correction = true) # Positive error => the triangle needs to shrink (less light) error_luminosity = Float64.(lens_pixels_area - image) - println(""" - solve_velocity_potential: - max/min error_luminosity: $(maximum(error_luminosity)) / $(minimum(error_luminosity)) - """) + println( + """ + solve_velocity_potential: + max/min error_luminosity: $(maximum(error_luminosity)) / $(minimum(error_luminosity)) + """, + ) @assert test_average_absolute(error_luminosity) """ solve_velocity_potential: error_luminosity values seem too large @@ -129,7 +128,7 @@ function solve_velocity_potential!(mesh, image, prefix; clamp_correction = true) while ( 1e-5 < abs(max_update) < 10 * start_max_update && - 1e-6 < abs((max_update - old_max_update) / old_max_update) && + 1e-2 < abs((max_update - old_max_update) / old_max_update) && new_divergence < 100.0 ) @@ -137,17 +136,18 @@ function solve_velocity_potential!(mesh, image, prefix; clamp_correction = true) iteration_count % 100 == 0 && println("Converging for intensity: $(max_update)") old_max_update = max_update - println( - """ - solve_velocity_potential: before propagation - max/min ϕ = $(maximum(mesh.corners.ϕ)) / $(minimum(mesh.corners.ϕ)) - iteration count = $(iteration_count) - max_update = $(max_update) - """, - ) + println(""" + solve_velocity_potential: before propagation + max/min ϕ = $(maximum(mesh.corners.ϕ)) / $(minimum(mesh.corners.ϕ)) + iteration count = $(iteration_count) + max_update = $(max_update) + """) # Solve the Poisson equation where the divergence of the gradient of ϕ is equal to the luminosity error. # High error => Too much luminosity. + mean_ϕ = sum(mesh.corners.ϕ) / length(mesh.corners.ϕ) + mesh.corners.ϕ .-= mean_ϕ + ϕ, max_update = propagate_poisson( mesh.corners.ϕ, error_luminosity; @@ -156,6 +156,8 @@ function solve_velocity_potential!(mesh, image, prefix; clamp_correction = true) mean_ϕ = sum(ϕ) / length(ϕ) mesh.corners.ϕ = ϕ .- mean_ϕ + + println( """ solve_velocity_potential: after propagation @@ -231,7 +233,7 @@ function move_horizontally(mesh::FaceMesh, image; f = Focal_Length, clamp_correc # Note: Higher location means closer to the caustics => negative sign # true_H is _POSTS_SIZED_ true_H = zeros(Float64, size(mesh.corners.ϕ)) - true_H = -mesh.corners.ϕ .+ H + @. true_H = -mesh.corners.ϕ + H # Normals. # N_row/N_col are _POSTS_SIZED_ @@ -364,34 +366,48 @@ function propagate_poisson( # Default correction ratio to adjust δ is ω / 4.0 ω_clamped = ω / 4.0 + maximum_δ = maximum(abs.(δ)) + # We limit the changes of the potential to a maximum - max_correction_max = 2.0 - max_correction_μ = 5.0 - - abs_δ = abs.(δ) - maximum_δ = maximum(abs_δ) - - # A correction factor is calculated to limit too wide changes on the field ϕ. - if clamp_correction - μ_δ = average(abs_δ) - - if maximum_δ > max_correction_max - ω_clamped = min(ω_clamped, max_correction_max / maximum_δ) - println( - "Propagation clamped for maximum_δ. $(maximum_δ) > $(max_correction_max)", - ) - elseif μ_δ > max_correction_μ - ω_clamped = min(ω_clamped, max_correction_μ / μ_δ) - println("Propagation clamped for average δ. $(μ_δ) > $(max_correction_μ)") - end + max_correction_ratio = 10.0 - if ω / 4.0 * maximum_δ < max_correction_max - ω_clamped = ω / 4.0 - else - ω_clamped = max_correction_max / maximum_δ - end + if 1.94 / 4.0 * maximum_δ < max_correction_ratio + correction_ratio = 1.94 / 4.0 + else + correction_ratio = max_correction_ratio / maximum_δ end + # if δ > 0, the intensity loss is too high, or the Laplacian is too high at that point. + # => increase flow towards outside + # => decrease the flow towards the inside. + # => increase divergence of the flow + # => increase the height of the potential there so that gradient are locally increasing + # => correction has to be of the same sign as δ. + @. ϕ[1:N_Pixel_Height, 1:N_Pixel_Width] += + correction_ratio * δ[1:N_Pixel_Height, 1:N_Pixel_Width] + + # # We limit the changes of the potential to a maximum + # max_correction_max = 10.0 + # max_correction_μ = 20.0 + + # abs_δ = abs.(δ) + # maximum_δ = maximum(abs_δ) + + # # A correction factor is calculated to limit too wide changes on the field ϕ. + # if clamp_correction + # μ_δ = average(abs_δ) + + # if ω_clamped * maximum_δ > max_correction_max + # ω_clamped = min(ω_clamped, max_correction_max / maximum_δ) + # println( + # "Propagation clamped for maximum_δ. $(maximum_δ) > $(max_correction_max)", + # ) + # elseif ω_clamped * μ_δ > max_correction_μ + # ω_clamped = min(ω_clamped, max_correction_μ / μ_δ) + # println("Propagation clamped for average δ. $(μ_δ) > $(max_correction_μ)") + # end + # end + # In the case of the velocity potential, # if δ > 0, the Laplacian is too high at that point (∇²ϕ is too low). @@ -406,9 +422,9 @@ function propagate_poisson( # => either decrease the values of the potential around that point, or increase the value of the potential at that point. # => Increase the value of ϕ at that point means a positive change when δ > 0. # δ > 0 => correction of the SAME sign. - ϕ2 = zeros(Float64, size(ϕ)) - @. ϕ2[1:N_Pixel_Height, 1:N_Pixel_Width] = ϕ[1:N_Pixel_Height, 1:N_Pixel_Width] + ω_clamped * δ[1:N_Pixel_Height, 1:N_Pixel_Width] - @assert !any(isnan.(ϕ2)) """ + @. ϕ[1:N_Pixel_Height, 1:N_Pixel_Width] += + ω_clamped * δ[1:N_Pixel_Height, 1:N_Pixel_Width] + @assert !any(isnan.(ϕ)) """ Relaxation: Updated ϕ contains NaN!! @@ -416,7 +432,7 @@ function propagate_poisson( """ max_update = ω_clamped * maximum_δ - return ϕ2, max_update + return ϕ, max_update end @@ -441,11 +457,11 @@ function march_mesh!(mesh::FaceMesh) # _POSTS_SIZED_ ∇ϕᵤ, ∇ϕᵥ = ∇(mesh.corners.ϕ) - # Normalize the vectors - vector_length = zeros(Float64, N_Pixel_Height + 1, N_Pixel_Width + 1) - @. vector_length = sqrt(∇ϕᵤ^2 + ∇ϕᵥ^2) - ∇ϕᵤ[vector_length .!= 0.0] ./= vector_length[vector_length .!= 0.0] - ∇ϕᵥ[vector_length .!= 0.0] ./= vector_length[vector_length .!= 0.0] + # # Normalize the vectors + # vector_length = zeros(Float64, N_Pixel_Height + 1, N_Pixel_Width + 1) + # @. vector_length = sqrt(∇ϕᵤ^2 + ∇ϕᵥ^2) + # ∇ϕᵤ[vector_length .!= 0.0] ./= vector_length[vector_length .!= 0.0] + # ∇ϕᵥ[vector_length .!= 0.0] ./= vector_length[vector_length .!= 0.0] @assert !any(isnan.(∇ϕᵤ)) """ @@ -484,37 +500,63 @@ function march_mesh!(mesh::FaceMesh) mesh_r = copy(mesh.corners.r) mesh_c = copy(mesh.corners.c) - # Get the time, at that velocity, for the area of the triangle to become nil. - # _FENCES_SIZED_ - top_triangles = [triangle3D(mesh, row, col, :top) for row ∈ 1:N_Pixel_Height, col ∈ 1:N_Pixel_Width] - bot_triangles = [triangle3D(mesh, row, col, :bottom) for row ∈ 1:N_Pixel_Height, col ∈ 1:N_Pixel_Width] - - # Get the maximum moximum move along the distance of the gradient - # _POSTS_SIZED_ - max_move = zeros(Float64, N_Pixel_Height + 1, N_Pixel_Width + 1) - max_move[1:N_Pixel_Height, 1:N_Pixel_Width] = min.(find_maximum_t.(top_triangles), find_maximum_t.(bot_triangles)) - @. max_move[isnan(max_move)] = 0.0 - - - println(""" - march_mesh!: - max_move max/min t: $(maximum(max_move)) / $(minimum(max_move)) - TOP max/min t: $(maximum(find_maximum_t.(top_triangles))) / $(minimum(find_maximum_t.(top_triangles))) - BOT max/min t: $(maximum(find_maximum_t.(bot_triangles))) / $(minimum(find_maximum_t.(bot_triangles))) - """) - - + # # Get the time, at that velocity, for the area of the triangle to become nil. + # # _FENCES_SIZED_ + # top_triangles = [triangle3D(mesh, row, col, :top) for row ∈ 1:N_Pixel_Height, col ∈ 1:N_Pixel_Width] + # bot_triangles = [triangle3D(mesh, row, col, :bottom) for row ∈ 1:N_Pixel_Height, col ∈ 1:N_Pixel_Width] + + # # Get the maximum moximum move along the distance of the gradient + # # _POSTS_SIZED_ + # max_move = zeros(Float64, N_Pixel_Height + 1, N_Pixel_Width + 1) + # max_move[1:N_Pixel_Height, 1:N_Pixel_Width] = min.(find_maximum_t.(top_triangles), find_maximum_t.(bot_triangles)) + # @. max_move[isnan(max_move)] = 0.0 + + + # println(""" + # march_mesh!: + # max_move max/min t: $(maximum(max_move)) / $(minimum(max_move)) + # TOP max/min t: $(maximum(find_maximum_t.(top_triangles))) / $(minimum(find_maximum_t.(top_triangles))) + # BOT max/min t: $(maximum(find_maximum_t.(bot_triangles))) / $(minimum(find_maximum_t.(bot_triangles))) + # """) + + # Get the time, at that velocity, for the area of the triangle to be nil. + # We are only interested by positive values to only move in the direction of the gradient + height, width = size(mesh.corners.ϕ) + for row ∈ 1:height-1, col ∈ 1:width-1 + list_triangles = + [triangle3D(mesh, row, col, :top), triangle3D(mesh, row, col, :bottom)] + list_maximum_t = [ + time for time ∈ find_maximum_t.(list_triangles) if + !isnan(time) && time > 0.0 && time < 10.0 + ] + + if !isempty(list_maximum_t) + min_positive_t = minimum(list_maximum_t) + + # @assert all(typeof.(t1) .== Float64) && all(typeof.(t2) .== Float64) "March mesh: Maximum times are not numerical at $(row), $(col)" + + max_shift = max(abs(∇ϕᵤ[row, col]), abs(∇ϕᵥ[row, col])) + + # No shift more than 20 pixels + max_pixel_move = 20.0 + δ = min(min_positive_t / 2.0, max_pixel_move / max_shift) + mesh.corners.r[row, col] = + clamp(mesh.corners.r[row, col] + δ * ∇ϕᵤ[row, col], 1, height - 1) + mesh.corners.c[row, col] = + clamp(mesh.corners.c[row, col] + δ * ∇ϕᵥ[row, col], 1, width - 1) + end + end - # Maximum movement along either coordinate - max_pixel_move = 10.0 + # # Maximum movement along either coordinate + # max_pixel_move = 10.0 - # δ = zeros(Float64, N_Pixel_Height + 1, N_Pixel_Width + 1) - # δ = min.(max_move / 2.0, max_pixel_move) - δ = max_move / 2.0 - println("Size δ = $(size(δ))") + # # δ = zeros(Float64, N_Pixel_Height + 1, N_Pixel_Width + 1) + # # δ = min.(max_move / 2.0, max_pixel_move) + # δ = max_move / 2.0 + # println("Size δ = $(size(δ))") - @. mesh.corners.r += δ * ∇ϕᵤ - @. mesh.corners.c += δ * ∇ϕᵥ + # @. mesh.corners.r += δ * ∇ϕᵤ + # @. mesh.corners.c += δ * ∇ϕᵥ # Reset the border at the fixed values fixed coordinates. reset_border_values!(mesh.corners) diff --git a/src/math_utilities.jl b/src/math_utilities.jl index bdf252b..a49c08b 100644 --- a/src/math_utilities.jl +++ b/src/math_utilities.jl @@ -35,7 +35,6 @@ Approximates the gradient of a scalar field. """ function ∇(ϕ::AbstractMatrix{Float64}) # x, y only represents the first and the second variables. No reference to graphical representations. - ∇ϕx = zeros(Float64, size(ϕ)) # divergence on the right edge will be filled with zeros ∇ϕy = zeros(Float64, size(ϕ)) # divergence on bottom edge will be filled with zeros diff --git a/src/test_functions.jl b/src/test_functions.jl index 931ce99..275836a 100644 --- a/src/test_functions.jl +++ b/src/test_functions.jl @@ -85,18 +85,18 @@ end end @testset "More triangle area" begin - @test area(0, 1, 1 , 0, 0, 0) + @test area(0, 1, 1, 0, 0, 0) end -v1 = CausticsEngineering.Vertex3D(0.0, 1.0, 0.0 , 0.0, 0.0) -v2 = CausticsEngineering.Vertex3D(1.0, 0.0, 0.0 , 0.0, 0.0) -v3 = CausticsEngineering.Vertex3D(0.0, 0.0, 0.0 , 0.0, 0.0) +v1 = CausticsEngineering.Vertex3D(0.0, 1.0, 0.0, 0.0, 0.0) +v2 = CausticsEngineering.Vertex3D(1.0, 0.0, 0.0, 0.0, 0.0) +v3 = CausticsEngineering.Vertex3D(0.0, 0.0, 0.0, 0.0, 0.0) CausticsEngineering.area(v1, v2, v3) -v1 = CausticsEngineering.Vertex3D(0.0, 2.0, 0.0 , 0.0, 0.0) -v2 = CausticsEngineering.Vertex3D(2.0, 0.0, 0.0 , 0.0, 0.0) -v3 = CausticsEngineering.Vertex3D(0.0, 0.0, 0.0 , 0.0, 0.0) +v1 = CausticsEngineering.Vertex3D(0.0, 2.0, 0.0, 0.0, 0.0) +v2 = CausticsEngineering.Vertex3D(2.0, 0.0, 0.0, 0.0, 0.0) +v3 = CausticsEngineering.Vertex3D(0.0, 0.0, 0.0, 0.0, 0.0) CausticsEngineering.area(v1, v2, v3) fm = CausticsEngineering.FaceMesh(512, 512); diff --git a/src/utilities.jl b/src/utilities.jl index 374ce8a..a4c0a10 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -340,7 +340,7 @@ end """ $(SIGNATURES) """ -area(t::Tuple{Vertex3D, Vertex3D, Vertex3D}) = area(t...) +area(t::Tuple{Vertex3D,Vertex3D,Vertex3D}) = area(t...) """ $(SIGNATURES) @@ -354,8 +354,10 @@ has been shifted and flexed around. function get_lens_pixels_area(mesh::FaceMesh) height, width = size(mesh) - top_tri_area = area.([triangle3D(mesh, row, col, :bottom) for row ∈ 1:height, col ∈ 1:width]) - bot_tri_area = area.([triangle3D(mesh, row, col, :bottom) for row ∈ 1:height, col ∈ 1:width]) + top_tri_area = + area.([triangle3D(mesh, row, col, :bottom) for row ∈ 1:height, col ∈ 1:width]) + bot_tri_area = + area.([triangle3D(mesh, row, col, :bottom) for row ∈ 1:height, col ∈ 1:width]) total_area = top_tri_area + bot_tri_area From 76baa6628e2c7a550e9cf73940334ab669e8b8ba Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Fri, 17 Sep 2021 14:18:32 +0200 Subject: [PATCH 35/58] Tracking convergence bug --- src/create_mesh.jl | 348 +++++++++++++++++------------------------- src/math_utilities.jl | 8 +- src/mesh.jl | 14 +- src/scratchpad.jl | 3 +- 4 files changed, 148 insertions(+), 225 deletions(-) diff --git a/src/create_mesh.jl b/src/create_mesh.jl index 7a4ca2b..fdac851 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -15,15 +15,20 @@ function engineer_caustics(source_image; clamp_correction = true) println("Image size: $(N_Pixel_Height) x $(N_Pixel_Width)") + # mesh is the same size as the image with an extra row/column to have coordinates to # cover each image corner with a triangle. mesh = FaceMesh(N_Pixel_Height, N_Pixel_Width) # The total energy going through the lens is equal to the amount of energy on the caustics + total_energy_lens = N_Pixel_Height * N_Pixel_Width * 1.0 # 1 unit of energy per pixel + total_energy_caustics = sum(imageBW) + average_energy_per_pixel = average(imageBW) + # imageBW is normalised to the same (sort of) _energy_ as the original image. - imageBW = imageBW / average(imageBW) + imageBW = imageBW / average_energy_per_pixel - # start_max_update has no particular meaning. + # start_max_update has no particular meing. # It is basically the initial max_update. But then is used to initialise other variables so that # not to stop the `while` loop on the first iteration start_max_update = 1_000.0 @@ -34,17 +39,17 @@ function engineer_caustics(source_image; clamp_correction = true) old_error_luminosity = 2 * error_luminosity iteration_count = 0 - while (1e-6 < abs(max_update) < 10 * start_max_update && - # 1e-4 < abs((max_update - old_max_update) / old_max_update) && - iteration_count < 1_024) + # abs((error_luminosity - old_error_luminosity) / old_error_luminosity) > 0.0 && + # abs((max_update - old_max_update) / old_max_update) > 0.0 && + while ( + abs(max_update) > 1e-5 && + error_luminosity > 1e-5 && + iteration_count < 10_000 + ) iteration_count += 1 println( - """ - engineer_caustics: - STARTING VERTICAL ITERATION $(iteration_count) -------------------------------------------- - - """, + "\nSTARTING VERTICAL ITERATION $(iteration_count) --------------------------------------------", ) old_max_update = max_update @@ -52,30 +57,20 @@ function engineer_caustics(source_image; clamp_correction = true) max_update, error_luminosity = solve_velocity_potential!( mesh, imageBW, - "loss_it$(iteration_count)"; + "it$(iteration_count)"; clamp_correction = clamp_correction, ) print( - """ - engineer_caustics: - Vertical move max update = $(max_update) -- Mean error luminosity = $(error_luminosity) - """, + "Vertical move max update = $(max_update) -- Mean error luminosity = $(error_luminosity)\n", ) end - println("\nSTARTING HORIZONTAL ITERATION AFTER $(iteration_count) iterations ---\n") + println("\nSTARTING HORIZONTAL ITERATION ---") ϕ, max_update = move_horizontally(mesh, imageBW; f = Focal_Length, clamp_correction = true) mesh.corners.ϕ .= ϕ - - println(""" - engineer_caustics: - max/min ϕ = $(maximum(abs.(ϕ))) / $(minimum(abs.(ϕ))) - size ϕ = $(size(ϕ)) - average ϕ = $(average_absolute(ϕ)) - Horizontal max update = $(max_update) - """) + println("\t Horizontal max update = $(max_update)") # Move the around a nil average. mean_ϕ = average(mesh.corners.ϕ) @@ -99,21 +94,34 @@ function solve_velocity_potential!(mesh, image, prefix; clamp_correction = true) # Get the area of each individual pixel as stretch/shrunk on the lens. Area = energy. # _FENCES_SIZED_ lens_pixels_area = get_lens_pixels_area(mesh) + @assert test_average_absolute(lens_pixels_area) """ + + solve_velocity_potential: + area_distorted_corners values seem too large + $(maximum(lens_pixels_area)) / $(minimum(lens_pixels_area)) + + """ # Positive error => the triangle needs to shrink (less light) error_luminosity = Float64.(lens_pixels_area - image) - println( - """ - solve_velocity_potential: - max/min error_luminosity: $(maximum(error_luminosity)) / $(minimum(error_luminosity)) - """, - ) + error_luminosity = error_luminosity .- average(error_luminosity) @assert test_average_absolute(error_luminosity) """ solve_velocity_potential: error_luminosity values seem too large max/min error_luminosity = $(maximum(error_luminosity)) / $(minimum(error_luminosity)) """ + + + # Save the loss image as a png + println( + """ + Luminosity error: + Max/min luminosity error: $(maximum(error_luminosity)) / $(minimum(error_luminosity)) + Average abs loss: $(average_absolute(error_luminosity)) + Average loss: $(average(error_luminosity)) + """, + ) save_plot_scalar_field!(error_luminosity, prefix * "_loss", image) @@ -124,52 +132,36 @@ function solve_velocity_potential!(mesh, image, prefix; clamp_correction = true) max_update = start_max_update old_max_update = 2 * start_max_update iteration_count = 0 - new_divergence = 0.0 while ( - 1e-5 < abs(max_update) < 10 * start_max_update && - 1e-2 < abs((max_update - old_max_update) / old_max_update) && - new_divergence < 100.0 + abs(max_update) > 1e-5 && + iteration_count <= 1_000 ) - iteration_count += 1 - iteration_count % 100 == 0 && println("Converging for intensity: $(max_update)") - old_max_update = max_update - println(""" - solve_velocity_potential: before propagation - max/min ϕ = $(maximum(mesh.corners.ϕ)) / $(minimum(mesh.corners.ϕ)) - iteration count = $(iteration_count) - max_update = $(max_update) - """) - - # Solve the Poisson equation where the divergence of the gradient of ϕ is equal to the luminosity error. - # High error => Too much luminosity. - mean_ϕ = sum(mesh.corners.ϕ) / length(mesh.corners.ϕ) - mesh.corners.ϕ .-= mean_ϕ - - ϕ, max_update = propagate_poisson( - mesh.corners.ϕ, - error_luminosity; - clamp_correction = clamp_correction, - ) - - mean_ϕ = sum(ϕ) / length(ϕ) - mesh.corners.ϕ = ϕ .- mean_ϕ - - println( + iteration_count % 10 == 0 && println("Converging for intensity: $(max_update)") + iteration_count % 10 == 0 && println( """ - solve_velocity_potential: after propagation - max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) + solve_velocity_potential: max/min mesh.corners.ϕ = $(maximum(mesh.corners.ϕ)) / $(minimum(mesh.corners.ϕ)) iteration count = $(iteration_count) max_update = $(max_update) """, ) + # Solve the Poisson equation where the divergence of the gradient of ϕ is equal to the luminosity error. + # High error => Too much luminosity. + ϕ, max_update = propagate_poisson( + mesh.corners.ϕ, + error_luminosity; + clamp_correction = clamp_correction, + ) + + mesh.corners.ϕ[:, :] .= ϕ[:, :] @assert test_average_absolute(mesh.corners.ϕ) """ + solve_velocity_potential: ϕ values seem too large iteration count = $(iteration_count) max/min mesh.corners.ϕ = $(maximum(mesh.corners.ϕ)) / $(minimum(mesh.corners.ϕ)) @@ -178,17 +170,14 @@ function solve_velocity_potential!(mesh, image, prefix; clamp_correction = true) max_update = $(max_update) """ - new_divergence = maximum( - abs.( - mesh.corners.ϕ[begin+1:end, begin:end-1] .- - mesh.corners.ϕ[begin:end-1, begin:end-1] .+ - mesh.corners.ϕ[begin:end-1, begin+1:end] .- - mesh.corners.ϕ[begin:end-1, begin:end-1], - ), - ) - end + mesh.corners.ϕ[:, :] .-= average(mesh.corners.ϕ) + + # Relevel ϕ around its average. It doesn't matter for potential fields + mean_ϕ = average(mesh.corners.ϕ) + mesh.corners.ϕ .-= mean_ϕ + println( """ @@ -233,16 +222,19 @@ function move_horizontally(mesh::FaceMesh, image; f = Focal_Length, clamp_correc # Note: Higher location means closer to the caustics => negative sign # true_H is _POSTS_SIZED_ true_H = zeros(Float64, size(mesh.corners.ϕ)) - @. true_H = -mesh.corners.ϕ + H + true_H = -mesh.corners.ϕ .+ H # Normals. # N_row/N_col are _POSTS_SIZED_ N_row = zeros(Float64, size(true_H)) N_col = zeros(Float64, size(true_H)) - @. N_row[1:end, 1:end] = - tan(atan(d_row[1:end, 1:end] / true_H[1:end, 1:end]) / (n₁ - n₂)) - @. N_col[1:end, 1:end] = - tan(atan(d_col[1:end, 1:end] / true_H[1:end, 1:end]) / (n₁ - n₂)) + N_row = tan.(atan.(d_row ./ true_H) / (n₁ - n₂)) + N_col = tan.(atan.(d_col ./ true_H) / (n₁ - n₂)) + + # @. N_row[1:end, 1:end] = + # tan(atan(d_row[1:end, 1:end] / true_H[1:end, 1:end]) / (n₁ - n₂)) + # @. N_col[1:end, 1:end] = + # tan(atan(d_col[1:end, 1:end] / true_H[1:end, 1:end]) / (n₁ - n₂)) # We need to find the divergence of the Vector field described by Nx and Ny # div_row/div_col are _FENCES_SIZED_ @@ -254,6 +246,10 @@ function move_horizontally(mesh::FaceMesh, image; f = Focal_Length, clamp_correc # divergence_direction = zeros(Float64, size(div_row)) # divergence_direction is _FENCES_SIZED_ divergence_direction = div_row + div_col + + # Normalise + divergence_direction .-= average(divergence_direction) + @assert test_average_absolute(divergence_direction) """ ALERT: horiz. @@ -265,11 +261,14 @@ function move_horizontally(mesh::FaceMesh, image; f = Focal_Length, clamp_correc ## ## CHECK SIGN!!! ## - true_H, max_update = propagate_poisson( - true_H, - -divergence_direction; - clamp_correction = clamp_correction, - ) + max_update = Inf + while max_update >= 1e-5 + true_H, max_update = propagate_poisson( + true_H, + divergence_direction; + clamp_correction = clamp_correction, + ) + end @assert test_average_absolute(true_H) """ ALERT: @@ -365,46 +364,27 @@ function propagate_poisson( # Default correction ratio to adjust δ is ω / 4.0 ω_clamped = ω / 4.0 - - maximum_δ = maximum(abs.(δ)) + δ *= ω / 4.0 # We limit the changes of the potential to a maximum - max_correction_ratio = 10.0 + max_correction_max = 1e12 + max_correction_μ = 100.0 + abs_δ = abs.(δ) + maximum_δ = maximum(abs_δ) - if 1.94 / 4.0 * maximum_δ < max_correction_ratio - correction_ratio = 1.94 / 4.0 - else - correction_ratio = max_correction_ratio / maximum_δ - end - - # if δ > 0, the intensity loss is too high, or the Laplacian is too high at that point. - # => increase flow towards outside - # => decrease the flow towards the inside. - # => increase divergence of the flow - # => increase the height of the potential there so that gradient are locally increasing - # => correction has to be of the same sign as δ. - @. ϕ[1:N_Pixel_Height, 1:N_Pixel_Width] += - correction_ratio * δ[1:N_Pixel_Height, 1:N_Pixel_Width] - # # We limit the changes of the potential to a maximum - # max_correction_max = 10.0 - # max_correction_μ = 20.0 - - # abs_δ = abs.(δ) - # maximum_δ = maximum(abs_δ) - - # # A correction factor is calculated to limit too wide changes on the field ϕ. + # A correction factor is calculated to limit too wide changes on the field ϕ. # if clamp_correction # μ_δ = average(abs_δ) - # if ω_clamped * maximum_δ > max_correction_max + # if maximum_δ > max_correction_max # ω_clamped = min(ω_clamped, max_correction_max / maximum_δ) - # println( - # "Propagation clamped for maximum_δ. $(maximum_δ) > $(max_correction_max)", - # ) - # elseif ω_clamped * μ_δ > max_correction_μ + # # println( + # # "Propagation clamped for maximum_δ. $(maximum_δ) > $(max_correction_max)", + # # ) + # elseif μ_δ > max_correction_μ # ω_clamped = min(ω_clamped, max_correction_μ / μ_δ) - # println("Propagation clamped for average δ. $(μ_δ) > $(max_correction_μ)") + # # println("Propagation clamped for average δ. $(μ_δ) > $(max_correction_μ)") # end # end @@ -431,8 +411,10 @@ function propagate_poisson( """ - max_update = ω_clamped * maximum_δ - return ϕ, max_update + # max_update = ω_clamped * maximum_δ + + + return ϕ, maximum_δ end @@ -446,128 +428,76 @@ $(SIGNATURES) """ function march_mesh!(mesh::FaceMesh) - println(""" - March mesh: - max/min ϕ = $(maximum(abs.(mesh.corners.ϕ))) / $(minimum(abs.(mesh.corners.ϕ))) - size ϕ = $(size(mesh.corners.ϕ)) - average ϕ = $(average_absolute(mesh.corners.ϕ)) - """) - # Calculate the gradient of the velocity potential. - # _POSTS_SIZED_ ∇ϕᵤ, ∇ϕᵥ = ∇(mesh.corners.ϕ) - # # Normalize the vectors - # vector_length = zeros(Float64, N_Pixel_Height + 1, N_Pixel_Width + 1) - # @. vector_length = sqrt(∇ϕᵤ^2 + ∇ϕᵥ^2) - # ∇ϕᵤ[vector_length .!= 0.0] ./= vector_length[vector_length .!= 0.0] - # ∇ϕᵥ[vector_length .!= 0.0] ./= vector_length[vector_length .!= 0.0] - - @assert !any(isnan.(∇ϕᵤ)) """ - - march_mesh!: - ∇ϕᵤ contains NaN!! - - """ - @assert !any(isnan.(∇ϕᵥ)) """ - - march_mesh!: - ∇ϕᵥ contains NaN!! - - """ - - println(""" - march_mesh!: - max/min ∇ϕᵤ = $(maximum(abs.(∇ϕᵤ))) / $(minimum(abs.(∇ϕᵤ))) - size ∇ϕᵤ = $(size(∇ϕᵤ)) - average ∇ϕᵤ = $(average_absolute(∇ϕᵤ)) - max/min ∇ϕᵥ = $(maximum(abs.(∇ϕᵥ))) / $(minimum(abs.(∇ϕᵥ))) - size ∇ϕᵥ = $(size(∇ϕᵥ)) - average ∇ϕᵥ = $(average_absolute(∇ϕᵥ)) - """) - # For each point in the mesh we need to figure out its velocity # However all the nodes located at a border will never move # I.e. velocity (Vx, Vy) = (0, 0) and the square of acrylate will remain # of the same size. - # _POSTS_SIZED_ + # + # CHECK - SIGN? + # mesh.corners.vr .= -∇ϕᵤ mesh.corners.vc .= -∇ϕᵥ # Just in case... reset_border_values!(mesh.corners) + # Basically infinity time to shrink a triangle to nothing. + min_positive_t = Inf + mesh_r = copy(mesh.corners.r) mesh_c = copy(mesh.corners.c) - # # Get the time, at that velocity, for the area of the triangle to become nil. - # # _FENCES_SIZED_ - # top_triangles = [triangle3D(mesh, row, col, :top) for row ∈ 1:N_Pixel_Height, col ∈ 1:N_Pixel_Width] - # bot_triangles = [triangle3D(mesh, row, col, :bottom) for row ∈ 1:N_Pixel_Height, col ∈ 1:N_Pixel_Width] - - # # Get the maximum moximum move along the distance of the gradient - # # _POSTS_SIZED_ - # max_move = zeros(Float64, N_Pixel_Height + 1, N_Pixel_Width + 1) - # max_move[1:N_Pixel_Height, 1:N_Pixel_Width] = min.(find_maximum_t.(top_triangles), find_maximum_t.(bot_triangles)) - # @. max_move[isnan(max_move)] = 0.0 - - - # println(""" - # march_mesh!: - # max_move max/min t: $(maximum(max_move)) / $(minimum(max_move)) - # TOP max/min t: $(maximum(find_maximum_t.(top_triangles))) / $(minimum(find_maximum_t.(top_triangles))) - # BOT max/min t: $(maximum(find_maximum_t.(bot_triangles))) / $(minimum(find_maximum_t.(bot_triangles))) - # """) - # Get the time, at that velocity, for the area of the triangle to be nil. # We are only interested by positive values to only move in the direction of the gradient - height, width = size(mesh.corners.ϕ) - for row ∈ 1:height-1, col ∈ 1:width-1 - list_triangles = - [triangle3D(mesh, row, col, :top), triangle3D(mesh, row, col, :bottom)] - list_maximum_t = [ - time for time ∈ find_maximum_t.(list_triangles) if - !isnan(time) && time > 0.0 && time < 10.0 - ] - - if !isempty(list_maximum_t) - min_positive_t = minimum(list_maximum_t) - - # @assert all(typeof.(t1) .== Float64) && all(typeof.(t2) .== Float64) "March mesh: Maximum times are not numerical at $(row), $(col)" - - max_shift = max(abs(∇ϕᵤ[row, col]), abs(∇ϕᵥ[row, col])) - - # No shift more than 20 pixels - max_pixel_move = 20.0 - δ = min(min_positive_t / 2.0, max_pixel_move / max_shift) - mesh.corners.r[row, col] = - clamp(mesh.corners.r[row, col] + δ * ∇ϕᵤ[row, col], 1, height - 1) - mesh.corners.c[row, col] = - clamp(mesh.corners.c[row, col] + δ * ∇ϕᵥ[row, col], 1, width - 1) - end - end + list_triangles = vcat( + [ + triangle3D(mesh, row, col, :top) for row ∈ 1:N_Pixel_Height, + col ∈ 1:N_Pixel_Width + ], + [ + triangle3D(mesh, row, col, :bottom) for row ∈ 1:N_Pixel_Height, + col ∈ 1:N_Pixel_Width + ], + ) + + list_maximum_t = + [time for time ∈ find_maximum_t.(list_triangles) if !isnothing(time) && !isnan(time) && time > 0.0] + + if !isempty(list_maximum_t) + min_positive_t = minimum(list_maximum_t) - # # Maximum movement along either coordinate - # max_pixel_move = 10.0 + # # Maximum movement along either coordinate + # max_shift = max(maximum(abs.(∇ϕᵤ)), maximum(abs.(∇ϕᵥ))) - # # δ = zeros(Float64, N_Pixel_Height + 1, N_Pixel_Width + 1) - # # δ = min.(max_move / 2.0, max_pixel_move) - # δ = max_move / 2.0 - # println("Size δ = $(size(δ))") + # # No shift more than 10 pixels + # max_pixel_move = 10.0 + δ = min_positive_t / 2.0 - # @. mesh.corners.r += δ * ∇ϕᵤ - # @. mesh.corners.c += δ * ∇ϕᵥ + δ = min_positive_t / 2.0 + mesh.corners.r += δ * ∇ϕᵤ + mesh.corners.c += δ * ∇ϕᵥ + end # Reset the border at the fixed values fixed coordinates. reset_border_values!(mesh.corners) println(""" - march_mesh!: - Average mesh changes on row = $(average_absolute(mesh.corners.r - mesh_r)) - Average mesh changes on col = $(average_absolute(mesh.corners.c - mesh_c)) - Top left rows: $(mesh.corners.r[1:5, 1:5]) - Top right rows: $(mesh.corners.r[1:5, end-5:end]) - """) + March mesh: + max/min Vu = $(maximum(abs.(∇ϕᵤ))) / $(minimum(abs.(∇ϕᵤ))) + max/min Vv = $(maximum(abs.(∇ϕᵥ))) / $(minimum(abs.(∇ϕᵥ))) + Average mesh changes on row = $(average_absolute(mesh.corners.r - mesh_r)) + Average mesh changes on col = $(average_absolute(mesh.corners.c - mesh_c)) + + """) + @assert 1 - 1e-4 < average(get_lens_pixels_area(mesh)) < 1 + 1e-4 """ + + march_mesh!: average energy per pixel is too different from 1.0 + Total energy per pixel: $(average(get_lens_pixels_area(mesh))) + + """ return nothing end diff --git a/src/math_utilities.jl b/src/math_utilities.jl index a49c08b..3785a65 100644 --- a/src/math_utilities.jl +++ b/src/math_utilities.jl @@ -21,10 +21,10 @@ test_average_absolute(m::AbstractMatrix) = (average_absolute(m)) < 1e6 $(SIGNATURES) """ function smallest_positive(x1::Float64, x2::Float64) - (x1 >= 0.0 && x2 < 0.0) && return x1 - (x1 < 0.0 && x2 >= 0.0) && return x2 - (x1 >= 0.0 && x2 >= 0.0) && return min(x1, x2) - return 0.0 + (x1 > 0.0 && x2 < 0.0) && return x1 + (x1 < 0.0 && x2 > 0.0) && return x2 + (x1 > 0.0 && x2 > 0.0) && return min(x1, x2) + return nothing end diff --git a/src/mesh.jl b/src/mesh.jl index cb9f0fa..c5bbc9c 100644 --- a/src/mesh.jl +++ b/src/mesh.jl @@ -4,12 +4,6 @@ $(SIGNATURES) Given 3 points and their velocities, calculate the time `t` required to bring the area of that triangle to zero """ function find_maximum_t(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) - # If a triangle is too small, no move - if area(p1, p2, p3) < 1e-3 - return 0.0 - end - - # Three points A, B and C, with coordinates (x, y) # The area of a triangle is 1/2 * [ Ax (By - Cy) + Bx (Cy - Ay) + Cx (Ay - By)] # where each point of the triangle is where it will be after time t @@ -38,21 +32,21 @@ function find_maximum_t(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) # if a = 0, this is just a linear equation. if a == 0 && b != 0 - return min(smallest_positive(-c / b, c / b), 2.0) + return smallest_positive(-c / b, c / b) else discriminant = b^2 - 4a * c # If there is a solution if discriminant >= 0 d = sqrt(discriminant) - return min(smallest_positive((-b - d) / 2a, (-b + d) / 2a), 2.0) + return smallest_positive((-b - d) / 2a, (-b + d) / 2a) end end # There can be no solution if, after translation, B abd C move in parallel direction. # C will never end up on the line AB. # Very unlikely with Float64. - # Negative numbers are filtered out when calculating the minimum jiggle ratio - return 0.0 + # If nothing found, no move + return nothing end find_maximum_t(p::Tuple{Vertex3D,Vertex3D,Vertex3D}) = find_maximum_t(p[1], p[2], p[3]) diff --git a/src/scratchpad.jl b/src/scratchpad.jl index 88f3742..efbc036 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -15,10 +15,9 @@ image = Images.load("./examples/personal/statue_of_liberty_3.jpg"); # Check curr image = Images.load("./examples/personal/caricature.jpg"); # Check current working directory with pwd() image = Images.load("./examples/personal/image.jpg"); # Check current working directory with pwd() -image = Images.load("./examples/personal/portrait.jpg"); # Check current working directory with pwd() image = Images.load("./examples/personal/bilal.jpg"); # Check current working directory with pwd() -mesh, imageBW = engineer_caustics(image; clamp_correction = true); +mesh, imageBW = engineer_caustics(image; clamp_correction = false); imageBW = Float64.(Gray.(image)); From 12c93cefc14e02ac3ae0b5c706c06c7e4d4dab2a Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Fri, 17 Sep 2021 15:58:39 +0200 Subject: [PATCH 36/58] Tracking convergence bug --- src/create_mesh.jl | 204 +++++------------------------------------- src/math_utilities.jl | 23 +++-- src/mesh.jl | 2 +- src/scratchpad.jl | 4 +- src/utilities.jl | 6 +- 5 files changed, 45 insertions(+), 194 deletions(-) diff --git a/src/create_mesh.jl b/src/create_mesh.jl index fdac851..7afb8df 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -3,7 +3,7 @@ $(SIGNATURES) """ -function engineer_caustics(source_image; clamp_correction = true) +function engineer_caustics(source_image) imageBW = Float64.(Gray.(source_image)) @@ -41,11 +41,7 @@ function engineer_caustics(source_image; clamp_correction = true) # abs((error_luminosity - old_error_luminosity) / old_error_luminosity) > 0.0 && # abs((max_update - old_max_update) / old_max_update) > 0.0 && - while ( - abs(max_update) > 1e-5 && - error_luminosity > 1e-5 && - iteration_count < 10_000 - ) + while (abs(max_update) > 1e-5 && error_luminosity > 1e-5 && iteration_count < 10) iteration_count += 1 println( @@ -54,12 +50,8 @@ function engineer_caustics(source_image; clamp_correction = true) old_max_update = max_update old_error_luminosity = error_luminosity - max_update, error_luminosity = solve_velocity_potential!( - mesh, - imageBW, - "it$(iteration_count)"; - clamp_correction = clamp_correction, - ) + max_update, error_luminosity = + solve_velocity_potential!(mesh, imageBW, "it$(iteration_count)") print( "Vertical move max update = $(max_update) -- Mean error luminosity = $(error_luminosity)\n", ) @@ -67,14 +59,11 @@ function engineer_caustics(source_image; clamp_correction = true) println("\nSTARTING HORIZONTAL ITERATION ---") - ϕ, max_update = - move_horizontally(mesh, imageBW; f = Focal_Length, clamp_correction = true) - mesh.corners.ϕ .= ϕ + mesh.corners.ϕ, max_update = move_horizontally(mesh, imageBW; f = Focal_Length) println("\t Horizontal max update = $(max_update)") # Move the around a nil average. - mean_ϕ = average(mesh.corners.ϕ) - mesh.corners.ϕ = mesh.corners.ϕ .- mean_ϕ + mesh.corners.ϕ .-= average(mesh.corners.ϕ) return mesh, imageBW end @@ -87,31 +76,17 @@ $(SIGNATURES) ϕ is the _velocity potential_. The velocity represents the direction towards which the mesh vertices should move. Zones of high luminosity should be covered with more triangles and should attract more vertices. """ -function solve_velocity_potential!(mesh, image, prefix; clamp_correction = true) +function solve_velocity_potential!(mesh, image, prefix) # Keep that to track how much progress is made mesh_ϕ = copy(mesh.corners.ϕ) # Get the area of each individual pixel as stretch/shrunk on the lens. Area = energy. # _FENCES_SIZED_ lens_pixels_area = get_lens_pixels_area(mesh) - @assert test_average_absolute(lens_pixels_area) """ - - solve_velocity_potential: - area_distorted_corners values seem too large - $(maximum(lens_pixels_area)) / $(minimum(lens_pixels_area)) - - """ # Positive error => the triangle needs to shrink (less light) error_luminosity = Float64.(lens_pixels_area - image) error_luminosity = error_luminosity .- average(error_luminosity) - @assert test_average_absolute(error_luminosity) """ - - solve_velocity_potential: error_luminosity values seem too large - max/min error_luminosity = $(maximum(error_luminosity)) / $(minimum(error_luminosity)) - - """ - # Save the loss image as a png println( @@ -133,14 +108,10 @@ function solve_velocity_potential!(mesh, image, prefix; clamp_correction = true) old_max_update = 2 * start_max_update iteration_count = 0 - while ( - abs(max_update) > 1e-5 && - iteration_count <= 1_000 - ) + while (abs(max_update) > 1e-5 && iteration_count < 1) iteration_count += 1 old_max_update = max_update - iteration_count % 10 == 0 && println("Converging for intensity: $(max_update)") iteration_count % 10 == 0 && println( """ @@ -151,33 +122,14 @@ function solve_velocity_potential!(mesh, image, prefix; clamp_correction = true) """, ) + # Re-level ϕ around its average. It doesn't matter for potential fields + mesh.corners.ϕ .-= average(mesh.corners.ϕ) + # Solve the Poisson equation where the divergence of the gradient of ϕ is equal to the luminosity error. # High error => Too much luminosity. - ϕ, max_update = propagate_poisson( - mesh.corners.ϕ, - error_luminosity; - clamp_correction = clamp_correction, - ) - - mesh.corners.ϕ[:, :] .= ϕ[:, :] - @assert test_average_absolute(mesh.corners.ϕ) """ - - solve_velocity_potential: ϕ values seem too large - iteration count = $(iteration_count) - max/min mesh.corners.ϕ = $(maximum(mesh.corners.ϕ)) / $(minimum(mesh.corners.ϕ)) - - max/min error_luminosity = $(maximum(error_luminosity)) / $(minimum(error_luminosity)) - max_update = $(max_update) - - """ + mesh.corners.ϕ, max_update = propagate_poisson(mesh.corners.ϕ, error_luminosity) end - mesh.corners.ϕ[:, :] .-= average(mesh.corners.ϕ) - - # Relevel ϕ around its average. It doesn't matter for potential fields - mean_ϕ = average(mesh.corners.ϕ) - mesh.corners.ϕ .-= mean_ϕ - println( """ @@ -202,7 +154,7 @@ end """ $(SIGNATURES) """ -function move_horizontally(mesh::FaceMesh, image; f = Focal_Length, clamp_correction = true) +function move_horizontally(mesh::FaceMesh, image; f = Focal_Length) # height indexes rows, width indexes columns height, width = size(mesh) @@ -250,33 +202,10 @@ function move_horizontally(mesh::FaceMesh, image; f = Focal_Length, clamp_correc # Normalise divergence_direction .-= average(divergence_direction) - @assert test_average_absolute(divergence_direction) """ - - ALERT: horiz. - Δ divergence_direction seem too large - max/min = $(maximum(divergence_direction)) / $(minimum(divergence_direction)) - - """ - - ## - ## CHECK SIGN!!! - ## max_update = Inf while max_update >= 1e-5 - true_H, max_update = propagate_poisson( - true_H, - divergence_direction; - clamp_correction = clamp_correction, - ) + true_H, max_update = propagate_poisson(true_H, divergence_direction) end - @assert test_average_absolute(true_H) """ - - ALERT: - horiz. Δ corner_heights is too large - max/min corner_heights = $(maximum(true_H)) / $(minimum(true_H)) - - """ - println("Convergence horiz. Δ stopped with max_update of $(max_update)") return true_H, max_update @@ -306,87 +235,31 @@ In order of how to think about the flow of the program: should be. """ -function propagate_poisson( - ϕ::Matrix{Float64}, - ∇²ϕ::Matrix{Float64}; - clamp_correction = true, -) +function propagate_poisson(ϕ::Matrix{Float64}, ∇²ϕ::Matrix{Float64}) # Ensure that border conditions are as they should (= 0.0) fill_borders!(∇²ϕ, 0.0) - @assert test_average_absolute(ϕ) """ - - Relaxation: - ϕ values seem too large - max/min ∇ϕ = $(maximum(∇²ϕ)) / $(minimum(∇²ϕ)) - max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) - - """ - - @assert test_average_absolute(∇²ϕ) """ - - Relaxation: - ∇²ϕ values seem too large - max/min ∇²ϕ = $(maximum(∇²ϕ)) / $(minimum(∇²ϕ)) - max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) - - """ - - @assert any(isnan.(ϕ)) == false "Relaxation: calling with a ϕ that contains NaN!!" - @assert any(isnan.(∇²ϕ)) == false "Relaxation: calling with a ∇²ϕ that contains NaN!!" - ################################################################################################################## # From the velocity potential field ϕ, we calculate its gradient (the velocity), then its divergence. # This is then compared to the intensity loss - # Laplacian # Lϕ represent the approximation of the Laplacian of ϕ (second-order value) Lϕ = laplacian(ϕ) - # In the case of the velocity potential, δ is the difference between the divergence of the luminosity error # and the current one for the current field ϕ (divergence of its gradient). # High luminosity error ∇²ϕ means that the triangles are too bright = too large. # The Laplacian Lϕ has to converge towards the ∇²ϕ. Difference to calculate speed of the descent. δ = Lϕ - ∇²ϕ - @assert test_average_absolute(δ) """ - - Relaxation: - difference between luminosity error and estimated Laplacian seem too large - max/min δ = $(maximum(δ)) / $(minimum(δ)) - max/min target Lϕ = $(maximum(Lϕ)) / $(minimum(Lϕ)) - max/min ϕ = $(maximum(ϕ)) / $(minimum(ϕ)) - - """ # Default correction ratio to adjust δ is ω / 4.0 - ω_clamped = ω / 4.0 δ *= ω / 4.0 # We limit the changes of the potential to a maximum - max_correction_max = 1e12 - max_correction_μ = 100.0 - abs_δ = abs.(δ) - maximum_δ = maximum(abs_δ) - - - # A correction factor is calculated to limit too wide changes on the field ϕ. - # if clamp_correction - # μ_δ = average(abs_δ) - - # if maximum_δ > max_correction_max - # ω_clamped = min(ω_clamped, max_correction_max / maximum_δ) - # # println( - # # "Propagation clamped for maximum_δ. $(maximum_δ) > $(max_correction_max)", - # # ) - # elseif μ_δ > max_correction_μ - # ω_clamped = min(ω_clamped, max_correction_μ / μ_δ) - # # println("Propagation clamped for average δ. $(μ_δ) > $(max_correction_μ)") - # end - # end + maximum_δ = maximum(abs.(δ)) # In the case of the velocity potential, # if δ > 0, the Laplacian is too high at that point (∇²ϕ is too low). @@ -402,17 +275,7 @@ function propagate_poisson( # => either decrease the values of the potential around that point, or increase the value of the potential at that point. # => Increase the value of ϕ at that point means a positive change when δ > 0. # δ > 0 => correction of the SAME sign. - @. ϕ[1:N_Pixel_Height, 1:N_Pixel_Width] += - ω_clamped * δ[1:N_Pixel_Height, 1:N_Pixel_Width] - @assert !any(isnan.(ϕ)) """ - - Relaxation: - Updated ϕ contains NaN!! - - """ - - # max_update = ω_clamped * maximum_δ - + @. ϕ[1:N_Pixel_Height, 1:N_Pixel_Width] += δ[1:N_Pixel_Height, 1:N_Pixel_Width] return ϕ, maximum_δ end @@ -435,11 +298,6 @@ function march_mesh!(mesh::FaceMesh) # However all the nodes located at a border will never move # I.e. velocity (Vx, Vy) = (0, 0) and the square of acrylate will remain # of the same size. - # - # CHECK - SIGN? - # - mesh.corners.vr .= -∇ϕᵤ - mesh.corners.vc .= -∇ϕᵥ # Just in case... reset_border_values!(mesh.corners) @@ -452,6 +310,9 @@ function march_mesh!(mesh::FaceMesh) # Get the time, at that velocity, for the area of the triangle to be nil. # We are only interested by positive values to only move in the direction of the gradient + mesh.corners.vr = -∇ϕᵤ + mesh.corners.vc = -∇ϕᵥ + list_triangles = vcat( [ triangle3D(mesh, row, col, :top) for row ∈ 1:N_Pixel_Height, @@ -463,23 +324,11 @@ function march_mesh!(mesh::FaceMesh) ], ) - list_maximum_t = - [time for time ∈ find_maximum_t.(list_triangles) if !isnothing(time) && !isnan(time) && time > 0.0] - - if !isempty(list_maximum_t) - min_positive_t = minimum(list_maximum_t) - - # # Maximum movement along either coordinate - # max_shift = max(maximum(abs.(∇ϕᵤ)), maximum(abs.(∇ϕᵥ))) + list_maximum_t = [time for time ∈ find_maximum_t.(list_triangles)] + δ = minimum(list_maximum_t) / 2.0 - # # No shift more than 10 pixels - # max_pixel_move = 10.0 - δ = min_positive_t / 2.0 - - δ = min_positive_t / 2.0 - mesh.corners.r += δ * ∇ϕᵤ - mesh.corners.c += δ * ∇ϕᵥ - end + mesh.corners.r += δ * ∇ϕᵤ + mesh.corners.c += δ * ∇ϕᵥ # Reset the border at the fixed values fixed coordinates. reset_border_values!(mesh.corners) @@ -493,11 +342,6 @@ function march_mesh!(mesh::FaceMesh) """) - @assert 1 - 1e-4 < average(get_lens_pixels_area(mesh)) < 1 + 1e-4 """ - - march_mesh!: average energy per pixel is too different from 1.0 - Total energy per pixel: $(average(get_lens_pixels_area(mesh))) - """ return nothing end diff --git a/src/math_utilities.jl b/src/math_utilities.jl index 3785a65..cbf2e31 100644 --- a/src/math_utilities.jl +++ b/src/math_utilities.jl @@ -24,7 +24,7 @@ function smallest_positive(x1::Float64, x2::Float64) (x1 > 0.0 && x2 < 0.0) && return x1 (x1 < 0.0 && x2 > 0.0) && return x2 (x1 > 0.0 && x2 > 0.0) && return min(x1, x2) - return nothing + return Inf end @@ -34,12 +34,19 @@ $(SIGNATURES) Approximates the gradient of a scalar field. """ function ∇(ϕ::AbstractMatrix{Float64}) + height, width = size(ϕ) + # x, y only represents the first and the second variables. No reference to graphical representations. - ∇ϕx = zeros(Float64, size(ϕ)) # divergence on the right edge will be filled with zeros - ∇ϕy = zeros(Float64, size(ϕ)) # divergence on bottom edge will be filled with zeros + ∇ϕx = zeros(Float64, height, width) # divergence on the right edge will be filled with zeros + ∇ϕy = zeros(Float64, height, width) # divergence on bottom edge will be filled with zeros + + for x ∈ 1:height-1, y ∈ 1:width-1 + ∇ϕx[x, y] = ϕ[x+1, y] - ϕ[x, y] + ∇ϕy[x, y] = ϕ[x, y+1] - ϕ[x, y] + end - @. ∇ϕx[begin:end-1, :] = ϕ[begin+1:end, :] - ϕ[begin:end-1, :] - @. ∇ϕy[:, begin:end-1] = ϕ[:, begin+1:end] - ϕ[:, begin:end-1] + # ∇ϕx[begin:end-1, :] = ϕ[begin+1:end, :] - ϕ[begin:end-1, :] + # ∇ϕy[:, begin:end-1] = ϕ[:, begin+1:end] - ϕ[:, begin:end-1] fill_borders!(∇ϕx, 0.0) fill_borders!(∇ϕy, 0.0) @@ -56,8 +63,6 @@ Calculate the second-order Laplace operator by convolution of a kernel. """ function laplacian(ϕ::AbstractMatrix{Float64}) height, width = size(ϕ) - height -= 1 - width -= 1 # Embed matrix within a larger matrix for better vectorization and avoid duplicated code # Padded matrix adds 1 row/col after the size of ϕ. @@ -71,8 +76,8 @@ function laplacian(ϕ::AbstractMatrix{Float64}) kernel = [[0.0 1.0 0.0]; [1.0 -4.0 1.0]; [0.0 1.0 0.0]] # Convolution - ∇²ϕ = zeros(Float64, height, width) - for row ∈ 1:height, col ∈ 1:width + ∇²ϕ = zeros(Float64, height - 1, width - 1) + for row ∈ 1:height-1, col ∈ 1:width-1 ∇²ϕ[row, col] = sum(padded_ϕ[row:row+2, col:col+2] .* kernel[1:3, 1:3]) end diff --git a/src/mesh.jl b/src/mesh.jl index c5bbc9c..b79dcff 100644 --- a/src/mesh.jl +++ b/src/mesh.jl @@ -46,7 +46,7 @@ function find_maximum_t(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) # C will never end up on the line AB. # Very unlikely with Float64. # If nothing found, no move - return nothing + return Inf end find_maximum_t(p::Tuple{Vertex3D,Vertex3D,Vertex3D}) = find_maximum_t(p[1], p[2], p[3]) diff --git a/src/scratchpad.jl b/src/scratchpad.jl index efbc036..e858171 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -17,7 +17,9 @@ image = Images.load("./examples/personal/caricature.jpg"); # Check current worki image = Images.load("./examples/personal/image.jpg"); # Check current working directory with pwd() image = Images.load("./examples/personal/bilal.jpg"); # Check current working directory with pwd() -mesh, imageBW = engineer_caustics(image; clamp_correction = false); +mesh, imageBW = engineer_caustics(image;); + +mesh, imageBW = original_engineer_caustics(image); imageBW = Float64.(Gray.(image)); diff --git a/src/utilities.jl b/src/utilities.jl index a4c0a10..6d13122 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -251,21 +251,21 @@ function triangle3D(mesh::FaceMesh, row::Int, col::Int, side = Union{:top,:botto ϕ1 = mesh.corners.ϕ[t1_row, t1_col] vr1 = mesh.corners.vr[t1_row, t1_col] vc1 = mesh.corners.vc[t1_row, t1_col] - @assert r1^2 + c1^2 <= max_distance_squared "Coordinate $(r1), $(c1), $(ϕ1) of point #1 at $(row), $(col), side = $(side) makes no sense " + # @assert r1^2 + c1^2 <= max_distance_squared "Coordinate $(r1), $(c1), $(ϕ1) of point #1 at $(row), $(col), side = $(side) makes no sense " r2 = mesh.corners.r[t2_row, t2_col] c2 = mesh.corners.c[t2_row, t2_col] ϕ2 = mesh.corners.ϕ[t2_row, t2_col] vr2 = mesh.corners.vr[t2_row, t2_col] vc2 = mesh.corners.vc[t2_row, t2_col] - @assert r2^2 + c2^2 <= max_distance_squared "Coordinate $(r2), $(c2), $(ϕ2) of point #2 at $(row), $(col), side = $(side) makes no sense " + # @assert r2^2 + c2^2 <= max_distance_squared "Coordinate $(r2), $(c2), $(ϕ2) of point #2 at $(row), $(col), side = $(side) makes no sense " r3 = mesh.corners.r[t3_row, t3_col] c3 = mesh.corners.c[t3_row, t3_col] ϕ3 = mesh.corners.ϕ[t3_row, t3_col] vr3 = mesh.corners.vr[t3_row, t3_col] vc3 = mesh.corners.vc[t3_row, t3_col] - @assert r3^2 + c3^2 <= max_distance_squared "Coordinate $(r3), $(c3), $(ϕ3) of point #3 at $(row), $(col), side = $(side) makes no sense " + # @assert r3^2 + c3^2 <= max_distance_squared "Coordinate $(r3), $(c3), $(ϕ3) of point #3 at $(row), $(col), side = $(side) makes no sense " p1 = Vertex3D(r1, c1, ϕ1, vr1, vc1) p2 = Vertex3D(r2, c2, ϕ2, vr2, vc2) From 29e0c188127f368efa1b943c821da9cf91a4ecf5 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Sun, 19 Sep 2021 13:37:08 +0200 Subject: [PATCH 37/58] Tracking convergence bug --- src/CausticsEngineering.jl | 13 +- src/create_mesh.jl | 236 ++++++++++++++----------------------- src/math_utilities.jl | 33 ++---- src/mesh.jl | 26 +--- src/scratchpad.jl | 73 +++++++++++- src/utilities.jl | 49 ++++---- 6 files changed, 205 insertions(+), 225 deletions(-) diff --git a/src/CausticsEngineering.jl b/src/CausticsEngineering.jl index 8548f9a..4be0315 100644 --- a/src/CausticsEngineering.jl +++ b/src/CausticsEngineering.jl @@ -38,9 +38,16 @@ export FieldVertex3D, FaceMesh, + # math + average, + average_absolute, + laplacian, + ∇, + # Mesh create_solid, create_solid_as_dict, + get_lens_pixels_area, # Plotting plot_as_quiver, @@ -49,8 +56,10 @@ export save_obj!, # Main procedures - main, - engineer_caustics + propagate_poisson, + march_mesh!, + engineer_caustics, + main end # End module diff --git a/src/create_mesh.jl b/src/create_mesh.jl index 7afb8df..d8b1e60 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -14,44 +14,27 @@ function engineer_caustics(source_image) global Meters_Per_Pixel = Caustics_Long_Side / N_Pixel_Height println("Image size: $(N_Pixel_Height) x $(N_Pixel_Width)") - - # mesh is the same size as the image with an extra row/column to have coordinates to # cover each image corner with a triangle. mesh = FaceMesh(N_Pixel_Height, N_Pixel_Width) # The total energy going through the lens is equal to the amount of energy on the caustics - total_energy_lens = N_Pixel_Height * N_Pixel_Width * 1.0 # 1 unit of energy per pixel - total_energy_caustics = sum(imageBW) average_energy_per_pixel = average(imageBW) # imageBW is normalised to the same (sort of) _energy_ as the original image. imageBW = imageBW / average_energy_per_pixel - # start_max_update has no particular meing. - # It is basically the initial max_update. But then is used to initialise other variables so that - # not to stop the `while` loop on the first iteration - start_max_update = 1_000.0 - max_update = start_max_update - old_max_update = 2 * start_max_update - - error_luminosity = 1e6 * N_Pixel_Height * N_Pixel_Width - old_error_luminosity = 2 * error_luminosity - iteration_count = 0 - - # abs((error_luminosity - old_error_luminosity) / old_error_luminosity) > 0.0 && - # abs((max_update - old_max_update) / old_max_update) > 0.0 && - while (abs(max_update) > 1e-5 && error_luminosity > 1e-5 && iteration_count < 10) - iteration_count += 1 + max_update = Inf + counter = 0 + while (abs(max_update) > 1e-5 && counter < 5_000) + counter += 1 println( - "\nSTARTING VERTICAL ITERATION $(iteration_count) --------------------------------------------", + "\nSTARTING VERTICAL ITERATION $(counter) --------------------------------------------", ) - old_max_update = max_update - old_error_luminosity = error_luminosity max_update, error_luminosity = - solve_velocity_potential!(mesh, imageBW, "it$(iteration_count)") + solve_velocity_potential!(mesh, imageBW, "it$(counter)") print( "Vertical move max update = $(max_update) -- Mean error luminosity = $(error_luminosity)\n", ) @@ -77,11 +60,13 @@ $(SIGNATURES) Zones of high luminosity should be covered with more triangles and should attract more vertices. """ function solve_velocity_potential!(mesh, image, prefix) - # Keep that to track how much progress is made - mesh_ϕ = copy(mesh.corners.ϕ) + + # Start with a new clean field + height, width = size(mesh) # Get the area of each individual pixel as stretch/shrunk on the lens. Area = energy. # _FENCES_SIZED_ + mesh.corners.ϕ = zeros(Float64, height + 1, width + 1) lens_pixels_area = get_lens_pixels_area(mesh) # Positive error => the triangle needs to shrink (less light) @@ -89,63 +74,41 @@ function solve_velocity_potential!(mesh, image, prefix) error_luminosity = error_luminosity .- average(error_luminosity) # Save the loss image as a png - println( - """ - Luminosity error: - Max/min luminosity error: $(maximum(error_luminosity)) / $(minimum(error_luminosity)) - Average abs loss: $(average_absolute(error_luminosity)) - Average loss: $(average(error_luminosity)) - """, - ) save_plot_scalar_field!(error_luminosity, prefix * "_loss", image) + println(""" - # start_max_update has no particular meeting. - # It is basically the initial max_update. But then is used to initialise other variables so that - # not to stop the `while` loop on the first iteration - start_max_update = 1_000.0 - max_update = start_max_update - old_max_update = 2 * start_max_update - iteration_count = 0 - - while (abs(max_update) > 1e-5 && iteration_count < 1) - iteration_count += 1 - old_max_update = max_update - - iteration_count % 10 == 0 && println( - """ + solve_velocity_potential! before loop: + $(field_summary(lens_pixels_area, "Pixel area")) + $(field_summary(error_luminosity, "luminosity error")) + """) - solve_velocity_potential: - max/min mesh.corners.ϕ = $(maximum(mesh.corners.ϕ)) / $(minimum(mesh.corners.ϕ)) - iteration count = $(iteration_count) - max_update = $(max_update) - """, + max_update = Inf + counter = 0 + while (abs(max_update) > 1e-5 && counter < 5_000) + counter += 1 + counter % 500 == 0 && println( + """ solve_velocity_potential! during loop at count $(counter) with max_update = $(round(max_update, sigdigits=4)): + $(field_summary(mesh.corners.ϕ, "mesh.corners.ϕ")) + """, ) # Re-level ϕ around its average. It doesn't matter for potential fields - mesh.corners.ϕ .-= average(mesh.corners.ϕ) + # mesh.corners.ϕ .-= average(mesh.corners.ϕ) - # Solve the Poisson equation where the divergence of the gradient of ϕ is equal to the luminosity error. - # High error => Too much luminosity. - mesh.corners.ϕ, max_update = propagate_poisson(mesh.corners.ϕ, error_luminosity) + # Solve the Poisson equation tp converge the divergence of the gradient of ϕ towards the luminosity error. + max_update = propagate_poisson!(mesh.corners.ϕ, error_luminosity) end - println( - """ - - Luminosity convergence stopped at step $(iteration_count) with - max_update = $(max_update) - max / min error_luminosity = $(maximum(abs.(error_luminosity))) / $(minimum(abs.(error_luminosity))) - Average mesh changes on ϕ = $(average_absolute(mesh.corners.ϕ - mesh_ϕ)) - max ϕ divergence = $(maximum(abs.(mesh.corners.ϕ[begin+1:end, begin:end-1] .- mesh_ϕ[begin:end-1, begin:end-1] .+ - mesh.corners.ϕ[begin:end-1, begin+1:end] .- mesh_ϕ[begin:end-1, begin:end-1]))) - - """, - ) + println(""" solve_velocity_potential! stopped at step $(counter) with + $(field_summary(error_luminosity, "luminosity error")) + $(field_summary(mesh.corners.ϕ, "mesh.corners.ϕ")) + max_update = $(max_update) + """) # Now we need to march the mesh row,col corner locations according to this gradient. march_mesh!(mesh) - plot_as_quiver(mesh, n_steps = 50, scale = 1.0, max_length = N_Pixel_Height / 20) + plot_as_quiver(mesh, n_steps = 50, scale = 1.0, max_length = height / 20) return max_update, average_absolute(error_luminosity) end @@ -195,18 +158,19 @@ function move_horizontally(mesh::FaceMesh, image; f = Focal_Length) div_row[1:end, 1:end] = N_row[2:end, 1:end-1] .- N_row[1:end-1, 1:end-1] div_col[1:end, 1:end] = N_col[1:end-1, 2:end] .- N_col[1:end-1, 1:end-1] - # divergence_direction = zeros(Float64, size(div_row)) + # Normalised divergence # divergence_direction is _FENCES_SIZED_ divergence_direction = div_row + div_col - - # Normalise - divergence_direction .-= average(divergence_direction) + # divergence_direction .-= average(divergence_direction) max_update = Inf + counter = 0 while max_update >= 1e-5 - true_H, max_update = propagate_poisson(true_H, divergence_direction) + counter += 1 + max_update = propagate_poisson!(true_H, divergence_direction) + counter % 100 && println("Convergence horiz. Δ max update = $(max_update)") end - println("Convergence horiz. Δ stopped with max_update of $(max_update)") + println("Convergence horiz. Δ stopped with max_update of $(max_update) at counter = $(counter)") return true_H, max_update end @@ -223,61 +187,45 @@ https://math.stackexchange.com/questions/3790299/how-to-iteratively-solve-poisso - ϕ is the potential to be solved subject to the Poisson equation and is the same size as the corners (_POSTS_SIZED_) - target is ∇ϕ and is of the size in pixels (_FENCES_SIZED_) -In order of how to think about the flow of the program: +In order of how to think about the flow of the program for the velocity potential, + - if δ > 0, the Laplacian is too high at that point (∇²ϕ is too low). + - To decrease the Laplacian ∇²ϕ, note that ∇² is a divergence (of a gradient) that represents net flow going outside. -- High ∇ϕ (intensity loss function for the velocity potential) means that the triangles are too bright -- High brightness => triangle are too wide: a wide triangle collects a large amount of light and focuses is - onto a signle pixel of the caustics. -- Too wide => need velocity towards the centroid of the triangle to bring its corners closer and decrease its - surface. -- Velocity toward the centre => divergence of the velocities should be negative. That is ∇²ϕ < 0. -- The higher ∇ϕ (the actual loss given a particular target caustics), the lower ∇²ϕ (of the current estimated ϕ) - should be. + - Decrease the Laplacian + - => decrease a divergence + - => decrease flow towards outside + - The flow is a gradient of the potential ϕ. + - => decrease flow towards outside + - => either decrease the values of the potential around that point, or increase the value of the potential at that point. + - => Increase the value of ϕ at that point means a positive change when δ > 0. + - δ > 0 => correction of the SAME sign. """ -function propagate_poisson(ϕ::Matrix{Float64}, ∇²ϕ::Matrix{Float64}) - +function propagate_poisson!(ϕ::Matrix{Float64}, ∇²ϕ::Matrix{Float64}) # Ensure that border conditions are as they should (= 0.0) + height, width = size(∇²ϕ) fill_borders!(∇²ϕ, 0.0) ################################################################################################################## # From the velocity potential field ϕ, we calculate its gradient (the velocity), then its divergence. # This is then compared to the intensity loss + max_δ = 0.0 + for row ∈ 1:height, col ∈ 1:width + ∇²ϕ_est = + ϕ[max(1, row - 1), col] + + ϕ[min(height, row + 1), col] + + ϕ[row, max(1, col - 1)] + + ϕ[row, min(width, col + 1)] - 4.0 * ϕ[row, col] - # Laplacian - # Lϕ represent the approximation of the Laplacian of ϕ (second-order value) - Lϕ = laplacian(ϕ) - - # In the case of the velocity potential, δ is the difference between the divergence of the luminosity error - # and the current one for the current field ϕ (divergence of its gradient). - - # High luminosity error ∇²ϕ means that the triangles are too bright = too large. - # The Laplacian Lϕ has to converge towards the ∇²ϕ. Difference to calculate speed of the descent. - δ = Lϕ - ∇²ϕ - - # Default correction ratio to adjust δ is ω / 4.0 - δ *= ω / 4.0 + δ = ∇²ϕ_est - ∇²ϕ[row, col] + δ /= 8.0 - # We limit the changes of the potential to a maximum - maximum_δ = maximum(abs.(δ)) + ϕ[row, col] += δ - # In the case of the velocity potential, - # if δ > 0, the Laplacian is too high at that point (∇²ϕ is too low). - - # To decrease the Laplacian ∇²ϕ, note that ∇² is a divergence (of a gradient) that represents net flow going outside. - # - # Decrease the Laplacian - # => decrease a divergence - # => decrease flow towards outside - # - # The flow is a gradient of the potential ϕ. - # => decrease flow towards outside - # => either decrease the values of the potential around that point, or increase the value of the potential at that point. - # => Increase the value of ϕ at that point means a positive change when δ > 0. - # δ > 0 => correction of the SAME sign. - @. ϕ[1:N_Pixel_Height, 1:N_Pixel_Width] += δ[1:N_Pixel_Height, 1:N_Pixel_Width] + max_δ = max(max_δ, abs(δ)) + end - return ϕ, maximum_δ + return max_δ end @@ -296,52 +244,40 @@ function march_mesh!(mesh::FaceMesh) # For each point in the mesh we need to figure out its velocity # However all the nodes located at a border will never move - # I.e. velocity (Vx, Vy) = (0, 0) and the square of acrylate will remain - # of the same size. - - # Just in case... - reset_border_values!(mesh.corners) - - # Basically infinity time to shrink a triangle to nothing. - min_positive_t = Inf - + # I.e. velocity (Vx, Vy) = (0, 0) and the square of acrylate will remain of the same size. + # reset_border_values!(mesh.corners) mesh_r = copy(mesh.corners.r) mesh_c = copy(mesh.corners.c) # Get the time, at that velocity, for the area of the triangle to be nil. # We are only interested by positive values to only move in the direction of the gradient - mesh.corners.vr = -∇ϕᵤ - mesh.corners.vc = -∇ϕᵥ + mesh.corners.vr .= -∇ϕᵤ + mesh.corners.vc .= -∇ϕᵥ - list_triangles = vcat( - [ - triangle3D(mesh, row, col, :top) for row ∈ 1:N_Pixel_Height, - col ∈ 1:N_Pixel_Width - ], - [ - triangle3D(mesh, row, col, :bottom) for row ∈ 1:N_Pixel_Height, - col ∈ 1:N_Pixel_Width - ], - ) + height, width = size(mesh) - list_maximum_t = [time for time ∈ find_maximum_t.(list_triangles)] - δ = minimum(list_maximum_t) / 2.0 + for row ∈ 1:height, col ∈ 1:width + list_triangles = [triangle3D(mesh, row, col, :top), triangle3D(mesh, row, col, :bottom) ] - mesh.corners.r += δ * ∇ϕᵤ - mesh.corners.c += δ * ∇ϕᵥ + if !isempty(list_triangles) + list_maximum_t = [time for time ∈ find_maximum_t.(list_triangles) if !isnothing(time)] - # Reset the border at the fixed values fixed coordinates. - reset_border_values!(mesh.corners) + if !isempty(list_maximum_t) + δ = minimum(list_maximum_t) / 8.0 + + mesh.corners.r[row, col] -= δ * ∇ϕᵤ[row, col] + mesh.corners.c[row, col] -= δ * ∇ϕᵥ[row, col] + end + end + end println(""" March mesh: - max/min Vu = $(maximum(abs.(∇ϕᵤ))) / $(minimum(abs.(∇ϕᵤ))) - max/min Vv = $(maximum(abs.(∇ϕᵥ))) / $(minimum(abs.(∇ϕᵥ))) - Average mesh changes on row = $(average_absolute(mesh.corners.r - mesh_r)) - Average mesh changes on col = $(average_absolute(mesh.corners.c - mesh_c)) + $(field_summary(∇ϕᵤ, "Vu")) + $(field_summary(∇ϕᵥ, "Vu")) + $(field_summary(mesh.corners.r - mesh_r, "mesh changes on row")) + $(field_summary(mesh.corners.c - mesh_c, "mesh changes on col")) """) - - return nothing end diff --git a/src/math_utilities.jl b/src/math_utilities.jl index cbf2e31..58c7e48 100644 --- a/src/math_utilities.jl +++ b/src/math_utilities.jl @@ -24,7 +24,7 @@ function smallest_positive(x1::Float64, x2::Float64) (x1 > 0.0 && x2 < 0.0) && return x1 (x1 < 0.0 && x2 > 0.0) && return x2 (x1 > 0.0 && x2 > 0.0) && return min(x1, x2) - return Inf + return nothing end @@ -40,13 +40,8 @@ function ∇(ϕ::AbstractMatrix{Float64}) ∇ϕx = zeros(Float64, height, width) # divergence on the right edge will be filled with zeros ∇ϕy = zeros(Float64, height, width) # divergence on bottom edge will be filled with zeros - for x ∈ 1:height-1, y ∈ 1:width-1 - ∇ϕx[x, y] = ϕ[x+1, y] - ϕ[x, y] - ∇ϕy[x, y] = ϕ[x, y+1] - ϕ[x, y] - end - - # ∇ϕx[begin:end-1, :] = ϕ[begin+1:end, :] - ϕ[begin:end-1, :] - # ∇ϕy[:, begin:end-1] = ϕ[:, begin+1:end] - ϕ[:, begin:end-1] + ∇ϕx[begin:end-1, :] = ϕ[begin+1:end, :] - ϕ[begin:end-1, :] + ∇ϕy[:, begin:end-1] = ϕ[:, begin+1:end] - ϕ[:, begin:end-1] fill_borders!(∇ϕx, 0.0) fill_borders!(∇ϕy, 0.0) @@ -55,7 +50,6 @@ function ∇(ϕ::AbstractMatrix{Float64}) end - """ $(SIGNATURES) @@ -69,17 +63,16 @@ function laplacian(ϕ::AbstractMatrix{Float64}) # ϕ is inserted in padded matrix within 1:1+height+1 x 1:1+width+1. # The rest of the padded matrix (its borders) are set at 0.0. padded_ϕ = zeros(Float64, 1 + height + 1, 1 + width + 1) - padded_ϕ[2:height+1, 2:width+1] .= ϕ[1:height, 1:width] - - # The Laplace operator can be calculated by convolving a kernel. - # See https://www.wikiwand.com/en/Discrete_Laplace_operator for simple example in 2D - kernel = [[0.0 1.0 0.0]; [1.0 -4.0 1.0]; [0.0 1.0 0.0]] + padded_ϕ[begin+1:end-1, begin+1:end-1] = ϕ # Convolution - ∇²ϕ = zeros(Float64, height - 1, width - 1) - for row ∈ 1:height-1, col ∈ 1:width-1 - ∇²ϕ[row, col] = sum(padded_ϕ[row:row+2, col:col+2] .* kernel[1:3, 1:3]) - end - - return ∇²ϕ + ∇²ϕ = + padded_ϕ[begin+1-1:end-1-1, begin+1:end-1] + + padded_ϕ[begin+1+1:end-1+1, begin+1:end-1] + + padded_ϕ[begin+1:end-1, begin+1-1:end-1-1] + + padded_ϕ[begin+1:end-1, begin+1+1:end-1+1] - + 4.0 * padded_ϕ[begin+1:end-1, begin+1:end-1] + + return ∇²ϕ[1:end-1, 1:end-1] end + diff --git a/src/mesh.jl b/src/mesh.jl index b79dcff..c79161e 100644 --- a/src/mesh.jl +++ b/src/mesh.jl @@ -46,36 +46,12 @@ function find_maximum_t(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) # C will never end up on the line AB. # Very unlikely with Float64. # If nothing found, no move - return Inf + return nothing end find_maximum_t(p::Tuple{Vertex3D,Vertex3D,Vertex3D}) = find_maximum_t(p[1], p[2], p[3]) - - -""" -$(SIGNATURES) - -This function will take a `grid_definition x grid_definition` matrix and returns a -`grid_definition x grid_definition` mesh. - -""" -function matrix_to_mesh(ϕ::Matrix{Float64}) - height, width = size(ϕ) - - mesh = FaceMesh(height, width) - - # 1 more corner than corners! Therefore compiler needs to specify exact indices. - mesh.corners.ϕ[1:height, 1:width] .= ϕ[1:height, 1:width] - - # The borders' height is forced at 0. - reset_border_values!(mesh.corners) - - return mesh -end - - """ $(SIGNATURES) diff --git a/src/scratchpad.jl b/src/scratchpad.jl index e858171..1688345 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -14,10 +14,10 @@ image = Images.load("./examples/personal/statue_of_liberty_2.jpg"); # Check curr image = Images.load("./examples/personal/statue_of_liberty_3.jpg"); # Check current working directory with pwd() image = Images.load("./examples/personal/caricature.jpg"); # Check current working directory with pwd() -image = Images.load("./examples/personal/image.jpg"); # Check current working directory with pwd() +image = Images.load("./examples/personal/portrait.jpg"); # Check current working directory with pwd() image = Images.load("./examples/personal/bilal.jpg"); # Check current working directory with pwd() -mesh, imageBW = engineer_caustics(image;); +mesh, imageBW = engineer_caustics(image); mesh, imageBW = original_engineer_caustics(image); @@ -142,3 +142,72 @@ using MeshViz import GLMakie MeshViz.viz(cat_mesh3D) MeshViz.viz(cat_mesh2D) + + + + + + + + + +imageBW = Float64.(Gray.(image)) + +# Set global size parameters +height, width = size(imageBW) +global N_Pixel_Height = height +global N_Pixel_Width = width +global Meters_Per_Pixel = Caustics_Long_Side / N_Pixel_Height +println("Image size: $(N_Pixel_Height) x $(N_Pixel_Width)") + +# mesh is the same size as the image with an extra row/column to have coordinates to +# cover each image corner with a triangle. +mesh = FaceMesh(N_Pixel_Height, N_Pixel_Width) + +# The total energy going through the lens is equal to the amount of energy on the caustics +total_energy_lens = N_Pixel_Height * N_Pixel_Width * 1.0 # 1 unit of energy per pixel +total_energy_caustics = sum(imageBW) +average_energy_per_pixel = average(imageBW) + +# imageBW is normalised to the same (sort of) _energy_ as the original image. +imageBW = imageBW / average_energy_per_pixel + +lens_pixels_area = get_lens_pixels_area(mesh) + +# Positive error => the triangle needs to shrink (less light) +error_luminosity = Float64.(lens_pixels_area - imageBW) +error_luminosity = error_luminosity .- average(error_luminosity) + +# Save the loss image as a png +println( + """ +Luminosity: + Max/min pixel areas: $(maximum(lens_pixels_area)) / $(minimum(lens_pixels_area)) + Average pixel areas: $(average_absolute(lens_pixels_area)) + Average pixel areas: $(average(lens_pixels_area)) + + Max/min luminosity error: $(maximum(error_luminosity)) / $(minimum(error_luminosity)) + Average abs error: $(average_absolute(error_luminosity)) + Average error: $(average(error_luminosity)) + """, +) + + + + + + + + + + + + + + + + + + + + diff --git a/src/utilities.jl b/src/utilities.jl index 6d13122..bb89caf 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -143,7 +143,7 @@ function reset_border_values!(corners::FieldVertex3D) end -Base.size(fv::FieldVertex3D) = FieldVertex3D.size +Base.size(fv::FieldVertex3D) = fv.size """ @@ -155,7 +155,7 @@ function Vertex3D(fv::FieldVertex3D, row, col) if (1 <= row <= height + 1) && (1 <= col <= width + 1) Vertex3D( fv.r[row, col], - fv.y[row, col], + fv.c[row, col], fv.ϕ[row, col], fv.vr[row, col], fv.vc[row, col], @@ -243,33 +243,14 @@ function triangle3D(mesh::FaceMesh, row::Int, col::Int, side = Union{:top,:botto end t1_row, t1_col = t[1] + p1 = Vertex3D(mesh.corners, t1_row, t1_col) + t2_row, t2_col = t[2] + p2 = Vertex3D(mesh.corners, t2_row, t2_col) + t3_row, t3_col = t[3] + p3 = Vertex3D(mesh.corners, t3_row, t3_col) - r1 = mesh.corners.r[t1_row, t1_col] - c1 = mesh.corners.c[t1_row, t1_col] - ϕ1 = mesh.corners.ϕ[t1_row, t1_col] - vr1 = mesh.corners.vr[t1_row, t1_col] - vc1 = mesh.corners.vc[t1_row, t1_col] - # @assert r1^2 + c1^2 <= max_distance_squared "Coordinate $(r1), $(c1), $(ϕ1) of point #1 at $(row), $(col), side = $(side) makes no sense " - - r2 = mesh.corners.r[t2_row, t2_col] - c2 = mesh.corners.c[t2_row, t2_col] - ϕ2 = mesh.corners.ϕ[t2_row, t2_col] - vr2 = mesh.corners.vr[t2_row, t2_col] - vc2 = mesh.corners.vc[t2_row, t2_col] - # @assert r2^2 + c2^2 <= max_distance_squared "Coordinate $(r2), $(c2), $(ϕ2) of point #2 at $(row), $(col), side = $(side) makes no sense " - - r3 = mesh.corners.r[t3_row, t3_col] - c3 = mesh.corners.c[t3_row, t3_col] - ϕ3 = mesh.corners.ϕ[t3_row, t3_col] - vr3 = mesh.corners.vr[t3_row, t3_col] - vc3 = mesh.corners.vc[t3_row, t3_col] - # @assert r3^2 + c3^2 <= max_distance_squared "Coordinate $(r3), $(c3), $(ϕ3) of point #3 at $(row), $(col), side = $(side) makes no sense " - - p1 = Vertex3D(r1, c1, ϕ1, vr1, vc1) - p2 = Vertex3D(r2, c2, ϕ2, vr2, vc2) - p3 = Vertex3D(r3, c3, ϕ3, vr3, vc3) return (p1, p2, p3) else # return (missing, missing, missing) @@ -364,3 +345,19 @@ function get_lens_pixels_area(mesh::FaceMesh) average_energy_per_pixel = average(total_area) return total_area / average_energy_per_pixel end + + +""" +$(SIGNATURES) + +""" +function field_summary(field, fieldname) + max = round(maximum(field), sigdigits = 4) + min = round(minimum(field), sigdigits = 4) + avg = round(average(field), sigdigits = 4) + abs = round(average_absolute(field), sigdigits = 4) + + return """$(fieldname) (Max/Min/Avg/Avg abs.): $(max) / $(min) / $(avg) / $(abs)""" +end + + From 59853ddf82f76248582586c247a5f502bd35eaf6 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Sun, 19 Sep 2021 15:27:37 +0200 Subject: [PATCH 38/58] Tracking convergence bug --- src/CausticsEngineering.jl | 3 +++ src/create_mesh.jl | 55 ++++++++++++++++++++------------------ src/math_utilities.jl | 14 +++++++++- src/scratchpad.jl | 26 ++++++++++++++++++ 4 files changed, 71 insertions(+), 27 deletions(-) diff --git a/src/CausticsEngineering.jl b/src/CausticsEngineering.jl index 8548f9a..4e79daa 100644 --- a/src/CausticsEngineering.jl +++ b/src/CausticsEngineering.jl @@ -38,6 +38,9 @@ export FieldVertex3D, FaceMesh, + # Math + average, average_absolute, + # Mesh create_solid, create_solid_as_dict, diff --git a/src/create_mesh.jl b/src/create_mesh.jl index db71b9e..184bffa 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -24,12 +24,8 @@ function engineer_caustics(source_image) mesh = FaceMesh(height, width) # The total energy going through the lens is equal to the amount of energy on the caustics - total_energy_lens = height * width * 1 # 1 unit of energy per pixel - total_energy_caustics = sum(imageBW) - correction_ratio = sum(imageBW) / (width * height) - # imageBW is normalised to the same (sort of) _energy_ as the original image. - imageBW = imageBW ./ correction_ratio + imageBW /= average(imageBW) # start_max_update has no particular meing. # It is basically the initial max_update. But then is used to initialise other variables so that @@ -43,10 +39,10 @@ function engineer_caustics(source_image) iteration_count = 0 while ( - abs(max_update) > 0.0 && - abs((error_luminosity - old_error_luminosity) / old_error_luminosity) > 0.01 && + abs(max_update) > 1e-3 && + abs((error_luminosity - old_error_luminosity) / old_error_luminosity) > 0.00 && abs((max_update - old_max_update) / old_max_update) > 0.0 && - iteration_count < 10_000 + iteration_count < 5_000 ) iteration_count += 1 @@ -85,11 +81,16 @@ $(SIGNATURES) Zones of high luminosity should be covered with more triangles and should attract more vertices. """ function solve_velocity_potential!(mesh, image, prefix) + + fill!(mesh.corners.ϕ, 0.) + height, width = size(mesh.corners.ϕ) + + # Remember mesh is (will be) `grid_definition x grid_definition` just like the image # `grid_definition x grid_definition`, so LJ is `grid_definition x grid_definition`. area_distorted_corners = get_area_corners(mesh) - @assert average_absolute(area_distorted_corners) """ + @assert test_average_absolute(area_distorted_corners) """ solve_velocity_potential: area_distorted_corners values seem too large $(maximum(area_distorted_corners)) / $(minimum(area_distorted_corners)) @@ -98,7 +99,9 @@ function solve_velocity_potential!(mesh, image, prefix) # Positive error => the triangle needs to shrink (less light) error_luminosity = Float64.(area_distorted_corners - image) - @assert average_absolute(error_luminosity) """ + error_luminosity .-= average(error_luminosity) + + @assert test_average_absolute(error_luminosity) """ solve_velocity_potential: error_luminosity values seem too large max/min error_luminosity = $(maximum(error_luminosity)) / $(minimum(error_luminosity)) @@ -129,8 +132,8 @@ function solve_velocity_potential!(mesh, image, prefix) new_divergence_mean = 1_000.0 while ( - abs(max_update) > 0.0 && - abs((max_update - old_max_update) / old_max_update) >= 0.01 && + abs(max_update) > 1e-3 && + abs((max_update - old_max_update) / old_max_update) >= 0.0 && new_divergence_max >= 0.0 ) @@ -155,7 +158,7 @@ function solve_velocity_potential!(mesh, image, prefix) ϕ, max_update = propagate_poisson(mesh.corners.ϕ, error_luminosity) mesh.corners.ϕ[:, :] .= ϕ[:, :] - @assert average_absolute(mesh.corners.ϕ) """ + @assert test_average_absolute(mesh.corners.ϕ) """ solve_velocity_potential: ϕ values seem too large iteration count = $(iteration_count) @@ -255,7 +258,7 @@ function move_horizontally(mesh::FaceMesh, image; f = Focal_Length) # divergence_direction = zeros(Float64, size(div_row)) # divergence_direction is _FENCES_SIZED_ divergence_direction = div_row + div_col - @assert average_absolute(divergence_direction) """ + @assert test_average_absolute(divergence_direction) """ ALERT: horiz. Δ divergence_direction seem too large max/min = $(maximum(divergence_direction)) / $(minimum(divergence_direction)) @@ -263,7 +266,7 @@ function move_horizontally(mesh::FaceMesh, image; f = Focal_Length) true_H, max_update = propagate_poisson(true_H, -divergence_direction; clamp_correction = false) - @assert average_absolute(true_H) """ + @assert test_average_absolute(true_H) """ ALERT: horiz. Δ corner_heights is too large max/min corner_heights = $(maximum(true_H)) / $(minimum(true_H)) @@ -306,7 +309,7 @@ function propagate_poisson( # Ensure that border conditions are as they should fill_borders!(∇²ϕ, 0.0) - @assert average_absolute(ϕ) """ + @assert test_average_absolute(ϕ) """ Relaxation: ϕ values seem too large max/min ∇ϕ = $(maximum(∇²ϕ)) / $(minimum(∇²ϕ)) @@ -314,7 +317,7 @@ function propagate_poisson( """ - @assert average_absolute(∇²ϕ) """ + @assert test_average_absolute(∇²ϕ) """ Relaxation: ∇²ϕ values seem too large max/min ∇²ϕ = $(maximum(∇²ϕ)) / $(minimum(∇²ϕ)) @@ -351,7 +354,7 @@ function propagate_poisson( # High intensity loss ∇²ϕ means that the triangles are too bright, too large. # This has to converge towards the ∇²ϕ. Difference to calculate speed of the descent. δ = Lϕ - ∇²ϕ - @assert average_absolute(δ) """ + @assert test_average_absolute(δ) """ Relaxation: difference between intensity loss and estimated Laplacian seem too large max/min δ = $(maximum(δ)) / $(minimum(δ)) @@ -374,14 +377,14 @@ function propagate_poisson( max_correction_μ = 5.0 max_correction_in_between = 10.0 - if maximum_δ > max_correction_max - correction_ratio = min(correction_ratio, max_correction_max / maximum_δ) - elseif μ_δ > max_correction_μ - correction_ratio = min(correction_ratio, max_correction_μ / μ_δ) - elseif (μ_δ + maximum_δ) / 2 > max_correction_in_between - correction_ratio = - min(correction_ratio, max_correction_in_between / ((μ_δ + maximum_δ) / 2)) - end + # if maximum_δ > max_correction_max + # correction_ratio = min(correction_ratio, max_correction_max / maximum_δ) + # elseif μ_δ > max_correction_μ + # correction_ratio = min(correction_ratio, max_correction_μ / μ_δ) + # elseif (μ_δ + maximum_δ) / 2 > max_correction_in_between + # correction_ratio = + # min(correction_ratio, max_correction_in_between / ((μ_δ + maximum_δ) / 2)) + # end end # if δ > 0, the intensity loss is too high, or the Laplacian is too high at that point. diff --git a/src/math_utilities.jl b/src/math_utilities.jl index 3271353..4b9151c 100644 --- a/src/math_utilities.jl +++ b/src/math_utilities.jl @@ -1,7 +1,19 @@ """ $(SIGNATURES) """ -average_absolute(m::AbstractMatrix) = (sum(abs.(m)) / length(m)) < 1e10 +average(m::AbstractMatrix) = sum(m) / length(m) + + +""" +$(SIGNATURES) +""" +average_absolute(m::AbstractMatrix) = sum(abs.(m)) / length(m) + + +""" +$(SIGNATURES) +""" +test_average_absolute(m::AbstractMatrix) = average_absolute(m) < 1e10 """ diff --git a/src/scratchpad.jl b/src/scratchpad.jl index 1976b32..20c46e2 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -128,3 +128,29 @@ using MeshViz import GLMakie MeshViz.viz(cat_mesh3D) MeshViz.viz(cat_mesh2D) + + + + + +# engineer_caustics +image = Images.load("./examples/cat_posing.jpg"); # Check current working directory with pwd() +imageBW = Float64.(Gray.(image)); +imageBW /= average(imageBW); +height, width = size(imageBW) +mesh = CausticsEngineering.FaceMesh(height, width); + +# solve_velocity_potential +mesh.corners.ϕ +fill!(mesh.corners.ϕ, 0.); + +height, width = size(mesh.corners.ϕ) + +area_distorted_corners = CausticsEngineering.get_area_corners(mesh) +error_luminosity = Float64.(area_distorted_corners - imageBW) +error_luminosity = error_luminosity .- average(error_luminosity) + +sum(error_luminosity) +average(error_luminosity) +average_absolute(error_luminosity) + From 6939ec098639727a3e09c2159eac60c826f2c5e3 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Sun, 19 Sep 2021 15:30:18 +0200 Subject: [PATCH 39/58] Tracking convergence bug --- src/create_mesh.jl | 7 ++----- 1 file changed, 2 insertions(+), 5 deletions(-) diff --git a/src/create_mesh.jl b/src/create_mesh.jl index d8b1e60..8b47ca3 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -18,11 +18,8 @@ function engineer_caustics(source_image) # cover each image corner with a triangle. mesh = FaceMesh(N_Pixel_Height, N_Pixel_Width) - # The total energy going through the lens is equal to the amount of energy on the caustics - average_energy_per_pixel = average(imageBW) - # imageBW is normalised to the same (sort of) _energy_ as the original image. - imageBW = imageBW / average_energy_per_pixel + imageBW ./= average_energy_per_pixel max_update = Inf counter = 0 @@ -71,7 +68,7 @@ function solve_velocity_potential!(mesh, image, prefix) # Positive error => the triangle needs to shrink (less light) error_luminosity = Float64.(lens_pixels_area - image) - error_luminosity = error_luminosity .- average(error_luminosity) + error_luminosity .-= average(error_luminosity) # Save the loss image as a png save_plot_scalar_field!(error_luminosity, prefix * "_loss", image) From 250e0008b408f5a1b8c454ca3cf278bc8a8956eb Mon Sep 17 00:00:00 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zglN)Eojdq3kMIe8zz!+|EV7F@RSI-)kP>z7=leX(ab_s9L7D=itkC2Y_Hzf5oZ}9L zIK?yc@i-&g&5yaAG*i6M&{4EDLW9dX3mjGpD6)$MmjkAr8lSHLj1uB)I=`@8e9X*jU5&4i< h*pLZUnV<>&_5)5ms7LO&A!z^r002ovPDHLkV1mws%Lf1e literal 0 HcmV?d00001 From 883cda296e06fa02f37d0668983c6fcc73713a45 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Sun, 19 Sep 2021 17:06:52 +0200 Subject: [PATCH 41/58] Tracking convergence bug --- src/create_mesh.jl | 160 ++++++++++++++++++++++++++++++--------------- src/scratchpad.jl | 110 +++++++++++++++++++++++++++++++ 2 files changed, 217 insertions(+), 53 deletions(-) diff --git a/src/create_mesh.jl b/src/create_mesh.jl index 8b47ca3..40118bf 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -19,7 +19,7 @@ function engineer_caustics(source_image) mesh = FaceMesh(N_Pixel_Height, N_Pixel_Width) # imageBW is normalised to the same (sort of) _energy_ as the original image. - imageBW ./= average_energy_per_pixel + imageBW /= average(imageBW) max_update = Inf counter = 0 @@ -80,29 +80,28 @@ function solve_velocity_potential!(mesh, image, prefix) $(field_summary(error_luminosity, "luminosity error")) """) + max_update = Inf - counter = 0 - while (abs(max_update) > 1e-5 && counter < 5_000) - counter += 1 - counter % 500 == 0 && println( - """ solve_velocity_potential! during loop at count $(counter) with max_update = $(round(max_update, sigdigits=4)): + old_update = Inf + for i ∈ 1:typemax(Int64) + old_update = max_update + max_update = CausticsEngineering.propagate_poisson!(mesh.corners.ϕ, error_luminosity) + i % 500 == 0 && println( + """ solve_velocity_potential! during loop at count $(i) with max_update = $(round(max_update, sigdigits=4)): $(field_summary(mesh.corners.ϕ, "mesh.corners.ϕ")) """, ) - # Re-level ϕ around its average. It doesn't matter for potential fields - # mesh.corners.ϕ .-= average(mesh.corners.ϕ) - - # Solve the Poisson equation tp converge the divergence of the gradient of ϕ towards the luminosity error. - max_update = propagate_poisson!(mesh.corners.ϕ, error_luminosity) + if abs(old_update - max_update) <= 1e-6 || abs(max_update) <= 1e-4 + println(""" solve_velocity_potential! at count $(i) with + $(field_summary(error_luminosity, "luminosity error")) + $(field_summary(mesh.corners.ϕ, "mesh.corners.ϕ")) + max_update = $(max_update) + """) + break + end end - println(""" solve_velocity_potential! stopped at step $(counter) with - $(field_summary(error_luminosity, "luminosity error")) - $(field_summary(mesh.corners.ϕ, "mesh.corners.ϕ")) - max_update = $(max_update) - """) - # Now we need to march the mesh row,col corner locations according to this gradient. march_mesh!(mesh) plot_as_quiver(mesh, n_steps = 50, scale = 1.0, max_length = height / 20) @@ -160,13 +159,16 @@ function move_horizontally(mesh::FaceMesh, image; f = Focal_Length) divergence_direction = div_row + div_col # divergence_direction .-= average(divergence_direction) + max_update = Inf - counter = 0 - while max_update >= 1e-5 - counter += 1 - max_update = propagate_poisson!(true_H, divergence_direction) - counter % 100 && println("Convergence horiz. Δ max update = $(max_update)") + old_update = Inf + for i ∈ 1:typemax(Int64) + old_update = max_update + max_update = CausticsEngineering.propagate_poisson!(mesh.corners.ϕ, error_luminosity) + i % 100 == 0 && println("Convergence horiz. Δ max update = $(max_update)") + (abs(old_update - max_update) <= 1e-6 || abs(max_update) <= 1e-4) && break end + println("Convergence horiz. Δ stopped with max_update of $(max_update) at counter = $(counter)") return true_H, max_update @@ -203,26 +205,60 @@ function propagate_poisson!(ϕ::Matrix{Float64}, ∇²ϕ::Matrix{Float64}) height, width = size(∇²ϕ) fill_borders!(∇²ϕ, 0.0) - ################################################################################################################## - # From the velocity potential field ϕ, we calculate its gradient (the velocity), then its divergence. - # This is then compared to the intensity loss - max_δ = 0.0 - for row ∈ 1:height, col ∈ 1:width - ∇²ϕ_est = - ϕ[max(1, row - 1), col] + - ϕ[min(height, row + 1), col] + - ϕ[row, max(1, col - 1)] + - ϕ[row, min(width, col + 1)] - 4.0 * ϕ[row, col] - - δ = ∇²ϕ_est - ∇²ϕ[row, col] - δ /= 8.0 - - ϕ[row, col] += δ - - max_δ = max(max_δ, abs(δ)) - end - - return max_δ + # Laplacian + # Lϕ represent the approximation of the Laplacian of ϕ (second-order value) + Lϕ = laplacian(ϕ) + + # In the case of the velocity potential, δ is the difference between the divergence of the luminosity error + # and the current one for the current field ϕ (divergence of its gradient). + + # High luminosity error ∇²ϕ means that the triangles are too bright = too large. + # The Laplacian Lϕ has to converge towards the ∇²ϕ. Difference to calculate speed of the descent. + δ = Lϕ - ∇²ϕ + + # Default correction ratio to adjust δ is ω / 4.0 + δ *= ω / 4.0 + + # We limit the changes of the potential to a maximum + maximum_δ = maximum(abs.(δ)) + + # In the case of the velocity potential, + # if δ > 0, the Laplacian is too high at that point (∇²ϕ is too low). + + # To decrease the Laplacian ∇²ϕ, note that ∇² is a divergence (of a gradient) that represents net flow going outside. + # + # Decrease the Laplacian + # => decrease a divergence + # => decrease flow towards outside + # + # The flow is a gradient of the potential ϕ. + # => decrease flow towards outside + # => either decrease the values of the potential around that point, or increase the value of the potential at that point. + # => Increase the value of ϕ at that point means a positive change when δ > 0. + # δ > 0 => correction of the SAME sign. + ϕ[1:end-1, 1:end-1] .+= δ + ϕ .+= average(δ) + + # ################################################################################################################## + # # From the velocity potential field ϕ, we calculate its gradient (the velocity), then its divergence. + # # This is then compared to the intensity loss + # max_δ = 0.0 + # for row ∈ 1:height, col ∈ 1:width + # ∇²ϕ_est = + # ϕ[max(1, row - 1), col] + + # ϕ[min(height, row + 1), col] + + # ϕ[row, max(1, col - 1)] + + # ϕ[row, min(width, col + 1)] - 4.0 * ϕ[row, col] + + # δ = ∇²ϕ_est - ∇²ϕ[row, col] + # δ /= 2.0 + + # ϕ[row, col] += δ + + # max_δ = max(max_δ, abs(δ)) + # end + + return maximum_δ end @@ -253,20 +289,38 @@ function march_mesh!(mesh::FaceMesh) height, width = size(mesh) - for row ∈ 1:height, col ∈ 1:width - list_triangles = [triangle3D(mesh, row, col, :top), triangle3D(mesh, row, col, :bottom) ] + list_triangles = vcat( + [ + CausticsEngineering.triangle3D(mesh, row, col, :top) for row ∈ 1:height, col ∈ 1:width + ], + [ + CausticsEngineering.triangle3D(mesh, row, col, :bottom) for row ∈ 1:height, col ∈ 1:width + ], + ) - if !isempty(list_triangles) - list_maximum_t = [time for time ∈ find_maximum_t.(list_triangles) if !isnothing(time)] + list_maximum_t = [time for time ∈ CausticsEngineering.find_maximum_t.(list_triangles) if !isnothing(time) && time > 0.] + minimum(list_maximum_t) + maximum(list_maximum_t) - if !isempty(list_maximum_t) - δ = minimum(list_maximum_t) / 8.0 + δ = minimum(list_maximum_t) / 2.0 - mesh.corners.r[row, col] -= δ * ∇ϕᵤ[row, col] - mesh.corners.c[row, col] -= δ * ∇ϕᵥ[row, col] - end - end - end + mesh.corners.r += δ * ∇ϕᵤ + mesh.corners.c += δ * ∇ϕᵥ + + # for row ∈ 1:height, col ∈ 1:width + # list_triangles = [triangle3D(mesh, row, col, :top), triangle3D(mesh, row, col, :bottom) ] + + # if !isempty(list_triangles) + # list_maximum_t = [time for time ∈ find_maximum_t.(list_triangles) if !isnothing(time)] + + # if !isempty(list_maximum_t) + # δ = minimum(list_maximum_t) / 8.0 + + # mesh.corners.r[row, col] -= δ * ∇ϕᵤ[row, col] + # mesh.corners.c[row, col] -= δ * ∇ϕᵥ[row, col] + # end + # end + # end println(""" March mesh: diff --git a/src/scratchpad.jl b/src/scratchpad.jl index 1688345..3496a03 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -194,16 +194,125 @@ Luminosity: +########################################################## +## STEPPING + +using Revise, Debugger +using Images, Plots; +gr(); + +using CausticsEngineering + + +# engineer_caustics +image = Images.load("./examples/cat_posing.jpg"); # Check current working directory with pwd() +imageBW = Float64.(Gray.(image)); +imageBW /= average(imageBW); +sum(imageBW) + +height, width = size(imageBW) +mesh = CausticsEngineering.FaceMesh(height, width); + +# solve_velocity_potential +mesh.corners.ϕ +fill!(mesh.corners.ϕ, 0.); + +# height, width = size(mesh.corners.ϕ) + +area_distorted_corners = CausticsEngineering.get_lens_pixels_area(mesh); +error_luminosity = Float64.(area_distorted_corners - imageBW); +sum(error_luminosity) +average(error_luminosity) +average_absolute(error_luminosity) + +error_luminosity = error_luminosity .- average(error_luminosity); +sum(error_luminosity) +average(error_luminosity) +average_absolute(error_luminosity) + +Lϕ = CausticsEngineering.laplacian(mesh.corners.ϕ); +ls = sign(sum(Lϕ)) +la = sign(average(Lϕ)) +δ = Lϕ - error_luminosity; +δ ./= 4.0; +ds = sign(sum(δ)) +sa = sign(average(δ)) +println() +# average(δ) +# average_absolute(δ) +# println(maximum(abs.(δ))) +mesh.corners.ϕ[1:end-1, 1:end-1] .+= δ; +mesh.corners.ϕ .-= average(mesh.corners.ϕ); +sum(mesh.corners.ϕ) +average(mesh.corners.ϕ) +average_absolute(mesh.corners.ϕ) +sign(sum(δ)) +CausticsEngineering.save_plot_scalar_field!(error_luminosity, "trace_1", imageBW) +max_update = Inf +old_update = Inf +any(isnan.(error_luminosity)) +any(isnan.(mesh.corners.r)) +any(isnan.(mesh.corners.c)) +any(isnan.(mesh.corners.vr)) +any(isnan.(mesh.corners.vc)) +any(isnan.(mesh.corners.ϕ)) + +i = 0 +begin + i += 1 + old_update = max_update + max_update = CausticsEngineering.propagate_poisson!(mesh.corners.ϕ, error_luminosity) + # i % 100 == 0 && println(max_update) + # (abs(old_update - max_update) <= 1e-6 || abs(max_update) <= 1e-4) && break +end + +max_update +old_update + + +f() + + +∇ϕᵤ, ∇ϕᵥ = CausticsEngineering.∇(mesh.corners.ϕ) + +sum(∇ϕᵤ) +average(∇ϕᵤ) +average_absolute(∇ϕᵤ) + + +height, width = size(imageBW) +mesh.corners.vr .= -∇ϕᵤ +mesh.corners.vc .= -∇ϕᵥ +list_triangles = vcat( + [ + CausticsEngineering.triangle3D(mesh, row, col, :top) for row ∈ 1:height, col ∈ 1:width + ], + [ + CausticsEngineering.triangle3D(mesh, row, col, :bottom) for row ∈ 1:height, col ∈ 1:width + ], +) + +list_maximum_t = [time for time ∈ CausticsEngineering.find_maximum_t.(list_triangles) if !isnothing(time) && time > 0.] +minimum(list_maximum_t) +maximum(list_maximum_t) + +δ = minimum(list_maximum_t) / 2.0 + +mesh.corners.r += δ * ∇ϕᵤ +mesh.corners.c += δ * ∇ϕᵥ + + +end @@ -211,3 +320,4 @@ Luminosity: +nothing; From 034c4ec8885b0ee283b66cdad8e32f7a8b4a6bd9 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Mon, 20 Sep 2021 18:32:31 +0200 Subject: [PATCH 42/58] Tracking convergence bug --- examples/trace_1.png | Bin 248791 -> 0 bytes src/CausticsEngineering.jl | 8 +- src/create_mesh.jl | 150 ++++++++++++++++++------------------- src/io.jl | 2 - src/math_utilities.jl | 1 - src/mesh.jl | 3 +- src/scratchpad.jl | 136 ++++++++++++++++++++++++++------- src/utilities.jl | 10 ++- 8 files changed, 201 insertions(+), 109 deletions(-) delete mode 100644 examples/trace_1.png diff --git a/examples/trace_1.png b/examples/trace_1.png deleted file mode 100644 index 2a0709bc5c1476aa8675b8f5dd52c788a96f5fe1..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 248791 zcmX`S2UwE(`v=_liH0*5CYl?Z;6idz;Rf6rwQ}Ojow=$bp{1Dv6_s#rvr;tE(-d=% zI4jfgm@7wFj?A>o-pBKQ-xr<>l#A=)%l*CY&w3s*9PF$F`K0)c962J0vo?1+a^!!& 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zglN)Eojdq3kMIe8zz!+|EV7F@RSI-)kP>z7=leX(ab_s9L7D=itkC2Y_Hzf5oZ}9L zIK?yc@i-&g&5yaAG*i6M&{4EDLW9dX3mjGpD6)$MmjkAr8lSHLj1uB)I=`@8e9X*jU5&4i< h*pLZUnV<>&_5)5ms7LO&A!z^r002ovPDHLkV1mws%Lf1e diff --git a/src/CausticsEngineering.jl b/src/CausticsEngineering.jl index 4be0315..0e65014 100644 --- a/src/CausticsEngineering.jl +++ b/src/CausticsEngineering.jl @@ -1,11 +1,17 @@ module CausticsEngineering using DocStringExtensions -using Random, Meshes, Images +using Random, Images using Plots gr() +using Meshes, FileIO, MeshIO + + +include("../examples/personal/original.jl") + + include("parameters.jl") include("utilities.jl") include("math_utilities.jl") diff --git a/src/create_mesh.jl b/src/create_mesh.jl index 40118bf..9f77f24 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -21,20 +21,21 @@ function engineer_caustics(source_image) # imageBW is normalised to the same (sort of) _energy_ as the original image. imageBW /= average(imageBW) - max_update = Inf + marginal_change = max_update = Inf counter = 0 while (abs(max_update) > 1e-5 && counter < 5_000) counter += 1 + ϕ, ε, max_update = solve_velocity_potential!(mesh, imageBW, "it$(counter)") + marginal_change = average_absolute(ϕ - mesh.corners.ϕ) + + print(""" + RESULT AT ITERATION $(counter): + Vertical move max update = $(max_update) + Mean error luminosity = $(average_absolute(ε)) + Marginal change = $(marginal_change) + """) - println( - "\nSTARTING VERTICAL ITERATION $(counter) --------------------------------------------", - ) - - max_update, error_luminosity = - solve_velocity_potential!(mesh, imageBW, "it$(counter)") - print( - "Vertical move max update = $(max_update) -- Mean error luminosity = $(error_luminosity)\n", - ) + mesh.corners.ϕ .= ϕ end println("\nSTARTING HORIZONTAL ITERATION ---") @@ -57,56 +58,61 @@ $(SIGNATURES) Zones of high luminosity should be covered with more triangles and should attract more vertices. """ function solve_velocity_potential!(mesh, image, prefix) - # Start with a new clean field height, width = size(mesh) # Get the area of each individual pixel as stretch/shrunk on the lens. Area = energy. # _FENCES_SIZED_ - mesh.corners.ϕ = zeros(Float64, height + 1, width + 1) + # Illumination only depends on the position of the corners, not their heights. ϕ is not relevant. lens_pixels_area = get_lens_pixels_area(mesh) # Positive error => the triangle needs to shrink (less light) - error_luminosity = Float64.(lens_pixels_area - image) - error_luminosity .-= average(error_luminosity) + ε = Float64.(lens_pixels_area - image) + ε .-= average(ε) # Save the loss image as a png - save_plot_scalar_field!(error_luminosity, prefix * "_loss", image) + save_plot_scalar_field!(ε, prefix * "_loss", image) + + # Start with a clean, flat potential field. + ϕ = zeros(Float64, height + 1, width + 1) println(""" solve_velocity_potential! before loop: $(field_summary(lens_pixels_area, "Pixel area")) - $(field_summary(error_luminosity, "luminosity error")) + $(field_summary(ε, "luminosity error")) """) - - max_update = Inf - old_update = Inf - for i ∈ 1:typemax(Int64) - old_update = max_update - max_update = CausticsEngineering.propagate_poisson!(mesh.corners.ϕ, error_luminosity) - i % 500 == 0 && println( - """ solve_velocity_potential! during loop at count $(i) with max_update = $(round(max_update, sigdigits=4)): + count = 0 + new_update = 10_000 + old_update = 2 * new_update + while 1e-4 < new_update < old_update && (old_update - new_update) / old_update > 1e-4 + count += 1 + old_update = new_update + new_update, _ = CausticsEngineering.propagate_poisson!(ϕ, ε) + count % 500 == 0 && println( + """ solve_velocity_potential! during loop at count $(count) with max_update = $(round(new_update, sigdigits=4)): $(field_summary(mesh.corners.ϕ, "mesh.corners.ϕ")) """, ) - if abs(old_update - max_update) <= 1e-6 || abs(max_update) <= 1e-4 - println(""" solve_velocity_potential! at count $(i) with - $(field_summary(error_luminosity, "luminosity error")) - $(field_summary(mesh.corners.ϕ, "mesh.corners.ϕ")) - max_update = $(max_update) - """) - break - end end # Now we need to march the mesh row,col corner locations according to this gradient. - march_mesh!(mesh) + march_mesh!(mesh, ϕ) + + marginal_change = ϕ - mesh.corners.ϕ + println(""" + Result of marching + New ϕ: $(CausticsEngineering.field_summary(ϕ)) + Marginal update of ϕ: $(CausticsEngineering.field_summary(marginal_change)) + """) + + mesh.corners.ϕ .= ϕ + plot_as_quiver(mesh, n_steps = 50, scale = 1.0, max_length = height / 20) - return max_update, average_absolute(error_luminosity) + return ϕ, ε, new_update end @@ -164,12 +170,15 @@ function move_horizontally(mesh::FaceMesh, image; f = Focal_Length) old_update = Inf for i ∈ 1:typemax(Int64) old_update = max_update - max_update = CausticsEngineering.propagate_poisson!(mesh.corners.ϕ, error_luminosity) + max_update = + CausticsEngineering.propagate_poisson!(mesh.corners.ϕ, -divergence_direction) i % 100 == 0 && println("Convergence horiz. Δ max update = $(max_update)") (abs(old_update - max_update) <= 1e-6 || abs(max_update) <= 1e-4) && break end - println("Convergence horiz. Δ stopped with max_update of $(max_update) at counter = $(counter)") + println( + "Convergence horiz. Δ stopped with max_update of $(max_update) at counter = $(counter)", + ) return true_H, max_update end @@ -200,65 +209,49 @@ In order of how to think about the flow of the program for the velocity potentia - => Increase the value of ϕ at that point means a positive change when δ > 0. - δ > 0 => correction of the SAME sign. """ -function propagate_poisson!(ϕ::Matrix{Float64}, ∇²ϕ::Matrix{Float64}) +function propagate_poisson!(ϕ::Matrix{Float64}, ε::Matrix{Float64}) # Ensure that border conditions are as they should (= 0.0) - height, width = size(∇²ϕ) - fill_borders!(∇²ϕ, 0.0) + height, width = size(ε) + # fill_borders!(ε, 0.0) # Laplacian # Lϕ represent the approximation of the Laplacian of ϕ (second-order value) - Lϕ = laplacian(ϕ) + ∇²ϕ_est = laplacian(ϕ) # In the case of the velocity potential, δ is the difference between the divergence of the luminosity error # and the current one for the current field ϕ (divergence of its gradient). # High luminosity error ∇²ϕ means that the triangles are too bright = too large. # The Laplacian Lϕ has to converge towards the ∇²ϕ. Difference to calculate speed of the descent. - δ = Lϕ - ∇²ϕ + δ = ∇²ϕ_est - ε # Default correction ratio to adjust δ is ω / 4.0 - δ *= ω / 4.0 - - # We limit the changes of the potential to a maximum - maximum_δ = maximum(abs.(δ)) + # δ *= ω / 7.0 + δ *= 0.15 # In the case of the velocity potential, # if δ > 0, the Laplacian is too high at that point (∇²ϕ is too low). - - # To decrease the Laplacian ∇²ϕ, note that ∇² is a divergence (of a gradient) that represents net flow going outside. - # - # Decrease the Laplacian - # => decrease a divergence - # => decrease flow towards outside - # - # The flow is a gradient of the potential ϕ. - # => decrease flow towards outside - # => either decrease the values of the potential around that point, or increase the value of the potential at that point. - # => Increase the value of ϕ at that point means a positive change when δ > 0. - # δ > 0 => correction of the SAME sign. ϕ[1:end-1, 1:end-1] .+= δ - ϕ .+= average(δ) + + ϕ .-= average(ϕ) # ################################################################################################################## # # From the velocity potential field ϕ, we calculate its gradient (the velocity), then its divergence. # # This is then compared to the intensity loss - # max_δ = 0.0 - # for row ∈ 1:height, col ∈ 1:width - # ∇²ϕ_est = + # ∇²ϕ_est = zeros(Float64, size(ε)) + # δ = zeros(Float64, size(ε)) + # for row ∈ 1:height, col ∈ 1:width + # ∇²ϕ_est[row, col] = # ϕ[max(1, row - 1), col] + # ϕ[min(height, row + 1), col] + # ϕ[row, max(1, col - 1)] + # ϕ[row, min(width, col + 1)] - 4.0 * ϕ[row, col] - # δ = ∇²ϕ_est - ∇²ϕ[row, col] - # δ /= 2.0 - - # ϕ[row, col] += δ - - # max_δ = max(max_δ, abs(δ)) + # δ[row, col] = ω / 4.0 * (∇²ϕ_est[row, col] - ε[row, col]) + # ϕ[row, col] += δ[row, col] # end - return maximum_δ + return maximum(abs.(δ)), ∇²ϕ_est, δ end @@ -270,10 +263,10 @@ $(SIGNATURES) `march_mesh!` flexes the mesh """ -function march_mesh!(mesh::FaceMesh) +function march_mesh!(mesh::FaceMesh, ϕ::AbstractMatrix{Float64}) # Calculate the gradient of the velocity potential. - ∇ϕᵤ, ∇ϕᵥ = ∇(mesh.corners.ϕ) + ∇ϕᵤ, ∇ϕᵥ = ∇(ϕ) # For each point in the mesh we need to figure out its velocity # However all the nodes located at a border will never move @@ -291,21 +284,26 @@ function march_mesh!(mesh::FaceMesh) list_triangles = vcat( [ - CausticsEngineering.triangle3D(mesh, row, col, :top) for row ∈ 1:height, col ∈ 1:width + CausticsEngineering.triangle3D(mesh, row, col, :top) for row ∈ 1:height, + col ∈ 1:width ], [ - CausticsEngineering.triangle3D(mesh, row, col, :bottom) for row ∈ 1:height, col ∈ 1:width + CausticsEngineering.triangle3D(mesh, row, col, :bottom) for row ∈ 1:height, + col ∈ 1:width ], ) - list_maximum_t = [time for time ∈ CausticsEngineering.find_maximum_t.(list_triangles) if !isnothing(time) && time > 0.] + list_maximum_t = [ + time for time ∈ CausticsEngineering.find_maximum_t.(list_triangles) if + !isnothing(time) && time > 0.0 + ] minimum(list_maximum_t) maximum(list_maximum_t) - δ = minimum(list_maximum_t) / 2.0 + δ = minimum(list_maximum_t) / 1.2 - mesh.corners.r += δ * ∇ϕᵤ - mesh.corners.c += δ * ∇ϕᵥ + mesh.corners.r .+= δ * ∇ϕᵤ + mesh.corners.c .+= δ * ∇ϕᵥ # for row ∈ 1:height, col ∈ 1:width # list_triangles = [triangle3D(mesh, row, col, :top), triangle3D(mesh, row, col, :bottom) ] diff --git a/src/io.jl b/src/io.jl index d5d705b..cc49642 100644 --- a/src/io.jl +++ b/src/io.jl @@ -1,5 +1,3 @@ -using FileIO, MeshIO - # Utility function to name a vertex vertex_name(face::String, row::Int64, col::Int64)::String = "Vertex_$(name)_$(row)_$(col)" diff --git a/src/math_utilities.jl b/src/math_utilities.jl index 58c7e48..a3abfe7 100644 --- a/src/math_utilities.jl +++ b/src/math_utilities.jl @@ -75,4 +75,3 @@ function laplacian(ϕ::AbstractMatrix{Float64}) return ∇²ϕ[1:end-1, 1:end-1] end - diff --git a/src/mesh.jl b/src/mesh.jl index c79161e..12e8e98 100644 --- a/src/mesh.jl +++ b/src/mesh.jl @@ -265,8 +265,7 @@ function create_solid( # The connections are listed as a tuple of 3 arrays. # First array contains the first point of a triangle, and so on triangle_index = [ - (index_dict[v[1]], index_dict[v[2]], index_dict[v[3]]) for - v ∈ values(triangle_dict) + (index_dict[v[1]], index_dict[v[2]], index_dict[v[3]]) for v ∈ values(triangle_dict) ] return triangle_dict, vertex_dict, triangle_index, vertex_index diff --git a/src/scratchpad.jl b/src/scratchpad.jl index 3496a03..001ed79 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -19,7 +19,7 @@ image = Images.load("./examples/personal/bilal.jpg"); # Check current working di mesh, imageBW = engineer_caustics(image); -mesh, imageBW = original_engineer_caustics(image); +mesh, imageBW = CausticsEngineering.original_engineer_caustics(image); imageBW = Float64.(Gray.(image)); @@ -197,8 +197,7 @@ Luminosity: ########################################################## ## STEPPING -using Revise, Debugger -using Images, Plots; +using Revise, Debugger, Images, Plots; gr(); using CausticsEngineering @@ -211,46 +210,131 @@ imageBW /= average(imageBW); sum(imageBW) height, width = size(imageBW) -mesh = CausticsEngineering.FaceMesh(height, width); + + + # solve_velocity_potential -mesh.corners.ϕ -fill!(mesh.corners.ϕ, 0.); +mesh = CausticsEngineering.FaceMesh(height, width); +CausticsEngineering.field_summary(mesh.corners.ϕ) -# height, width = size(mesh.corners.ϕ) +origmesh = CausticsEngineering.squareMesh(width + 1, height + 1); +origϕ = zeros(width, height); +CausticsEngineering.field_summary(origϕ) + +# height, width = size(mesh.corners.ϕ) area_distorted_corners = CausticsEngineering.get_lens_pixels_area(mesh); +origarea_distorted_corners = CausticsEngineering.getPixelArea(origmesh); +CausticsEngineering.field_summary(area_distorted_corners) +CausticsEngineering.field_summary(area_distorted_corners - origarea_distorted_corners) + error_luminosity = Float64.(area_distorted_corners - imageBW); -sum(error_luminosity) -average(error_luminosity) -average_absolute(error_luminosity) +CausticsEngineering.field_summary(error_luminosity) + +origerror_luminosity = Float64.(origarea_distorted_corners - imageBW); +CausticsEngineering.field_summary(origerror_luminosity) + +CausticsEngineering.field_summary(error_luminosity - origerror_luminosity) + error_luminosity = error_luminosity .- average(error_luminosity); -sum(error_luminosity) -average(error_luminosity) -average_absolute(error_luminosity) +CausticsEngineering.field_summary(error_luminosity) + +origerror_luminosity = origerror_luminosity .- average(origerror_luminosity); +CausticsEngineering.field_summary(origerror_luminosity) + +CausticsEngineering.field_summary(error_luminosity - origerror_luminosity) + + +mesh = CausticsEngineering.FaceMesh(height, width); +CausticsEngineering.field_summary(mesh.corners.ϕ) Lϕ = CausticsEngineering.laplacian(mesh.corners.ϕ); -ls = sign(sum(Lϕ)) -la = sign(average(Lϕ)) +CausticsEngineering.field_summary(Lϕ) δ = Lϕ - error_luminosity; -δ ./= 4.0; -ds = sign(sum(δ)) -sa = sign(average(δ)) -println() -# average(δ) -# average_absolute(δ) -# println(maximum(abs.(δ))) +δ .*= CausticsEngineering.ω / 4.0; +CausticsEngineering.field_summary(δ) + + mesh.corners.ϕ[1:end-1, 1:end-1] .+= δ; mesh.corners.ϕ .-= average(mesh.corners.ϕ); +CausticsEngineering.field_summary(mesh.corners.ϕ) + + +mesh = CausticsEngineering.FaceMesh(height, width); +CausticsEngineering.field_summary(CausticsEngineering.laplacian(mesh.corners.ϕ) - error_luminosity) + +max_update, Lϕ, δ = CausticsEngineering.propagate_poisson!(mesh.corners.ϕ, error_luminosity); +CausticsEngineering.field_summary(mesh.corners.ϕ) +CausticsEngineering.field_summary(Lϕ) +CausticsEngineering.field_summary(δ) + + +origϕ = zeros(width, height); +max_update, origLϕ, origδ = CausticsEngineering.orig_propagate_poisson!(origϕ, origerror_luminosity); +CausticsEngineering.field_summary(origϕ) +CausticsEngineering.field_summary(origLϕ) +CausticsEngineering.field_summary(origδ) + + + + + + + +mesh = CausticsEngineering.FaceMesh(height, width); +new_update = 10_000 +old_update = 2*new_update +for i ∈ 1:1_000 + old_update = new_update + new_update, Lϕ, δ = CausticsEngineering.propagate_poisson!(mesh.corners.ϕ, error_luminosity) + i % 50 == 0 && println(""" + $(i) => $(max_update) + $(CausticsEngineering.field_summary(mesh.corners.ϕ)) + $(CausticsEngineering.field_summary(Lϕ)) + $(CausticsEngineering.field_summary(δ)) + """ + ) + if new_update > old_update || i == 5_000 + new_update, Lϕ, δ = CausticsEngineering.orig_propagate_poisson!(origϕ, origerror_luminosity) + println(""" + $(i) => $(new_update) + $(CausticsEngineering.field_summary(mesh.corners.ϕ)) + $(CausticsEngineering.field_summary(Lϕ)) + $(CausticsEngineering.field_summary(δ)) + """ + ) + break + end +end + +origϕ = zeros(width, height); +for i ∈ 1:5_000 + max_update,origLϕ, origδ = CausticsEngineering.orig_propagate_poisson!(origϕ, origerror_luminosity); + i % 500 == 0 && println(""" + $(i) => $(max_update) + $(CausticsEngineering.field_summary(origϕ)) + $(CausticsEngineering.field_summary(origLϕ)) + $(CausticsEngineering.field_summary(origδ)) + """ + ) + if max_update <= 1e-3 + max_update, origLϕ, origδ = CausticsEngineering.orig_propagate_poisson!(origϕ, origerror_luminosity); + println(CausticsEngineering.field_summary(origϕ)) + println(CausticsEngineering.field_summary(origLϕ)) + println(CausticsEngineering.field_summary(origδ)) + break + end +end + + + + -sum(mesh.corners.ϕ) -average(mesh.corners.ϕ) -average_absolute(mesh.corners.ϕ) -sign(sum(δ)) CausticsEngineering.save_plot_scalar_field!(error_luminosity, "trace_1", imageBW) diff --git a/src/utilities.jl b/src/utilities.jl index bb89caf..3048c5a 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -352,12 +352,20 @@ $(SIGNATURES) """ function field_summary(field, fieldname) + s = round(sum(field), sigdigits = 4) max = round(maximum(field), sigdigits = 4) min = round(minimum(field), sigdigits = 4) avg = round(average(field), sigdigits = 4) abs = round(average_absolute(field), sigdigits = 4) - return """$(fieldname) (Max/Min/Avg/Avg abs.): $(max) / $(min) / $(avg) / $(abs)""" + return """$(fieldname) (Sum/Max/Min/Avg/Avg abs.): $(s) / $(max) / $(min) / $(avg) / $(abs)""" end +""" +$(SIGNATURES) + +""" +field_summary(field) = field_summary(field, "") + + From 3d4dd722d3c79c02610b0528150051bef7ddd1a9 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Mon, 20 Sep 2021 21:17:16 +0200 Subject: [PATCH 43/58] Tracking area convergence bug --- src/create_mesh.jl | 65 ++++++++++++++++++++++++-------------------- src/scratchpad.jl | 68 ++++++++++++++++++++++++---------------------- src/utilities.jl | 11 ++++---- 3 files changed, 76 insertions(+), 68 deletions(-) diff --git a/src/create_mesh.jl b/src/create_mesh.jl index 9f77f24..3480b33 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -25,8 +25,11 @@ function engineer_caustics(source_image) counter = 0 while (abs(max_update) > 1e-5 && counter < 5_000) counter += 1 - ϕ, ε, max_update = solve_velocity_potential!(mesh, imageBW, "it$(counter)") - marginal_change = average_absolute(ϕ - mesh.corners.ϕ) + + ϕ = mesh.corners.ϕ + mesh.corners.ϕ, mesh.corners.r, mesh.corners.c, ε, max_update = + solve_velocity_potential!(mesh, imageBW, "it$(counter)") + marginal_change = average_absolute(mesh.corners.ϕ - ϕ) print(""" RESULT AT ITERATION $(counter): @@ -35,7 +38,7 @@ function engineer_caustics(source_image) Marginal change = $(marginal_change) """) - mesh.corners.ϕ .= ϕ + plot_as_quiver(mesh, n_steps = 50, scale = 1.0, max_length = height / 20) end println("\nSTARTING HORIZONTAL ITERATION ---") @@ -89,30 +92,28 @@ function solve_velocity_potential!(mesh, image, prefix) while 1e-4 < new_update < old_update && (old_update - new_update) / old_update > 1e-4 count += 1 old_update = new_update - new_update, _ = CausticsEngineering.propagate_poisson!(ϕ, ε) + + ϕ, _, _, new_update = CausticsEngineering.propagate_poisson(ϕ, ε) + count % 500 == 0 && println( - """ solve_velocity_potential! during loop at count $(count) with max_update = $(round(new_update, sigdigits=4)): - $(field_summary(mesh.corners.ϕ, "mesh.corners.ϕ")) - """, + """ +solve_velocity_potential! during loop at count $(count) with max_update = $(round(new_update, sigdigits=4)): + $(field_summary(mesh.corners.ϕ, "ϕ")) +""", ) - end # Now we need to march the mesh row,col corner locations according to this gradient. - march_mesh!(mesh, ϕ) + coord_r, coord_c = march_mesh(mesh, ϕ) - marginal_change = ϕ - mesh.corners.ϕ + # marginal_change = ϕ - mesh.corners.ϕ + # Marginal update of ϕ: $(CausticsEngineering.field_summary(marginal_change)) println(""" Result of marching New ϕ: $(CausticsEngineering.field_summary(ϕ)) - Marginal update of ϕ: $(CausticsEngineering.field_summary(marginal_change)) """) - mesh.corners.ϕ .= ϕ - - plot_as_quiver(mesh, n_steps = 50, scale = 1.0, max_length = height / 20) - - return ϕ, ε, new_update + return ϕ, coord_r, coord_c, ε, new_update end @@ -166,13 +167,15 @@ function move_horizontally(mesh::FaceMesh, image; f = Focal_Length) # divergence_direction .-= average(divergence_direction) + ϕ = mesh.corners.ϕ + max_update = Inf old_update = Inf for i ∈ 1:typemax(Int64) old_update = max_update - max_update = - CausticsEngineering.propagate_poisson!(mesh.corners.ϕ, -divergence_direction) + ϕ, _, _, max_update = propagate_poisson(ϕ, -divergence_direction) i % 100 == 0 && println("Convergence horiz. Δ max update = $(max_update)") + (abs(old_update - max_update) <= 1e-6 || abs(max_update) <= 1e-4) && break end @@ -180,7 +183,7 @@ function move_horizontally(mesh::FaceMesh, image; f = Focal_Length) "Convergence horiz. Δ stopped with max_update of $(max_update) at counter = $(counter)", ) - return true_H, max_update + return ϕ, max_update end @@ -209,7 +212,7 @@ In order of how to think about the flow of the program for the velocity potentia - => Increase the value of ϕ at that point means a positive change when δ > 0. - δ > 0 => correction of the SAME sign. """ -function propagate_poisson!(ϕ::Matrix{Float64}, ε::Matrix{Float64}) +function propagate_poisson(ϕ::Matrix{Float64}, ε::Matrix{Float64}) # Ensure that border conditions are as they should (= 0.0) height, width = size(ε) # fill_borders!(ε, 0.0) @@ -231,9 +234,10 @@ function propagate_poisson!(ϕ::Matrix{Float64}, ε::Matrix{Float64}) # In the case of the velocity potential, # if δ > 0, the Laplacian is too high at that point (∇²ϕ is too low). - ϕ[1:end-1, 1:end-1] .+= δ + ϕ_res = zeros(Float64, size(ϕ)) + ϕ_res[1:end-1, 1:end-1] = ϕ[1:end-1, 1:end-1] + δ - ϕ .-= average(ϕ) + ϕ_res .-= average(ϕ_res) # ################################################################################################################## # # From the velocity potential field ϕ, we calculate its gradient (the velocity), then its divergence. @@ -251,7 +255,7 @@ function propagate_poisson!(ϕ::Matrix{Float64}, ε::Matrix{Float64}) # ϕ[row, col] += δ[row, col] # end - return maximum(abs.(δ)), ∇²ϕ_est, δ + return ϕ_res, ∇²ϕ_est, δ, maximum(abs.(δ)) end @@ -263,7 +267,7 @@ $(SIGNATURES) `march_mesh!` flexes the mesh """ -function march_mesh!(mesh::FaceMesh, ϕ::AbstractMatrix{Float64}) +function march_mesh(mesh::FaceMesh, ϕ::AbstractMatrix{Float64}) # Calculate the gradient of the velocity potential. ∇ϕᵤ, ∇ϕᵥ = ∇(ϕ) @@ -272,8 +276,8 @@ function march_mesh!(mesh::FaceMesh, ϕ::AbstractMatrix{Float64}) # However all the nodes located at a border will never move # I.e. velocity (Vx, Vy) = (0, 0) and the square of acrylate will remain of the same size. # reset_border_values!(mesh.corners) - mesh_r = copy(mesh.corners.r) - mesh_c = copy(mesh.corners.c) + mesh_r = mesh.corners.r + mesh_c = mesh.corners.c # Get the time, at that velocity, for the area of the triangle to be nil. # We are only interested by positive values to only move in the direction of the gradient @@ -281,7 +285,6 @@ function march_mesh!(mesh::FaceMesh, ϕ::AbstractMatrix{Float64}) mesh.corners.vc .= -∇ϕᵥ height, width = size(mesh) - list_triangles = vcat( [ CausticsEngineering.triangle3D(mesh, row, col, :top) for row ∈ 1:height, @@ -293,6 +296,7 @@ function march_mesh!(mesh::FaceMesh, ϕ::AbstractMatrix{Float64}) ], ) + list_maximum_t = [ time for time ∈ CausticsEngineering.find_maximum_t.(list_triangles) if !isnothing(time) && time > 0.0 @@ -302,8 +306,8 @@ function march_mesh!(mesh::FaceMesh, ϕ::AbstractMatrix{Float64}) δ = minimum(list_maximum_t) / 1.2 - mesh.corners.r .+= δ * ∇ϕᵤ - mesh.corners.c .+= δ * ∇ϕᵥ + mesh_r .+= δ .* ∇ϕᵤ + mesh_c .+= δ .* ∇ϕᵥ # for row ∈ 1:height, col ∈ 1:width # list_triangles = [triangle3D(mesh, row, col, :top), triangle3D(mesh, row, col, :bottom) ] @@ -322,11 +326,12 @@ function march_mesh!(mesh::FaceMesh, ϕ::AbstractMatrix{Float64}) println(""" March mesh: + correction_ratio δ = $(δ) $(field_summary(∇ϕᵤ, "Vu")) $(field_summary(∇ϕᵥ, "Vu")) $(field_summary(mesh.corners.r - mesh_r, "mesh changes on row")) $(field_summary(mesh.corners.c - mesh_c, "mesh changes on col")) """) - return nothing + return mesh_r, mesh_c end diff --git a/src/scratchpad.jl b/src/scratchpad.jl index 001ed79..89e010a 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -217,18 +217,18 @@ height, width = size(imageBW) # solve_velocity_potential mesh = CausticsEngineering.FaceMesh(height, width); CausticsEngineering.field_summary(mesh.corners.ϕ) +area_distorted_corners = CausticsEngineering.get_lens_pixels_area(mesh); +CausticsEngineering.field_summary(area_distorted_corners) + origmesh = CausticsEngineering.squareMesh(width + 1, height + 1); origϕ = zeros(width, height); CausticsEngineering.field_summary(origϕ) - - -# height, width = size(mesh.corners.ϕ) -area_distorted_corners = CausticsEngineering.get_lens_pixels_area(mesh); origarea_distorted_corners = CausticsEngineering.getPixelArea(origmesh); -CausticsEngineering.field_summary(area_distorted_corners) + CausticsEngineering.field_summary(area_distorted_corners - origarea_distorted_corners) + error_luminosity = Float64.(area_distorted_corners - imageBW); CausticsEngineering.field_summary(error_luminosity) @@ -253,17 +253,21 @@ CausticsEngineering.field_summary(mesh.corners.ϕ) Lϕ = CausticsEngineering.laplacian(mesh.corners.ϕ); CausticsEngineering.field_summary(Lϕ) δ = Lϕ - error_luminosity; -δ .*= CausticsEngineering.ω / 4.0; +δ .*= 0.50; CausticsEngineering.field_summary(δ) -mesh.corners.ϕ[1:end-1, 1:end-1] .+= δ; -mesh.corners.ϕ .-= average(mesh.corners.ϕ); +ϕ = mesh.corners.ϕ[1:end-1, 1:end-1]; +ϕ .+= δ; +mesh.corners.ϕ[1:end-1, 1:end-1] .= ϕ .- average(ϕ); CausticsEngineering.field_summary(mesh.corners.ϕ) mesh = CausticsEngineering.FaceMesh(height, width); -CausticsEngineering.field_summary(CausticsEngineering.laplacian(mesh.corners.ϕ) - error_luminosity) +CausticsEngineering.field_summary( + CausticsEngineering.laplacian(mesh.corners.ϕ) - error_luminosity, +) + max_update, Lϕ, δ = CausticsEngineering.propagate_poisson!(mesh.corners.ϕ, error_luminosity); CausticsEngineering.field_summary(mesh.corners.ϕ) @@ -272,7 +276,8 @@ CausticsEngineering.field_summary(δ) origϕ = zeros(width, height); -max_update, origLϕ, origδ = CausticsEngineering.orig_propagate_poisson!(origϕ, origerror_luminosity); +max_update, origLϕ, origδ = + CausticsEngineering.orig_propagate_poisson!(origϕ, origerror_luminosity); CausticsEngineering.field_summary(origϕ) CausticsEngineering.field_summary(origLϕ) CausticsEngineering.field_summary(origδ) @@ -285,42 +290,43 @@ CausticsEngineering.field_summary(origδ) mesh = CausticsEngineering.FaceMesh(height, width); new_update = 10_000 -old_update = 2*new_update +old_update = 2 * new_update for i ∈ 1:1_000 old_update = new_update - new_update, Lϕ, δ = CausticsEngineering.propagate_poisson!(mesh.corners.ϕ, error_luminosity) + new_update, Lϕ, δ = + CausticsEngineering.propagate_poisson!(mesh.corners.ϕ, error_luminosity) i % 50 == 0 && println(""" $(i) => $(max_update) $(CausticsEngineering.field_summary(mesh.corners.ϕ)) $(CausticsEngineering.field_summary(Lϕ)) $(CausticsEngineering.field_summary(δ)) - """ - ) + """) if new_update > old_update || i == 5_000 - new_update, Lϕ, δ = CausticsEngineering.orig_propagate_poisson!(origϕ, origerror_luminosity) + new_update, Lϕ, δ = + CausticsEngineering.orig_propagate_poisson!(origϕ, origerror_luminosity) println(""" $(i) => $(new_update) $(CausticsEngineering.field_summary(mesh.corners.ϕ)) $(CausticsEngineering.field_summary(Lϕ)) $(CausticsEngineering.field_summary(δ)) - """ - ) + """) break end end origϕ = zeros(width, height); for i ∈ 1:5_000 - max_update,origLϕ, origδ = CausticsEngineering.orig_propagate_poisson!(origϕ, origerror_luminosity); + max_update, origLϕ, origδ = + CausticsEngineering.orig_propagate_poisson!(origϕ, origerror_luminosity) i % 500 == 0 && println(""" $(i) => $(max_update) $(CausticsEngineering.field_summary(origϕ)) $(CausticsEngineering.field_summary(origLϕ)) $(CausticsEngineering.field_summary(origδ)) - """ - ) + """) if max_update <= 1e-3 - max_update, origLϕ, origδ = CausticsEngineering.orig_propagate_poisson!(origϕ, origerror_luminosity); + max_update, origLϕ, origδ = + CausticsEngineering.orig_propagate_poisson!(origϕ, origerror_luminosity) println(CausticsEngineering.field_summary(origϕ)) println(CausticsEngineering.field_summary(origLϕ)) println(CausticsEngineering.field_summary(origδ)) @@ -379,14 +385,19 @@ mesh.corners.vr .= -∇ϕᵤ mesh.corners.vc .= -∇ϕᵥ list_triangles = vcat( [ - CausticsEngineering.triangle3D(mesh, row, col, :top) for row ∈ 1:height, col ∈ 1:width + CausticsEngineering.triangle3D(mesh, row, col, :top) for row ∈ 1:height, + col ∈ 1:width ], [ - CausticsEngineering.triangle3D(mesh, row, col, :bottom) for row ∈ 1:height, col ∈ 1:width + CausticsEngineering.triangle3D(mesh, row, col, :bottom) for row ∈ 1:height, + col ∈ 1:width ], ) -list_maximum_t = [time for time ∈ CausticsEngineering.find_maximum_t.(list_triangles) if !isnothing(time) && time > 0.] +list_maximum_t = [ + time for time ∈ CausticsEngineering.find_maximum_t.(list_triangles) if + !isnothing(time) && time > 0.0 +] minimum(list_maximum_t) maximum(list_maximum_t) @@ -395,13 +406,4 @@ maximum(list_maximum_t) mesh.corners.r += δ * ∇ϕᵤ mesh.corners.c += δ * ∇ϕᵥ - -end - - - - - - - nothing; diff --git a/src/utilities.jl b/src/utilities.jl index 3048c5a..bbd6f68 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -343,7 +343,11 @@ function get_lens_pixels_area(mesh::FaceMesh) total_area = top_tri_area + bot_tri_area average_energy_per_pixel = average(total_area) - return total_area / average_energy_per_pixel + luminosity_pixels = total_area / average_energy_per_pixel + + @assert abs(sum(luminosity_pixels) - height * width) < 1.0 "Total lens luminosity is incorrect" + + return luminosity_pixels end @@ -352,7 +356,7 @@ $(SIGNATURES) """ function field_summary(field, fieldname) - s = round(sum(field), sigdigits = 4) + s = round(sum(field), sigdigits = 6) max = round(maximum(field), sigdigits = 4) min = round(minimum(field), sigdigits = 4) avg = round(average(field), sigdigits = 4) @@ -366,6 +370,3 @@ $(SIGNATURES) """ field_summary(field) = field_summary(field, "") - - - From 4fa88d8a411f7da3b8e1182ae6649185feddd58f Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Tue, 21 Sep 2021 21:46:03 +0200 Subject: [PATCH 44/58] Tracking area convergence bug --- .gitignore | 1 + src/create_mesh.jl | 313 ++++++++++++++++++++++----------------------- src/plots.jl | 65 +++++++--- src/scratchpad.jl | 33 ++++- 4 files changed, 228 insertions(+), 184 deletions(-) diff --git a/.gitignore b/.gitignore index 4d09190..3127558 100644 --- a/.gitignore +++ b/.gitignore @@ -38,4 +38,5 @@ Manifest.toml *sync-conflict* src/debug_script.jl examples/personal +examples/*.png diff --git a/src/create_mesh.jl b/src/create_mesh.jl index 3480b33..3b93497 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -1,4 +1,3 @@ - """ $(SIGNATURES) @@ -21,24 +20,42 @@ function engineer_caustics(source_image) # imageBW is normalised to the same (sort of) _energy_ as the original image. imageBW /= average(imageBW) - marginal_change = max_update = Inf + marginal_change = nothing + max_update = Inf counter = 0 - while (abs(max_update) > 1e-5 && counter < 5_000) + while (abs(max_update) > 1e-6 && counter < 10_000) counter += 1 + print( + """ + ================================================================================================================ + STARTING ITERATION $(counter): + starting ϕ field = $(field_summary(mesh.corners.ϕ)) + + """, + ) + ϕ = mesh.corners.ϕ mesh.corners.ϕ, mesh.corners.r, mesh.corners.c, ε, max_update = solve_velocity_potential!(mesh, imageBW, "it$(counter)") - marginal_change = average_absolute(mesh.corners.ϕ - ϕ) - print(""" - RESULT AT ITERATION $(counter): - Vertical move max update = $(max_update) - Mean error luminosity = $(average_absolute(ε)) - Marginal change = $(marginal_change) - """) + marginal_change = mesh.corners.ϕ - ϕ + + print( + """ - plot_as_quiver(mesh, n_steps = 50, scale = 1.0, max_length = height / 20) + RESULT AT ITERATION $(counter): + Luminosity error = $(field_summary(ε)) + Vertical move max update = $(max_update) + Marginal change = $(field_summary(marginal_change)) + + end ϕ field = $(field_summary(mesh.corners.ϕ)) + ================================================================================================================ + + """, + ) + plot_as_quiver(mesh, n_steps = 50, scale = height / 10, max_length = height / 20) + average_absolute(marginal_change) < 1e-2 && break end println("\nSTARTING HORIZONTAL ITERATION ---") @@ -74,13 +91,17 @@ function solve_velocity_potential!(mesh, image, prefix) ε .-= average(ε) # Save the loss image as a png - save_plot_scalar_field!(ε, prefix * "_loss", image) + save_plot_scalar_field!(ε, "error_" * prefix, image) + + luminosity_ratio = sum(image) / sum(lens_pixels_area) + save( + "./examples/img_$(prefix).png", + Gray.(clamp.(lens_pixels_area * luminosity_ratio, 0.0, 1.0)), + ) # Start with a clean, flat potential field. ϕ = zeros(Float64, height + 1, width + 1) - println(""" - solve_velocity_potential! before loop: $(field_summary(lens_pixels_area, "Pixel area")) $(field_summary(ε, "luminosity error")) @@ -89,104 +110,97 @@ function solve_velocity_potential!(mesh, image, prefix) count = 0 new_update = 10_000 old_update = 2 * new_update - while 1e-4 < new_update < old_update && (old_update - new_update) / old_update > 1e-4 + while 1e-6 < new_update < old_update && + 1e-5 < (old_update - new_update) / old_update && + count < 10_000 + count += 1 old_update = new_update - ϕ, _, _, new_update = CausticsEngineering.propagate_poisson(ϕ, ε) + ϕ, ∇²ϕ_est, δ, new_update = CausticsEngineering.propagate_poisson(ϕ, ε) - count % 500 == 0 && println( - """ -solve_velocity_potential! during loop at count $(count) with max_update = $(round(new_update, sigdigits=4)): - $(field_summary(mesh.corners.ϕ, "ϕ")) -""", - ) + count % 1_000 == 0 && println(""" + Iteration $(count) - max_update = $(round(new_update, sigdigits=4)) + $(field_summary(mesh.corners.ϕ, "ϕ")) + $(field_summary(∇²ϕ_est, "∇²ϕ_est")) + $(field_summary(δ, "δ")) + """) end # Now we need to march the mesh row,col corner locations according to this gradient. coord_r, coord_c = march_mesh(mesh, ϕ) - # marginal_change = ϕ - mesh.corners.ϕ - # Marginal update of ϕ: $(CausticsEngineering.field_summary(marginal_change)) - println(""" - Result of marching - New ϕ: $(CausticsEngineering.field_summary(ϕ)) - """) - return ϕ, coord_r, coord_c, ε, new_update end + """ $(SIGNATURES) -""" -function move_horizontally(mesh::FaceMesh, image; f = Focal_Length) - - # height indexes rows, width indexes columns - height, width = size(mesh) - - # Coordinates on the caustics = simple rectangular values in corners. - # Coordinates on the lens face comes from corner field. - # d_row/d_col are _POSTS-SIZED_ - d_row = mesh.corners.rows_numbers - mesh.corners.r - d_col = mesh.corners.cols_numbers - mesh.corners.c - # The focal length is in meters. H is in corners. - H = f / Meters_Per_Pixel +ϕ is the height map. - # true_H is the real distance beteen the surface of the lens and the projection - # H is the initial distance from the surface of the carved face to the projection screen. - # H is constant and does not account for the change in heights due to carving. - # Note: Higher location means closer to the caustics => negative sign - # true_H is _POSTS_SIZED_ - true_H = zeros(Float64, size(mesh.corners.ϕ)) - true_H = -mesh.corners.ϕ .+ H +`march_mesh!` flexes the mesh +""" +function march_mesh(mesh::FaceMesh, ϕ::AbstractMatrix{Float64}) - # Normals. - # N_row/N_col are _POSTS_SIZED_ - N_row = zeros(Float64, size(true_H)) - N_col = zeros(Float64, size(true_H)) - N_row = tan.(atan.(d_row ./ true_H) / (n₁ - n₂)) - N_col = tan.(atan.(d_col ./ true_H) / (n₁ - n₂)) + # Calculate the gradient of the velocity potential. + ∇ϕᵤ, ∇ϕᵥ = ∇(ϕ) + # fill_borders!(∇ϕᵤ, 0.) + # fill_borders!(∇ϕᵥ, 0.) - # @. N_row[1:end, 1:end] = - # tan(atan(d_row[1:end, 1:end] / true_H[1:end, 1:end]) / (n₁ - n₂)) - # @. N_col[1:end, 1:end] = - # tan(atan(d_col[1:end, 1:end] / true_H[1:end, 1:end]) / (n₁ - n₂)) + # For each point in the mesh we need to figure out its velocity + # However all the nodes located at a border will never move + # I.e. velocity (Vx, Vy) = (0, 0) and the square of acrylate will remain of the same size. + # reset_border_values!(mesh.corners) + mesh_r = copy(mesh.corners.r) + mesh_c = copy(mesh.corners.c) - # We need to find the divergence of the Vector field described by Nx and Ny - # div_row/div_col are _FENCES_SIZED_ - div_row = zeros(Float64, height, width) - div_col = zeros(Float64, height, width) - div_row[1:end, 1:end] = N_row[2:end, 1:end-1] .- N_row[1:end-1, 1:end-1] - div_col[1:end, 1:end] = N_col[1:end-1, 2:end] .- N_col[1:end-1, 1:end-1] + # Get the time, at that velocity, for the area of the triangle to be nil. + # We are only interested by positive values to only move in the direction of the (opposite) gradient + mesh.corners.vr .= -∇ϕᵤ + mesh.corners.vc .= -∇ϕᵥ - # Normalised divergence - # divergence_direction is _FENCES_SIZED_ - divergence_direction = div_row + div_col - # divergence_direction .-= average(divergence_direction) + height, width = size(mesh) + list_triangles = vcat( + [ + CausticsEngineering.triangle3D(mesh, row, col, :top) for row ∈ 1:height, + col ∈ 1:width + ], + [ + CausticsEngineering.triangle3D(mesh, row, col, :bottom) for row ∈ 1:height, + col ∈ 1:width + ], + ) + list_maximum_t = [ + time for time ∈ CausticsEngineering.find_maximum_t.(list_triangles) if + !isnothing(time) && time > 0.0 + ] - ϕ = mesh.corners.ϕ + δ = minimum(list_maximum_t) / 3.0 + mesh_r .-= δ * ∇ϕᵤ + mesh_c .-= δ * ∇ϕᵥ - max_update = Inf - old_update = Inf - for i ∈ 1:typemax(Int64) - old_update = max_update - ϕ, _, _, max_update = propagate_poisson(ϕ, -divergence_direction) - i % 100 == 0 && println("Convergence horiz. Δ max update = $(max_update)") + println( + """ - (abs(old_update - max_update) <= 1e-6 || abs(max_update) <= 1e-4) && break - end + March mesh with correction_ratio δ = $(δ) + $(field_summary(∇ϕᵤ, "Vu")) + $(field_summary(∇ϕᵥ, "Vu")) + $(field_summary(mesh_r - mesh.corners.r , "new mesh changes on row")) + $(field_summary(mesh_c - mesh.corners.c, "new mesh changes on col")) + $(field_summary(mesh_r - mesh.corners.rows_numbers , "total mesh changes on row")) + $(field_summary(mesh_c - mesh.corners.cols_numbers, "total mesh changes on col")) - println( - "Convergence horiz. Δ stopped with max_update of $(max_update) at counter = $(counter)", + """, ) - return ϕ, max_update + return mesh_r, mesh_c end + """ $(SIGNATURES) @@ -215,7 +229,6 @@ In order of how to think about the flow of the program for the velocity potentia function propagate_poisson(ϕ::Matrix{Float64}, ε::Matrix{Float64}) # Ensure that border conditions are as they should (= 0.0) height, width = size(ε) - # fill_borders!(ε, 0.0) # Laplacian # Lϕ represent the approximation of the Laplacian of ϕ (second-order value) @@ -228,110 +241,86 @@ function propagate_poisson(ϕ::Matrix{Float64}, ε::Matrix{Float64}) # The Laplacian Lϕ has to converge towards the ∇²ϕ. Difference to calculate speed of the descent. δ = ∇²ϕ_est - ε - # Default correction ratio to adjust δ is ω / 4.0 - # δ *= ω / 7.0 - δ *= 0.15 + # Correction ratio to avoid setting the triangle to nothing + δ *= 0.20 # In the case of the velocity potential, # if δ > 0, the Laplacian is too high at that point (∇²ϕ is too low). ϕ_res = zeros(Float64, size(ϕ)) ϕ_res[1:end-1, 1:end-1] = ϕ[1:end-1, 1:end-1] + δ - ϕ_res .-= average(ϕ_res) - # ################################################################################################################## - # # From the velocity potential field ϕ, we calculate its gradient (the velocity), then its divergence. - # # This is then compared to the intensity loss - # ∇²ϕ_est = zeros(Float64, size(ε)) - # δ = zeros(Float64, size(ε)) - # for row ∈ 1:height, col ∈ 1:width - # ∇²ϕ_est[row, col] = - # ϕ[max(1, row - 1), col] + - # ϕ[min(height, row + 1), col] + - # ϕ[row, max(1, col - 1)] + - # ϕ[row, min(width, col + 1)] - 4.0 * ϕ[row, col] - - # δ[row, col] = ω / 4.0 * (∇²ϕ_est[row, col] - ε[row, col]) - # ϕ[row, col] += δ[row, col] - # end - return ϕ_res, ∇²ϕ_est, δ, maximum(abs.(δ)) end + """ $(SIGNATURES) - -ϕ is the height map. - -`march_mesh!` flexes the mesh """ -function march_mesh(mesh::FaceMesh, ϕ::AbstractMatrix{Float64}) - - # Calculate the gradient of the velocity potential. - ∇ϕᵤ, ∇ϕᵥ = ∇(ϕ) - - # For each point in the mesh we need to figure out its velocity - # However all the nodes located at a border will never move - # I.e. velocity (Vx, Vy) = (0, 0) and the square of acrylate will remain of the same size. - # reset_border_values!(mesh.corners) - mesh_r = mesh.corners.r - mesh_c = mesh.corners.c +function move_horizontally(mesh::FaceMesh, image; f = Focal_Length) + # height indexes rows, width indexes columns + height, width = size(mesh) - # Get the time, at that velocity, for the area of the triangle to be nil. - # We are only interested by positive values to only move in the direction of the gradient - mesh.corners.vr .= -∇ϕᵤ - mesh.corners.vc .= -∇ϕᵥ + # Coordinates on the caustics = simple rectangular values in corners. + # Coordinates on the lens face comes from corner field. + # d_row/d_col are _POSTS-SIZED_ + d_row = mesh.corners.rows_numbers - mesh.corners.r + d_col = mesh.corners.cols_numbers - mesh.corners.c - height, width = size(mesh) - list_triangles = vcat( - [ - CausticsEngineering.triangle3D(mesh, row, col, :top) for row ∈ 1:height, - col ∈ 1:width - ], - [ - CausticsEngineering.triangle3D(mesh, row, col, :bottom) for row ∈ 1:height, - col ∈ 1:width - ], - ) + # The focal length is in meters. H is in corners. + H = f / Meters_Per_Pixel + # true_H is the real distance beteen the surface of the lens and the projection + # H is the initial distance from the surface of the carved face to the projection screen. + # H is constant and does not account for the change in heights due to carving. + # Note: Higher location means closer to the caustics => negative sign + # true_H is _POSTS_SIZED_ + true_H = zeros(Float64, size(mesh.corners.ϕ)) + true_H = -mesh.corners.ϕ .+ H - list_maximum_t = [ - time for time ∈ CausticsEngineering.find_maximum_t.(list_triangles) if - !isnothing(time) && time > 0.0 - ] - minimum(list_maximum_t) - maximum(list_maximum_t) + # Normals. + # N_row/N_col are _POSTS_SIZED_ + N_row = zeros(Float64, size(true_H)) + N_col = zeros(Float64, size(true_H)) + N_row = tan.(atan.(d_row ./ true_H) / (n₁ - n₂)) + N_col = tan.(atan.(d_col ./ true_H) / (n₁ - n₂)) - δ = minimum(list_maximum_t) / 1.2 + # @. N_row[1:end, 1:end] = + # tan(atan(d_row[1:end, 1:end] / true_H[1:end, 1:end]) / (n₁ - n₂)) + # @. N_col[1:end, 1:end] = + # tan(atan(d_col[1:end, 1:end] / true_H[1:end, 1:end]) / (n₁ - n₂)) - mesh_r .+= δ .* ∇ϕᵤ - mesh_c .+= δ .* ∇ϕᵥ + # We need to find the divergence of the Vector field described by Nx and Ny + # div_row/div_col are _FENCES_SIZED_ + div_row = zeros(Float64, height, width) + div_col = zeros(Float64, height, width) + div_row[1:end, 1:end] = N_row[2:end, 1:end-1] .- N_row[1:end-1, 1:end-1] + div_col[1:end, 1:end] = N_col[1:end-1, 2:end] .- N_col[1:end-1, 1:end-1] - # for row ∈ 1:height, col ∈ 1:width - # list_triangles = [triangle3D(mesh, row, col, :top), triangle3D(mesh, row, col, :bottom) ] + # Normalised divergence + # divergence_direction is _FENCES_SIZED_ + divergence_direction = div_row + div_col + # divergence_direction .-= average(divergence_direction) - # if !isempty(list_triangles) - # list_maximum_t = [time for time ∈ find_maximum_t.(list_triangles) if !isnothing(time)] + ϕ = mesh.corners.ϕ - # if !isempty(list_maximum_t) - # δ = minimum(list_maximum_t) / 8.0 + max_update = Inf + old_update = Inf + for i ∈ 1:typemax(Int64) + old_update = max_update + ϕ, _, _, max_update = propagate_poisson(ϕ, -divergence_direction) - # mesh.corners.r[row, col] -= δ * ∇ϕᵤ[row, col] - # mesh.corners.c[row, col] -= δ * ∇ϕᵥ[row, col] - # end - # end - # end + i % 1_000 == 0 && + println("Convergence horiz. Δ at counter = $(i) max update = $(max_update)") + if abs(old_update - max_update) / old_update < 1e-5 || abs(max_update) <= 1e-6 + println( + "Convergence horiz. Δ stopped with max_update of $(max_update) at counter = $(i)", + ) + break + end + end - println(""" - March mesh: - correction_ratio δ = $(δ) - $(field_summary(∇ϕᵤ, "Vu")) - $(field_summary(∇ϕᵥ, "Vu")) - $(field_summary(mesh.corners.r - mesh_r, "mesh changes on row")) - $(field_summary(mesh.corners.c - mesh_c, "mesh changes on col")) - - """) - return mesh_r, mesh_c + return ϕ, max_update end diff --git a/src/plots.jl b/src/plots.jl index 710dfd7..9f47770 100644 --- a/src/plots.jl +++ b/src/plots.jl @@ -25,8 +25,11 @@ function plot_as_quiver( # Those gradients are the opposite direction. ϕ = -mesh.corners.ϕ - mat_vr = (reverser ? -1 : 1) .* mesh.corners.vr .* scale - mat_vc = (reversec ? -1 : 1) .* mesh.corners.vc .* scale + v_length = sqrt.(mesh.corners.vr .^ 2 + mesh.corners.vr .^ 2) + v_max = maximum(v_length) + + mat_vr = (reverser ? -1 : 1) .* mesh.corners.vr * scale / v_max + mat_vc = (reversec ? -1 : 1) .* mesh.corners.vc * scale / v_max mat_vr = clamp.(mat_vr, -max_length, max_length) mat_vc = clamp.(mat_vc, -max_length, max_length) @@ -130,28 +133,54 @@ end """ $(SIGNATURES) """ -function save_plot_scalar_field!(calculated_scalar_field, filename, img) - scalar_field = calculated_scalar_field' - - blue = zeros(size(scalar_field)) - red = zeros(size(scalar_field)) - green = zeros(size(scalar_field)) - - blue[scalar_field.>0] = scalar_field[scalar_field.>0] - red[scalar_field.<0] = -scalar_field[scalar_field.<0] +function save_plot_scalar_field!(scalar_field, filename, img) + blue = zeros(Float64, size(scalar_field)) + red = zeros(Float64, size(scalar_field)) + green = zeros(Float64, size(scalar_field)) + + height, width = size(scalar_field) + + for r ∈ 1:height, c ∈ 1:width + field = scalar_field[r, c] + if field < -1.0 + # Green if luminosity error < -1.0 + red[r, c] = 0.0 + blue[r, c] = 0.0 + green[r, c] = 1.0 + + elseif -1.0 <= field < 0.0 + # Red shade if negative + red[r, c] = -field + blue[r, c] = 0.0 + green[r, c] = 0.0 + + elseif 0.0 <= field < 1.0 + # Blue shade if positive + red[r, c] = 0.0 + blue[r, c] = field + green[r, c] = 0.0 + + elseif 1.0 <= field + # White if > 1 + red[r, c] = 1.0 + blue[r, c] = 1.0 + green[r, c] = 1.0 + end + end - rgbImg = RGB.(red, green, blue)' - save("./examples/$(filename).png", map(clamp01nan, rgbImg)) + rgbImg = RGB.(red, green, blue) + save("./examples/$(filename).png", rgbImg) end """ $(SIGNATURES) """ -function save_plot_scalar_field(calculated_scalar_field, prefix, img) - scalar_field = calculated_scalar_field' - normalised_D_max = scalar_field ./ maximum(scalar_field) - normalised_D_min = scalar_field ./ minimum(scalar_field) +function save_plot_scalar_field(scalar_field, prefix, img) + normalised_D_max = scalar_field + normalised_D_min = scalar_field + # normalised_D_max = scalar_field ./ maximum(scalar_field) + # normalised_D_min = scalar_field ./ minimum(scalar_field) blue = zeros(size(scalar_field)) red = zeros(size(scalar_field)) @@ -160,7 +189,7 @@ function save_plot_scalar_field(calculated_scalar_field, prefix, img) blue[scalar_field.>0] = normalised_D_max[scalar_field.>0] red[scalar_field.<0] = -normalised_D_min[scalar_field.<0] - rgbImg = RGB.(red, green, blue)' + rgbImg = map(clamp01nan, RGB.(red, green, blue)) save("./examples/$(prefix)_loss.png", map(clamp01nan, rgbImg)) println("Saving output image:") diff --git a/src/scratchpad.jl b/src/scratchpad.jl index 89e010a..b4a2b69 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -1,9 +1,11 @@ using Revise, Debugger -using Images, Plots; -gr(); +using Images, Plots +gr() using CausticsEngineering +image = Images.load("./examples/personal/goose.jpg"); # Check current working directory with pwd() + image = Images.load("./examples/cat_posing.jpg"); # Check current working directory with pwd() image = Images.load("./examples/personal/salvador_dali_1.jpg"); # Check current working directory with pwd() @@ -19,7 +21,32 @@ image = Images.load("./examples/personal/bilal.jpg"); # Check current working di mesh, imageBW = engineer_caustics(image); +imageBW = Float64.(Gray.(image)); +Gray.(imageBW) + +new_img = CausticsEngineering.get_lens_pixels_area(mesh); +luminosity_ratio = sum(imageBW) / sum(new_img) +Gray.(new_img * luminosity_ratio) + + +ε = Float64.(lens_pixels_area - image) +ε .-= average(ε) + +# Save the loss image as a png +save_plot_scalar_field!(ε, "loss_" * prefix, image) + + + + mesh, imageBW = CausticsEngineering.original_engineer_caustics(image); +imageBW = Float64.(Gray.(image)) +Gray.(imageBW) + +new_img = CausticsEngineering.get_lens_pixels_area(mesh) +luminosity_ratio = sum(imageBW) / sum(new_img) +Gray.(new_img * luminosity_ratio) + + imageBW = Float64.(Gray.(image)); @@ -212,8 +239,6 @@ sum(imageBW) height, width = size(imageBW) - - # solve_velocity_potential mesh = CausticsEngineering.FaceMesh(height, width); CausticsEngineering.field_summary(mesh.corners.ϕ) From 9473c949cf07d0e9431c75b57947a2304ac33a97 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Sat, 25 Sep 2021 12:06:17 +0200 Subject: [PATCH 45/58] Tracking area convergence bug --- .gitignore | 1 + src/CausticsEngineering.jl | 2 +- src/create_mesh.jl | 189 ++++++++++++++++++++----------------- src/math_utilities.jl | 4 +- src/plots.jl | 2 +- src/scratchpad.jl | 158 ++++++++++++++++++++++++------- src/utilities.jl | 26 ++--- 7 files changed, 245 insertions(+), 137 deletions(-) diff --git a/.gitignore b/.gitignore index 3127558..b20e1ca 100644 --- a/.gitignore +++ b/.gitignore @@ -40,3 +40,4 @@ src/debug_script.jl examples/personal examples/*.png + diff --git a/src/CausticsEngineering.jl b/src/CausticsEngineering.jl index 0e65014..e132126 100644 --- a/src/CausticsEngineering.jl +++ b/src/CausticsEngineering.jl @@ -62,7 +62,7 @@ export save_obj!, # Main procedures - propagate_poisson, + propagate_poisson!, march_mesh!, engineer_caustics, main diff --git a/src/create_mesh.jl b/src/create_mesh.jl index 3b93497..9f239f3 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -17,7 +17,7 @@ function engineer_caustics(source_image) # cover each image corner with a triangle. mesh = FaceMesh(N_Pixel_Height, N_Pixel_Width) - # imageBW is normalised to the same (sort of) _energy_ as the original image. + # imageBW is normalised to have 1 unit per pixel on average. imageBW /= average(imageBW) marginal_change = nothing @@ -36,8 +36,7 @@ function engineer_caustics(source_image) ) ϕ = mesh.corners.ϕ - mesh.corners.ϕ, mesh.corners.r, mesh.corners.c, ε, max_update = - solve_velocity_potential!(mesh, imageBW, "it$(counter)") + ε, max_update = solve_velocity_potential!(mesh, imageBW, "it$(counter)") marginal_change = mesh.corners.ϕ - ϕ @@ -55,12 +54,12 @@ function engineer_caustics(source_image) """, ) plot_as_quiver(mesh, n_steps = 50, scale = height / 10, max_length = height / 20) - average_absolute(marginal_change) < 1e-2 && break + average_absolute(marginal_change) < 1e-3 && break end println("\nSTARTING HORIZONTAL ITERATION ---") - mesh.corners.ϕ, max_update = move_horizontally(mesh, imageBW; f = Focal_Length) + max_update = solve_height_potential(mesh, imageBW; f = Focal_Length) println("\t Horizontal max update = $(max_update)") # Move the around a nil average. @@ -86,13 +85,21 @@ function solve_velocity_potential!(mesh, image, prefix) # Illumination only depends on the position of the corners, not their heights. ϕ is not relevant. lens_pixels_area = get_lens_pixels_area(mesh) - # Positive error => the triangle needs to shrink (less light) - ε = Float64.(lens_pixels_area - image) + # Positive error => the triangle needs to shrink (less light). Enforce nil average error. + ε = zeros(Float64, height + 1, width + 1) + ε[1:end-1, 1:end-1] = Float64.(lens_pixels_area - image) ε .-= average(ε) - # Save the loss image as a png - save_plot_scalar_field!(ε, "error_" * prefix, image) + println(""" + solve_velocity_potential! before loop: + $(field_summary(lens_pixels_area, "Pixel area")) + $(field_summary(ε, "luminosity error")) + """) + + # Save the loss image as a png. + save_plot_scalar_field!(ε, "error_$(prefix)") + # Save the generated image as a png. luminosity_ratio = sum(image) / sum(lens_pixels_area) save( "./examples/img_$(prefix).png", @@ -100,37 +107,45 @@ function solve_velocity_potential!(mesh, image, prefix) ) # Start with a clean, flat potential field. - ϕ = zeros(Float64, height + 1, width + 1) - println(""" - solve_velocity_potential! before loop: - $(field_summary(lens_pixels_area, "Pixel area")) - $(field_summary(ε, "luminosity error")) - """) - + mesh.corners.ϕ = zeros(Float64, height + 1, width + 1) + ϕ_b4 = copy(mesh.corners.ϕ) count = 0 - new_update = 10_000 + min_update = new_update = 10_000 old_update = 2 * new_update - while 1e-6 < new_update < old_update && - 1e-5 < (old_update - new_update) / old_update && - count < 10_000 - + while ( + 1e-5 < new_update < 1.5 * min_update && + 1e-4 < (old_update - new_update) / old_update && + count < 10_000 + ) count += 1 old_update = new_update + min_update = min(min_update, new_update) - ϕ, ∇²ϕ_est, δ, new_update = CausticsEngineering.propagate_poisson(ϕ, ε) + new_update, ∇²ϕ_est, δ = propagate_poisson!(mesh.corners.ϕ, ε) - count % 1_000 == 0 && println(""" + count % 1_000 == 1 && println(""" Iteration $(count) - max_update = $(round(new_update, sigdigits=4)) $(field_summary(mesh.corners.ϕ, "ϕ")) $(field_summary(∇²ϕ_est, "∇²ϕ_est")) $(field_summary(δ, "δ")) """) + + # Save the loss image as a png. + if count % 1_000 == 1 + save_plot_scalar_field!(∇²ϕ_est, "∇²ϕ_est_$(prefix)") + save_plot_scalar_field!(δ, "delta_$(prefix)") + save_plot_scalar_field!( + mesh.corners.ϕ - ϕ_b4, + "change_mesh.corners.ϕ_$(prefix)", + ) + + ϕ_b4 = copy(mesh.corners.ϕ) + end end # Now we need to march the mesh row,col corner locations according to this gradient. - coord_r, coord_c = march_mesh(mesh, ϕ) - - return ϕ, coord_r, coord_c, ε, new_update + δ = march_mesh!(mesh) + return ε, new_update end @@ -142,52 +157,42 @@ $(SIGNATURES) `march_mesh!` flexes the mesh """ -function march_mesh(mesh::FaceMesh, ϕ::AbstractMatrix{Float64}) +function march_mesh!(mesh::FaceMesh) + + # Calculate the gradient of the velocity potential and reverse its direction. + mesh.corners.vr, mesh.corners.vc = ∇(mesh.corners.ϕ) + mesh.corners.vr .*= -1.0 + mesh.corners.vc .*= -1.0 - # Calculate the gradient of the velocity potential. - ∇ϕᵤ, ∇ϕᵥ = ∇(ϕ) - # fill_borders!(∇ϕᵤ, 0.) - # fill_borders!(∇ϕᵥ, 0.) + # Clean up the mesh borders + reset_border_values!(mesh.corners) # For each point in the mesh we need to figure out its velocity # However all the nodes located at a border will never move # I.e. velocity (Vx, Vy) = (0, 0) and the square of acrylate will remain of the same size. - # reset_border_values!(mesh.corners) mesh_r = copy(mesh.corners.r) mesh_c = copy(mesh.corners.c) # Get the time, at that velocity, for the area of the triangle to be nil. # We are only interested by positive values to only move in the direction of the (opposite) gradient - mesh.corners.vr .= -∇ϕᵤ - mesh.corners.vc .= -∇ϕᵥ - height, width = size(mesh) list_triangles = vcat( - [ - CausticsEngineering.triangle3D(mesh, row, col, :top) for row ∈ 1:height, - col ∈ 1:width - ], - [ - CausticsEngineering.triangle3D(mesh, row, col, :bottom) for row ∈ 1:height, - col ∈ 1:width - ], + [triangle3D(mesh, row, col, :top) for row ∈ 1:height, col ∈ 1:width], + [triangle3D(mesh, row, col, :bottom) for row ∈ 1:height, col ∈ 1:width], ) - list_maximum_t = [ - time for time ∈ CausticsEngineering.find_maximum_t.(list_triangles) if - !isnothing(time) && time > 0.0 - ] + list_maximum_t = [t for t ∈ find_maximum_t.(list_triangles) if !isnothing(t) && t > 0.0] - δ = minimum(list_maximum_t) / 3.0 - mesh_r .-= δ * ∇ϕᵤ - mesh_c .-= δ * ∇ϕᵥ + δ = minimum(list_maximum_t) / 2.0 + mesh.corners.r .-= δ * mesh.corners.vr + mesh.corners.c .-= δ * mesh.corners.vc println( """ March mesh with correction_ratio δ = $(δ) - $(field_summary(∇ϕᵤ, "Vu")) - $(field_summary(∇ϕᵥ, "Vu")) + $(field_summary(mesh.corners.vr, "∇u")) + $(field_summary(mesh.corners.vc, "∇v")) $(field_summary(mesh_r - mesh.corners.r , "new mesh changes on row")) $(field_summary(mesh_c - mesh.corners.c, "new mesh changes on col")) $(field_summary(mesh_r - mesh.corners.rows_numbers , "total mesh changes on row")) @@ -196,7 +201,7 @@ function march_mesh(mesh::FaceMesh, ϕ::AbstractMatrix{Float64}) """, ) - return mesh_r, mesh_c + return δ end @@ -226,40 +231,53 @@ In order of how to think about the flow of the program for the velocity potentia - => Increase the value of ϕ at that point means a positive change when δ > 0. - δ > 0 => correction of the SAME sign. """ -function propagate_poisson(ϕ::Matrix{Float64}, ε::Matrix{Float64}) - # Ensure that border conditions are as they should (= 0.0) - height, width = size(ε) +function propagate_poisson!(ϕ::Matrix{Float64}, ε::Matrix{Float64}) + + height, width = size(ϕ) - # Laplacian - # Lϕ represent the approximation of the Laplacian of ϕ (second-order value) - ∇²ϕ_est = laplacian(ϕ) + ∇²ϕ_est = zeros(Float64, height, width) + δ = zeros(Float64, height, width) - # In the case of the velocity potential, δ is the difference between the divergence of the luminosity error - # and the current one for the current field ϕ (divergence of its gradient). + ω = 1.99 - # High luminosity error ∇²ϕ means that the triangles are too bright = too large. - # The Laplacian Lϕ has to converge towards the ∇²ϕ. Difference to calculate speed of the descent. - δ = ∇²ϕ_est - ε + for row = 1:height, col = 1:width + val_up = row == 1 ? 0.0 : ϕ[row-1, col] + val_down = row == height ? 0.0 : ϕ[row+1, col] + val_left = col == 1 ? 0.0 : ϕ[row, col-1] + val_right = col == width ? 0.0 : ϕ[row, col+1] - # Correction ratio to avoid setting the triangle to nothing - δ *= 0.20 + ∇²ϕ_est[row, col] = val_up + val_down + val_left + val_right - 4 * ϕ[row, col] + δ[row, col] = ω / 4.0 * (∇²ϕ_est[row, col] - ε[row, col]) + ϕ[row, col] += δ[row, col] + end - # In the case of the velocity potential, - # if δ > 0, the Laplacian is too high at that point (∇²ϕ is too low). - ϕ_res = zeros(Float64, size(ϕ)) - ϕ_res[1:end-1, 1:end-1] = ϕ[1:end-1, 1:end-1] + δ - ϕ_res .-= average(ϕ_res) + return maximum(abs.(δ)), ∇²ϕ_est, δ - return ϕ_res, ∇²ϕ_est, δ, maximum(abs.(δ)) -end + # # Laplacian + # # ∇²ϕ_est represent the estimate of the Laplacian of ϕ (second-order value) + # ∇²ϕ_est = laplacian(ϕ) + # # In the case of the velocity potential, δ is the difference between the divergence of the luminosity error + # # and the current one for the current field ϕ (divergence of its gradient). + # # High luminosity error ∇²ϕ means that the triangles are too bright = too large. + # # The Laplacian Lϕ has to converge towards the ∇²ϕ. Difference to calculate speed of the descent. + + # # Correction ratio to avoid setting the triangle to nothing + # δ = ω / 4.0 * (∇²ϕ_est - ε) + + # # In the case of the velocity potential, if δ > 0, the Laplacian is too high at that point (∇²ϕ is too low). + # ϕ[1:end-1, 1:end-1] .+= δ + + # return ∇²ϕ_est, δ, maximum(abs.(δ)) +end + """ $(SIGNATURES) """ -function move_horizontally(mesh::FaceMesh, image; f = Focal_Length) +function solve_height_potential(mesh::FaceMesh, image; f = Focal_Length) # height indexes rows, width indexes columns height, width = size(mesh) @@ -277,7 +295,7 @@ function move_horizontally(mesh::FaceMesh, image; f = Focal_Length) # H is constant and does not account for the change in heights due to carving. # Note: Higher location means closer to the caustics => negative sign # true_H is _POSTS_SIZED_ - true_H = zeros(Float64, size(mesh.corners.ϕ)) + true_H = zeros(Float64, height + 1, width + 1) true_H = -mesh.corners.ϕ .+ H # Normals. @@ -294,33 +312,32 @@ function move_horizontally(mesh::FaceMesh, image; f = Focal_Length) # We need to find the divergence of the Vector field described by Nx and Ny # div_row/div_col are _FENCES_SIZED_ - div_row = zeros(Float64, height, width) - div_col = zeros(Float64, height, width) - div_row[1:end, 1:end] = N_row[2:end, 1:end-1] .- N_row[1:end-1, 1:end-1] - div_col[1:end, 1:end] = N_col[1:end-1, 2:end] .- N_col[1:end-1, 1:end-1] + div_row = zeros(Float64, size(true_H)) + div_col = zeros(Float64, size(true_H)) + div_row[1:end-1, 1:end-1] = N_row[2:end, 1:end-1] .- N_row[1:end-1, 1:end-1] + div_col[1:end-1, 1:end-1] = N_col[1:end-1, 2:end] .- N_col[1:end-1, 1:end-1] # Normalised divergence # divergence_direction is _FENCES_SIZED_ divergence_direction = div_row + div_col # divergence_direction .-= average(divergence_direction) - ϕ = mesh.corners.ϕ - max_update = Inf old_update = Inf - for i ∈ 1:typemax(Int64) + for i ∈ 1:1e6 old_update = max_update - ϕ, _, _, max_update = propagate_poisson(ϕ, -divergence_direction) + max_update, _, _ = propagate_poisson!(mesh.corners.ϕ, -divergence_direction) - i % 1_000 == 0 && + i % 1_000 == 1 && println("Convergence horiz. Δ at counter = $(i) max update = $(max_update)") + if abs(old_update - max_update) / old_update < 1e-5 || abs(max_update) <= 1e-6 println( - "Convergence horiz. Δ stopped with max_update of $(max_update) at counter = $(i)", + "Convergence horiz. Δ stopped at counter = $(i) with max_update of $(max_update)", ) break end end - return ϕ, max_update + return max_update end diff --git a/src/math_utilities.jl b/src/math_utilities.jl index a3abfe7..148548a 100644 --- a/src/math_utilities.jl +++ b/src/math_utilities.jl @@ -63,9 +63,9 @@ function laplacian(ϕ::AbstractMatrix{Float64}) # ϕ is inserted in padded matrix within 1:1+height+1 x 1:1+width+1. # The rest of the padded matrix (its borders) are set at 0.0. padded_ϕ = zeros(Float64, 1 + height + 1, 1 + width + 1) - padded_ϕ[begin+1:end-1, begin+1:end-1] = ϕ + padded_ϕ[begin+1:end-1, begin+1:end-1] .= ϕ[1:end, 1:end] - # Convolution + # Convolution = up + down + left + right ∇²ϕ = padded_ϕ[begin+1-1:end-1-1, begin+1:end-1] + padded_ϕ[begin+1+1:end-1+1, begin+1:end-1] + diff --git a/src/plots.jl b/src/plots.jl index 9f47770..b3bfa82 100644 --- a/src/plots.jl +++ b/src/plots.jl @@ -133,7 +133,7 @@ end """ $(SIGNATURES) """ -function save_plot_scalar_field!(scalar_field, filename, img) +function save_plot_scalar_field!(scalar_field, filename) blue = zeros(Float64, size(scalar_field)) red = zeros(Float64, size(scalar_field)) green = zeros(Float64, size(scalar_field)) diff --git a/src/scratchpad.jl b/src/scratchpad.jl index b4a2b69..3aa3ffc 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -4,10 +4,12 @@ gr() using CausticsEngineering -image = Images.load("./examples/personal/goose.jpg"); # Check current working directory with pwd() - image = Images.load("./examples/cat_posing.jpg"); # Check current working directory with pwd() +image = Images.load("./examples/personal/slashdot.jpg"); # Check current working directory with pwd() + +image = Images.load("./examples/personal/goose.jpg"); # Check current working directory with pwd() + image = Images.load("./examples/personal/salvador_dali_1.jpg"); # Check current working directory with pwd() image = Images.load("./examples/personal/salvador_dali_2.jpg"); # Check current working directory with pwd() @@ -23,6 +25,11 @@ mesh, imageBW = engineer_caustics(image); imageBW = Float64.(Gray.(image)); Gray.(imageBW) +sum(imageBW) +sum(imageBW) / length(imageBW) + +CausticsEngineering.average(imageBW) + new_img = CausticsEngineering.get_lens_pixels_area(mesh); luminosity_ratio = sum(imageBW) / sum(new_img) @@ -33,8 +40,7 @@ Gray.(new_img * luminosity_ratio) ε .-= average(ε) # Save the loss image as a png -save_plot_scalar_field!(ε, "loss_" * prefix, image) - +save_plot_scalar_field!(ε, "loss_" * prefix) @@ -221,7 +227,7 @@ Luminosity: -########################################################## +#################################################################################################################### ## STEPPING using Revise, Debugger, Images, Plots; @@ -230,82 +236,124 @@ gr(); using CausticsEngineering -# engineer_caustics -image = Images.load("./examples/cat_posing.jpg"); # Check current working directory with pwd() +######################## Load image +image = Images.load("./examples/personal/slashdot.jpg"); # Check current working directory with pwd() imageBW = Float64.(Gray.(image)); imageBW /= average(imageBW); sum(imageBW) -height, width = size(imageBW) +h, w = size(imageBW) -# solve_velocity_potential -mesh = CausticsEngineering.FaceMesh(height, width); +######################## Create mesh +mesh = CausticsEngineering.FaceMesh(h, w); CausticsEngineering.field_summary(mesh.corners.ϕ) + +origmesh = CausticsEngineering.OriginalMesh(w + 1, h + 1); +origϕ = zeros(w, h); +CausticsEngineering.field_summary(origϕ) + + +######################## Lens luminosity area_distorted_corners = CausticsEngineering.get_lens_pixels_area(mesh); CausticsEngineering.field_summary(area_distorted_corners) - -origmesh = CausticsEngineering.squareMesh(width + 1, height + 1); -origϕ = zeros(width, height); -CausticsEngineering.field_summary(origϕ) origarea_distorted_corners = CausticsEngineering.getPixelArea(origmesh); +CausticsEngineering.field_summary(origarea_distorted_corners) + +CausticsEngineering.field_summary(area_distorted_corners - origarea_distorted_corners') -CausticsEngineering.field_summary(area_distorted_corners - origarea_distorted_corners) +######################## Laplacian +Lϕ = CausticsEngineering.laplacian(mesh.corners.ϕ); +CausticsEngineering.field_summary(Lϕ) + +function orig_laplacian(ϕ) + width, height = size(ϕ) + Lϕ = zeros(Float64, size(ϕ)) + + for x = 1:width, y = 1:height + val_up = (y == 1) ? 0.0 : ϕ[x, y-1] + val_down = (y == height) ? 0.0 : ϕ[x, y+1] + val_left = (x == 1) ? 0.0 : ϕ[max(1, x - 1), y] + val_right = (x == width) ? 0.0 : ϕ[x+1, y] + + Lϕ[x, y] = val_up + val_down + val_left + val_right - 4 * ϕ[x, y] + + # if Lϕ[x, y] != 0.0 + # println(val_up, val_down, val_left, val_right, ϕ[x, y], x, y) + # break + # end + end + return Lϕ +end + +origLϕ = orig_laplacian(origϕ); +CausticsEngineering.field_summary(origLϕ) -error_luminosity = Float64.(area_distorted_corners - imageBW); + +######################## Error luminosity +error_luminosity = zeros(Float64, h + 1, w + 1); +error_luminosity[1:end-1, 1:end-1] = Float64.(area_distorted_corners - imageBW); CausticsEngineering.field_summary(error_luminosity) -origerror_luminosity = Float64.(origarea_distorted_corners - imageBW); +origerror_luminosity = zeros(Float64, w + 1, h + 1); +origerror_luminosity[1:end-1, 1:end-1] = Float64.(origarea_distorted_corners - imageBW'); CausticsEngineering.field_summary(origerror_luminosity) -CausticsEngineering.field_summary(error_luminosity - origerror_luminosity) +CausticsEngineering.field_summary(error_luminosity - origerror_luminosity') +######################## Normalised error luminosity error_luminosity = error_luminosity .- average(error_luminosity); CausticsEngineering.field_summary(error_luminosity) origerror_luminosity = origerror_luminosity .- average(origerror_luminosity); CausticsEngineering.field_summary(origerror_luminosity) -CausticsEngineering.field_summary(error_luminosity - origerror_luminosity) - +CausticsEngineering.field_summary(error_luminosity - origerror_luminosity') -mesh = CausticsEngineering.FaceMesh(height, width); +######################## Distance to Laplacian & propagate +max_update, Lϕ, δ = CausticsEngineering.propagate_poisson!(mesh.corners.ϕ, error_luminosity); CausticsEngineering.field_summary(mesh.corners.ϕ) -Lϕ = CausticsEngineering.laplacian(mesh.corners.ϕ); CausticsEngineering.field_summary(Lϕ) -δ = Lϕ - error_luminosity; -δ .*= 0.50; CausticsEngineering.field_summary(δ) +max_update, origLϕ, origδ = + CausticsEngineering.orig_propagate_poisson!(origϕ, origerror_luminosity); +CausticsEngineering.field_summary(origϕ) +CausticsEngineering.field_summary(origLϕ) +CausticsEngineering.field_summary(origδ) + + + + + + + + +δ = Lϕ - error_luminosity; +CausticsEngineering.field_summary(δ) + +δ .*= 0.50; ϕ = mesh.corners.ϕ[1:end-1, 1:end-1]; ϕ .+= δ; mesh.corners.ϕ[1:end-1, 1:end-1] .= ϕ .- average(ϕ); CausticsEngineering.field_summary(mesh.corners.ϕ) + + mesh = CausticsEngineering.FaceMesh(height, width); CausticsEngineering.field_summary( CausticsEngineering.laplacian(mesh.corners.ϕ) - error_luminosity, ) -max_update, Lϕ, δ = CausticsEngineering.propagate_poisson!(mesh.corners.ϕ, error_luminosity); -CausticsEngineering.field_summary(mesh.corners.ϕ) -CausticsEngineering.field_summary(Lϕ) -CausticsEngineering.field_summary(δ) - -origϕ = zeros(width, height); -max_update, origLϕ, origδ = - CausticsEngineering.orig_propagate_poisson!(origϕ, origerror_luminosity); -CausticsEngineering.field_summary(origϕ) -CausticsEngineering.field_summary(origLϕ) -CausticsEngineering.field_summary(origδ) +origϕ = zeros(w, h); @@ -432,3 +480,43 @@ mesh.corners.r += δ * ∇ϕᵤ mesh.corners.c += δ * ∇ϕᵥ nothing; + + +function my_laplacian(ϕ::AbstractMatrix{Float64}) + height, width = size(ϕ) + + # Embed matrix within a larger matrix for better vectorization and avoid duplicated code + # Padded matrix adds 1 row/col after the size of ϕ. + # ϕ is inserted in padded matrix within 1:1+height+1 x 1:1+width+1. + # The rest of the padded matrix (its borders) are set at 0.0. + padded_ϕ = zeros(Float64, 1 + height + 1, 1 + width + 1) + padded_ϕ[begin+1:end-1, begin+1:end-1] .= ϕ[1:end, 1:end] + + # Convolution = up + down + left + right + ∇²ϕ = + padded_ϕ[begin+1-1:end-1-1, begin+1:end-1] + + padded_ϕ[begin+1+1:end-1+1, begin+1:end-1] + + padded_ϕ[begin+1:end-1, begin+1-1:end-1-1] + + padded_ϕ[begin+1:end-1, begin+1+1:end-1+1] - + 4.0 * padded_ϕ[begin+1:end-1, begin+1:end-1] + + return ∇²ϕ[1:end-1, 1:end-1] +end + + + + +m = [[1.0 2.0 3.0 2.0]; [4.0 5.0 6.0 5.0]; [7.0 8.0 9.0 8.0]; [10.0 11.0 12.0 11.0]] +h, w = size(m) +padded_m = zeros(Float64, 1 + h + 1, 1 + w + 1) +padded_m[begin+1:end-1, begin+1:end-1] .= m[1:end, 1:end] +padded_m + +padded_m[begin+1-1:end-1-1, begin+1:end-1] + +padded_m[begin+1+1:end-1+1, begin+1:end-1] + +padded_m[begin+1:end-1, begin+1-1:end-1-1] + +padded_m[begin+1:end-1, begin+1+1:end-1+1] - 4.0 * padded_m[begin+1:end-1, begin+1:end-1] + + +sum(CausticsEngineering.laplacian(m)) +sum(orig_laplacian(m)) diff --git a/src/utilities.jl b/src/utilities.jl index bbd6f68..1732d54 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -1,9 +1,9 @@ """ $(TYPEDEF) -## Coordinates. Represent the data of each topleft corner of a pixel. -## posts/fences: One more corner than number of pixels. - +Coordinates as row (vertical), columns (horizontal). Represent the data of each topleft corner of a pixel. +vr, vc: velocity vector of that corner. +Warning: posts/fences: One more corner than number of pixels. """ struct Vertex3D r::Float64 @@ -91,30 +91,30 @@ mutable struct FieldVertex3D r::AbstractMatrix{Float64} c::AbstractMatrix{Float64} + vr::AbstractMatrix{Float64} + vc::AbstractMatrix{Float64} # Velocity potential at each corner ϕ::AbstractMatrix{Float64} - vr::AbstractMatrix{Float64} - vc::AbstractMatrix{Float64} - rows_numbers::AbstractMatrix{Float64} cols_numbers::AbstractMatrix{Float64} end # Information about each corner surrounding a pixel. Posts&fences warning!!! function FieldVertex3D(height, width) + # Two matrices comtaining the row and column number of each element of the matrix rows_numbers = repeat(Float64.(1:height+1), 1, width + 1) cols_numbers = repeat(Float64.(1:width+1)', height + 1, 1) mr = rows_numbers mc = cols_numbers - mϕ = zeros(Float64, height + 1, width + 1) - mvr = zeros(Float64, height + 1, width + 1) mvc = zeros(Float64, height + 1, width + 1) - fv = FieldVertex3D((height, width), mr, mc, mϕ, mvr, mvc, rows_numbers, cols_numbers) + mϕ = zeros(Float64, height + 1, width + 1) + + fv = FieldVertex3D((height, width), mr, mc, mvr, mvc, mϕ, rows_numbers, cols_numbers) reset_border_values!(fv) return fv end @@ -123,10 +123,9 @@ end """ $(SIGNATURES) -Return the dimension of the mesh as the number of rectangles. It does not return the number of corner points. +Reset the values of the borders corners: all positions at integer values, all velocities at 0. """ function reset_border_values!(corners::FieldVertex3D) - # Reset the border at the fixed values fixed coordinates. corners.r[1, :] .= corners.rows_numbers[1, :] corners.r[end, :] .= corners.rows_numbers[end, :] @@ -135,6 +134,7 @@ function reset_border_values!(corners::FieldVertex3D) corners.c[1, :] .= corners.cols_numbers[1, :] corners.c[end, :] .= corners.cols_numbers[end, :] + corners.c[:, 1] .= corners.cols_numbers[:, 1] corners.c[:, end] .= corners.cols_numbers[:, end] @@ -156,9 +156,9 @@ function Vertex3D(fv::FieldVertex3D, row, col) Vertex3D( fv.r[row, col], fv.c[row, col], - fv.ϕ[row, col], fv.vr[row, col], fv.vc[row, col], + fv.ϕ[row, col], ) else missing @@ -323,6 +323,7 @@ $(SIGNATURES) """ area(t::Tuple{Vertex3D,Vertex3D,Vertex3D}) = area(t...) + """ $(SIGNATURES) @@ -365,6 +366,7 @@ function field_summary(field, fieldname) return """$(fieldname) (Sum/Max/Min/Avg/Avg abs.): $(s) / $(max) / $(min) / $(avg) / $(abs)""" end + """ $(SIGNATURES) From 47270364b5ac02bf3d5089f8ebb2409ff61673a5 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Sat, 25 Sep 2021 13:20:01 +0200 Subject: [PATCH 46/58] Minor --- .gitignore | 7 ++++++- src/scratchpad.jl | 15 --------------- 2 files changed, 6 insertions(+), 16 deletions(-) diff --git a/.gitignore b/.gitignore index 7607609..858cd5e 100644 --- a/.gitignore +++ b/.gitignore @@ -8,6 +8,11 @@ *.obj it*.png loss*.png +change*.png +delta*.png +error*.png +img*.png +orig*.png # Files generated by invoking Julia with --track-allocation @@ -39,4 +44,4 @@ Manifest.toml src/debug_script.jl -examples/personal \ No newline at end of file +examples/personal diff --git a/src/scratchpad.jl b/src/scratchpad.jl index 20c46e2..3f89e92 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -41,21 +41,6 @@ triangle_dict, vertex_dict, triangle_index, vertex_index = create_solid(mesh; bottom_distance = Bottom_Offset, top_distance = Top_Offset) -# Can be done in 2 steps -# -# triangle_dict, vertex_dict = create_solid_as_dict( -# mesh; -# bottom_distance = Bottom_Offset, -# top_distance = Top_Offset -# ) -# -# # Generate array or coordinates and indices usable to create traditional mesh objects -# _, _, triangle_index, vertex_index = create_solid( -# triangle_dict, -# vertex_dict; -# bottom_distance = Bottom_Offset, -# top_distance = Top_Offset, -# ) # Area of all the distorted pixels am = CausticsEngineering.get_area_corners(mesh) From d7527b584beb2b5c25958c619d7b37ec910c6d92 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Sat, 25 Sep 2021 20:29:23 +0200 Subject: [PATCH 47/58] Tracking area convergence bug --- src/scratchpad.jl | 13 +++++++------ 1 file changed, 7 insertions(+), 6 deletions(-) diff --git a/src/scratchpad.jl b/src/scratchpad.jl index 3aa3ffc..25deaea 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -231,7 +231,7 @@ Luminosity: ## STEPPING using Revise, Debugger, Images, Plots; -gr(); +gr() using CausticsEngineering @@ -326,11 +326,12 @@ CausticsEngineering.field_summary(origϕ) CausticsEngineering.field_summary(origLϕ) CausticsEngineering.field_summary(origδ) - - - - - +CausticsEngineering.field_summary(mesh.corners.ϕ[1:end-1, 1:end-1] - origϕ') +CausticsEngineering.field_summary(mesh.corners.ϕ[2:end, 1:end-1] - origϕ') +CausticsEngineering.field_summary(mesh.corners.ϕ[1:end-1, 2:end] - origϕ') +CausticsEngineering.field_summary(mesh.corners.ϕ[2:end, 2:end] - origϕ') +m = (mesh.corners.ϕ[1:end-1, 1:end-1] + mesh.corners.ϕ[2:end, 1:end-1] + mesh.corners.ϕ[1:end-1, 2:end] + mesh.corners.ϕ[2:end, 2:end]) / 4.; +CausticsEngineering.field_summary(m - origϕ') From 6a1b210b5b44935346355d78f533265e99326afe Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Sat, 25 Sep 2021 21:13:19 +0200 Subject: [PATCH 48/58] Tracking area convergence bug --- src/create_mesh.jl | 90 +++++++++++++++++++++++++++++++++------------- src/utilities.jl | 35 ++++++++++++------ 2 files changed, 89 insertions(+), 36 deletions(-) diff --git a/src/create_mesh.jl b/src/create_mesh.jl index dc2a531..6936519 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -21,50 +21,62 @@ function engineer_caustics(source_image) # imageBW is normalised to have 1 unit per pixel on average. imageBW /= average(imageBW) - marginal_change = nothing - max_update = Inf + marginal_change_top = marginal_change_bot = nothing + max_update_top = marginal_change_top = Inf counter = 0 - while (abs(max_update) > 1e-6 && counter < 10_000) + while (abs(max_update_top+marginal_change_bot) > 1e-6 && counter < 10_000) counter += 1 print( """ ================================================================================================================ STARTING ITERATION $(counter): - starting ϕ field = $(field_summary(mesh.corners.ϕ)) + starting ϕ TOP field = $(field_summary(mesh.corners.ϕ_top)) + starting ϕ BOT field = $(field_summary(mesh.corners.ϕ_bot)) """, ) - ϕ = mesh.corners.ϕ - ε, max_update = solve_velocity_potential!(mesh, imageBW, "it$(counter)") + ϕ_top = mesh.corners.ϕ_top + ε_top, max_update_top = solve_velocity_potential!(mesh.corners.ϕ_top, imageBW/2., "it$(counter)_top") + marginal_change_top = mesh.corners.ϕ_top - ϕ_top - marginal_change = mesh.corners.ϕ - ϕ + ϕ_bot = mesh.corners.ϕ_bot + ε_bot, max_update_bot = solve_velocity_potential!(mesh.corners.ϕ_bot, imageBW/2., "it$(counter)_bot") + marginal_change_bot = mesh.corners.ϕ_bot - ϕ_bot print( """ - RESULT AT ITERATION $(counter): - Luminosity error = $(field_summary(ε)) - Vertical move max update = $(max_update) - Marginal change = $(field_summary(marginal_change)) + RESULT AT ITERATION $(counter): + TOP + Luminosity error = $(field_summary(ε_top)) + Vertical move max update = $(max_update_top) + Marginal change = $(field_summary(marginal_change_top)) + end ϕ field = $(field_summary(mesh.corners.ϕ_top)) - end ϕ field = $(field_summary(mesh.corners.ϕ)) - ================================================================================================================ + BOT + end ϕ field = $(field_summary(mesh.corners.ϕ_bot)) + Luminosity error = $(field_summary(ε_bot)) + Vertical move max update = $(max_update_bot) + Marginal change = $(field_summary(marginal_change_bot)) + end ϕ field = $(field_summary(mesh.corners.ϕ_bot)) + + ================================================================================================================ """, ) - plot_as_quiver(mesh, n_steps = 50, scale = height / 10, max_length = height / 20) - average_absolute(marginal_change) < 1e-3 && break + plot_as_quiver(mesh.corners.ϕ_top, n_steps = 50, scale = height / 10, max_length = height / 20) + average_absolute(marginal_change_top + marginal_change_bot) < 1e-4 && break end println("\nSTARTING HORIZONTAL ITERATION ---") - max_update = solve_height_potential(mesh, imageBW; f = Focal_Length) - println("\t Horizontal max update = $(max_update)") + println("\t Horizontal max update TOP = $(max_update_top) / BOT = $(max_update_bot)") # Move the around a nil average. - mesh.corners.ϕ .-= average(mesh.corners.ϕ) + mesh.corners.ϕ_top .-= average(mesh.corners.ϕ_top) + mesh.corners.ϕ_bot .-= average(mesh.corners.ϕ_bot) return mesh, imageBW end @@ -84,29 +96,57 @@ function solve_velocity_potential!(mesh, image, prefix) # Get the area of each individual pixel as stretch/shrunk on the lens. Area = energy. # _FENCES_SIZED_ # Illumination only depends on the position of the corners, not their heights. ϕ is not relevant. - lens_pixels_area = get_lens_pixels_area(mesh) + lens_pixels_area_top, lens_pixels_area_bot = get_lens_pixels_area(mesh) # Positive error => the triangle needs to shrink (less light). Enforce nil average error. - ε = zeros(Float64, height + 1, width + 1) - ε[1:end-1, 1:end-1] = Float64.(lens_pixels_area - image) - ε .-= average(ε) + ε_top = zeros(Float64, height, width) + ε_bot = zeros(Float64, height, width) + + # Each triangle should have the luminosity of half a pixel + ε_top[1:end-1, 1:end-1] = Float64.(lens_pixels_area_top - image/2.) + ε_top .-= average(ε_top) + + ε_bot[1:end-1, 1:end-1] = Float64.(lens_pixels_area_bot - image/2.) + ε_bot .-= average(ε_bot) println(""" solve_velocity_potential! before loop: - $(field_summary(lens_pixels_area, "Pixel area")) - $(field_summary(ε, "luminosity error")) + $(field_summary(lens_pixels_area_top, "Pixel area")) + $(field_summary(ε_top, "luminosity error")) + $(field_summary(lens_pixels_area_bot, "Pixel area")) + $(field_summary(ε_bot, "luminosity error")) """) # Save the loss image as a png. - save_plot_scalar_field!(ε, "error_$(prefix)") + save_plot_scalar_field!(ε, "error_ε_$(prefix)") + save_plot_scalar_field!(ε_top, "error_εtop_$(prefix)") + save_plot_scalar_field!(ε_bot, "error_εbot_$(prefix)") # Save the generated image as a png. + lens_pixels_area = lens_pixels_area_top + lens_pixels_area_bot + save( + "./examples/img_noluminosityratio_$(prefix).png", + Gray.(clamp.(lens_pixels_area, 0.0, 1.0)), + ) + luminosity_ratio = sum(image) / sum(lens_pixels_area) save( "./examples/img_$(prefix).png", Gray.(clamp.(lens_pixels_area * luminosity_ratio, 0.0, 1.0)), ) + luminosity_ratio = sum(image/2.) / sum(lens_pixels_area_top) + save( + "./examples/img_$(prefix).png", + Gray.(clamp.(lens_pixels_area_top * luminosity_ratio, 0.0, 1.0)), + ) + + luminosity_ratio = sum(image/2.) / sum(lens_pixels_area_bot) + save( + "./examples/img_$(prefix).png", + Gray.(clamp.(lens_pixels_area * lens_pixels_area_bot, 0.0, 1.0)), + ) + # Start with a clean, flat potential field. mesh.corners.ϕ = zeros(Float64, height + 1, width + 1) ϕ_b4 = copy(mesh.corners.ϕ) diff --git a/src/utilities.jl b/src/utilities.jl index 1732d54..ae69431 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -1,7 +1,8 @@ """ $(TYPEDEF) -Coordinates as row (vertical), columns (horizontal). Represent the data of each topleft corner of a pixel. +Coordinates as row (vertical), columns (horizontal). Represent the data of each top corner of a pixel. +Topleft for top triangle, bottomleft for bottom triangle vr, vc: velocity vector of that corner. Warning: posts/fences: One more corner than number of pixels. """ @@ -95,7 +96,8 @@ mutable struct FieldVertex3D vc::AbstractMatrix{Float64} # Velocity potential at each corner - ϕ::AbstractMatrix{Float64} + ϕ_top::AbstractMatrix{Float64} + ϕ_bot::AbstractMatrix{Float64} rows_numbers::AbstractMatrix{Float64} cols_numbers::AbstractMatrix{Float64} @@ -112,9 +114,10 @@ function FieldVertex3D(height, width) mvr = zeros(Float64, height + 1, width + 1) mvc = zeros(Float64, height + 1, width + 1) - mϕ = zeros(Float64, height + 1, width + 1) + mϕ_top = zeros(Float64, height , width ) + mϕ_bot = zeros(Float64, height , width ) - fv = FieldVertex3D((height, width), mr, mc, mvr, mvc, mϕ, rows_numbers, cols_numbers) + fv = FieldVertex3D((height, width), mr, mc, mvr, mvc, mϕ_top, mϕ_bot, rows_numbers, cols_numbers) reset_border_values!(fv) return fv end @@ -152,13 +155,14 @@ $(SIGNATURES) function Vertex3D(fv::FieldVertex3D, row, col) height, width = size(fv) - if (1 <= row <= height + 1) && (1 <= col <= width + 1) + if (1 <= row <= height ) && (1 <= col <= width) Vertex3D( fv.r[row, col], fv.c[row, col], fv.vr[row, col], fv.vc[row, col], - fv.ϕ[row, col], + fv.ϕ_top[min(height, row), col(width, col)], + fv.ϕ_bot[min(height, row), col(width, col)], ) else missing @@ -336,10 +340,8 @@ has been shifted and flexed around. function get_lens_pixels_area(mesh::FaceMesh) height, width = size(mesh) - top_tri_area = - area.([triangle3D(mesh, row, col, :bottom) for row ∈ 1:height, col ∈ 1:width]) - bot_tri_area = - area.([triangle3D(mesh, row, col, :bottom) for row ∈ 1:height, col ∈ 1:width]) + top_tri_area = get_lens_pixels_area(mesh, :top) + bot_tri_area =get_lens_pixels_area(mesh, :bottom) total_area = top_tri_area + bot_tri_area @@ -348,10 +350,21 @@ function get_lens_pixels_area(mesh::FaceMesh) @assert abs(sum(luminosity_pixels) - height * width) < 1.0 "Total lens luminosity is incorrect" - return luminosity_pixels + # return luminosity_pixels + return top_tri_area, bot_tri_area end +function get_lens_pixels_area(mesh::FaceMesh, side::Union{:top, :bottom}) + height, width = size(mesh) + + # return luminosity_pixels + return area.([triangle3D(mesh, row, col, side) for row ∈ 1:height, col ∈ 1:width]) +end + + + + """ $(SIGNATURES) From 4f9de3c991439cb83c5b97f3988c16a6dc9b7325 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Sat, 25 Sep 2021 21:21:03 +0200 Subject: [PATCH 49/58] Tracking area convergence bug --- src/utilities.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/utilities.jl b/src/utilities.jl index 1732d54..9d23772 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -337,7 +337,7 @@ function get_lens_pixels_area(mesh::FaceMesh) height, width = size(mesh) top_tri_area = - area.([triangle3D(mesh, row, col, :bottom) for row ∈ 1:height, col ∈ 1:width]) + area.([triangle3D(mesh, row, col, :top) for row ∈ 1:height, col ∈ 1:width]) bot_tri_area = area.([triangle3D(mesh, row, col, :bottom) for row ∈ 1:height, col ∈ 1:width]) From fd50f9e13d65a72284ebd37e06443a0c788acb68 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Sat, 25 Sep 2021 21:47:28 +0200 Subject: [PATCH 50/58] Tracking area convergence bug --- src/create_mesh.jl | 128 +++++++++++++++++++++++++++++++++++++-------- 1 file changed, 106 insertions(+), 22 deletions(-) diff --git a/src/create_mesh.jl b/src/create_mesh.jl index 6936519..734a836 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -118,7 +118,7 @@ function solve_velocity_potential!(mesh, image, prefix) """) # Save the loss image as a png. - save_plot_scalar_field!(ε, "error_ε_$(prefix)") + save_plot_scalar_field!(ε_top+ε_bot, "error_ε_$(prefix)") save_plot_scalar_field!(ε_top, "error_εtop_$(prefix)") save_plot_scalar_field!(ε_bot, "error_εbot_$(prefix)") @@ -137,55 +137,86 @@ function solve_velocity_potential!(mesh, image, prefix) luminosity_ratio = sum(image/2.) / sum(lens_pixels_area_top) save( - "./examples/img_$(prefix).png", + "./examples/img_$(prefix)_top.png", Gray.(clamp.(lens_pixels_area_top * luminosity_ratio, 0.0, 1.0)), ) luminosity_ratio = sum(image/2.) / sum(lens_pixels_area_bot) save( - "./examples/img_$(prefix).png", + "./examples/img_$(prefix)_bot.png", Gray.(clamp.(lens_pixels_area * lens_pixels_area_bot, 0.0, 1.0)), ) # Start with a clean, flat potential field. - mesh.corners.ϕ = zeros(Float64, height + 1, width + 1) - ϕ_b4 = copy(mesh.corners.ϕ) + mesh.corners.ϕ_top = zeros(Float64, height, width) + mesh.corners.ϕ_bot = zeros(Float64, height, width) + + ϕ_b4_top = copy(mesh.corners.ϕ_top) + ϕ_b4_bot = copy(mesh.corners.ϕ_bot) + count = 0 - min_update = new_update = 10_000 - old_update = 2 * new_update + min_update_top = min_update_bot = new_update_top = new_update_bot = 10_000 + old_update_top = 2 * new_update_top + old_update_bot = 2 * new_update_bot while ( - 1e-5 < new_update < 1.5 * min_update && - 1e-4 < (old_update - new_update) / old_update && + 1e-5 < new_update_top + new_update_bot < 1.5 * min_update_top + 1.5 * min_update_bot && + 1e-4 < (old_update_top - new_update_top) / old_update_top && + 1e-4 < (old_update_bot - new_update_bot) / old_update_bot && count < 10_000 ) count += 1 - old_update = new_update - min_update = min(min_update, new_update) + old_update_top = new_update_top + old_update_bot = new_update_bot + min_update_top = min(min_update_top, new_update_top) + min_update_bot = min(min_update_bot, new_update_bot) - new_update, ∇²ϕ_est, δ = propagate_poisson!(mesh.corners.ϕ, ε) + new_update_top, ∇²ϕ_est_top, δ_top = propagate_poisson!(mesh.corners.ϕ_top,ε_top) + new_update_bot, ∇²ϕ_est_bot, δ_bot = propagate_poisson!(mesh.corners.ϕ_bot,ε_bot) count % 1_000 == 1 && println(""" - Iteration $(count) - max_update = $(round(new_update, sigdigits=4)) - $(field_summary(mesh.corners.ϕ, "ϕ")) - $(field_summary(∇²ϕ_est, "∇²ϕ_est")) - $(field_summary(δ, "δ")) - """) + TOP + Iteration $(count) - max_update = $(round(new_update_top, sigdigits=4)) + $(field_summary(mesh.corners.ϕ_top, "ϕ")) + $(field_summary(∇²ϕ_est_top, "∇²ϕ_est")) + $(field_summary(δ_top, "δ")) + BOTTOM + Iteration $(count) - max_update = $(round(new_update_bot, sigdigits=4)) + $(field_summary(mesh.corners.ϕ_bot, "ϕ")) + $(field_summary(∇²ϕ_est_bot, "∇²ϕ_est")) + $(field_summary(δ_bot, "δ")) + """) # Save the loss image as a png. if count % 1_000 == 1 - save_plot_scalar_field!(∇²ϕ_est, "∇²ϕ_est_$(prefix)") - save_plot_scalar_field!(δ, "delta_$(prefix)") + save_plot_scalar_field!(∇²ϕ_est_top, "∇²ϕ_est_$(prefix)") + save_plot_scalar_field!(δ_top, "delta_$(prefix)") save_plot_scalar_field!( - mesh.corners.ϕ - ϕ_b4, + mesh.corners.ϕ_bot + mesh.corners.ϕ_top -ϕ_b4_top -ϕ_b4_bot , "change_mesh.corners.ϕ_$(prefix)", ) - ϕ_b4 = copy(mesh.corners.ϕ) + save_plot_scalar_field!(∇²ϕ_est_top, "∇²ϕ_est_$(prefix)_top") + save_plot_scalar_field!(δ_top, "delta_$(prefix)_top") + save_plot_scalar_field!( + mesh.corners.ϕ_top - ϕ_b4_top, + "change_mesh.corners.ϕ_$(prefix)_top", + ) + + save_plot_scalar_field!(∇²ϕ_est_bot, "∇²ϕ_est_$(prefix)_bot") + save_plot_scalar_field!(δ_bot, "delta_$(prefix)_bot") + save_plot_scalar_field!( + mesh.corners.ϕ_bot - ϕ_b4_bot, + "change_mesh.corners.ϕ_$(prefix)_bot", + ) + + ϕ_b4_top = copy(mesh.corners.ϕ_top) + ϕ_b4_bot = copy(mesh.corners.ϕ_bot) end end # Now we need to march the mesh row,col corner locations according to this gradient. - δ = march_mesh!(mesh) + δ_top = march_mesh!(mesh, :top) + δ_bot = march_mesh!(mesh, :bottom) return ε, new_update end @@ -246,6 +277,59 @@ function march_mesh!(mesh::FaceMesh) end +function march_mesh!(mesh::FaceMesh, side::Union{:top, :bottom}) + + # Calculate the gradient of the velocity potential and reverse its direction. + if side == :top + mesh.corners.vr, mesh.corners.vc = ∇(mesh.corners.ϕ_top) + elseif side == :bottom + mesh.corners.vr, mesh.corners.vc = ∇(mesh.corners.ϕ_bot) + end + mesh.corners.vr .*= -1.0 + mesh.corners.vc .*= -1.0 + + # Clean up the mesh borders + reset_border_values!(mesh.corners) + + # For each point in the mesh we need to figure out its velocity + # However all the nodes located at a border will never move + # I.e. velocity (Vx, Vy) = (0, 0) and the square of acrylate will remain of the same size. + mesh_r = copy(mesh.corners.r) + mesh_c = copy(mesh.corners.c) + + # Get the time, at that velocity, for the area of the triangle to be nil. + # We are only interested by positive values to only move in the direction of the (opposite) gradient + height, width = size(mesh) + list_triangles = [triangle3D(mesh, row, col, side) for row ∈ 1:height, col ∈ 1:width] + list_maximum_t = [t for t ∈ find_maximum_t.(list_triangles) if !isnothing(t) && t > 0.0] + + δ = minimum(list_maximum_t) / 2.0 + if side == :top + mesh.corners.r[1:end-1, 1:end-1] .-= δ * mesh.corners.vr[1:end-1, 1:end-1] + mesh.corners.c[1:end-1, 1:end-1] .-= δ * mesh.corners.vc[1:end-1, 1:end-1] + elseif + mesh.corners.r[2:end, 2:end] .-= δ * mesh.corners.vr[1:end-1, 1:end-1] + mesh.corners.c[2:end, 2:end] .-= δ * mesh.corners.vc[1:end-1, 1:end-1] + end + + println( + """ + + March mesh with correction_ratio δ = $(δ) + $(field_summary(mesh.corners.vr, "∇u")) + $(field_summary(mesh.corners.vc, "∇v")) + $(field_summary(mesh_r - mesh.corners.r , "new mesh changes on row")) + $(field_summary(mesh_c - mesh.corners.c, "new mesh changes on col")) + $(field_summary(mesh_r - mesh.corners.rows_numbers , "total mesh changes on row")) + $(field_summary(mesh_c - mesh.corners.cols_numbers, "total mesh changes on col")) + + """, + ) + + return δ +end + + """ $(SIGNATURES) From 7bf9231000e40055c24642b532cd1017367b28d1 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Sat, 25 Sep 2021 22:39:33 +0200 Subject: [PATCH 51/58] Tracking area convergence bug --- src/create_mesh.jl | 67 +++++++++++++++++++++++++--------------------- src/scratchpad.jl | 3 +-- 2 files changed, 37 insertions(+), 33 deletions(-) diff --git a/src/create_mesh.jl b/src/create_mesh.jl index dc2a531..6905ad7 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -24,33 +24,43 @@ function engineer_caustics(source_image) marginal_change = nothing max_update = Inf counter = 0 - while (abs(max_update) > 1e-6 && counter < 10_000) + while (abs(max_update) > 1e-6 && counter < 4) counter += 1 print( """ - ================================================================================================================ - STARTING ITERATION $(counter): - starting ϕ field = $(field_summary(mesh.corners.ϕ)) + ================================================================================================================ + STARTING ITERATION $(counter): + starting ϕ field = $(field_summary(mesh.corners.ϕ)) - """, + """, ) - ϕ = mesh.corners.ϕ - ε, max_update = solve_velocity_potential!(mesh, imageBW, "it$(counter)") + start_r = deepcopy(mesh.corners.r) + start_c = deepcopy(mesh.corners.c) + start_ϕ = deepcopy(mesh.corners.ϕ) - marginal_change = mesh.corners.ϕ - ϕ + ε, max_update = solve_velocity_potential!(mesh, imageBW, "it$(counter)") + marginal_change = mesh.corners.ϕ - start_ϕ print( """ - RESULT AT ITERATION $(counter): - Luminosity error = $(field_summary(ε)) - Vertical move max update = $(max_update) - Marginal change = $(field_summary(marginal_change)) + RESULT AT ITERATION $(counter): + Luminosity error = $(field_summary(ε)) + Vertical move max update = $(max_update) + Marginal change = $(field_summary(marginal_change)) + + $(field_summary(mesh.corners.vr, "∇u")) + $(field_summary(mesh.corners.vc, "∇v")) + $(field_summary(mesh.corners.r - start_r, "new mesh changes on row")) + $(field_summary(mesh.corners.c - start_c, "new mesh changes on col")) + $(field_summary(mesh.corners.ϕ - start_ϕ, "new mesh changes on ϕ")) + $(field_summary(mesh.corners.r - mesh.corners.rows_numbers, "total mesh changes on row")) + $(field_summary(mesh.corners.c - mesh.corners.cols_numbers, "total mesh changes on col")) - end ϕ field = $(field_summary(mesh.corners.ϕ)) - ================================================================================================================ + end ϕ field = $(field_summary(mesh.corners.ϕ)) + ================================================================================================================ """, ) @@ -114,8 +124,8 @@ function solve_velocity_potential!(mesh, image, prefix) min_update = new_update = 10_000 old_update = 2 * new_update while ( - 1e-5 < new_update < 1.5 * min_update && - 1e-4 < (old_update - new_update) / old_update && + 1e-6 < new_update < 1.5 * min_update && + 1e-5 < (old_update - new_update) / old_update && count < 10_000 ) count += 1 @@ -135,10 +145,7 @@ function solve_velocity_potential!(mesh, image, prefix) if count % 1_000 == 1 save_plot_scalar_field!(∇²ϕ_est, "∇²ϕ_est_$(prefix)") save_plot_scalar_field!(δ, "delta_$(prefix)") - save_plot_scalar_field!( - mesh.corners.ϕ - ϕ_b4, - "change_mesh.corners.ϕ_$(prefix)", - ) + save_plot_scalar_field!(mesh.corners.ϕ - ϕ_b4, "change_mesh.corners.ϕ_$(prefix)") ϕ_b4 = copy(mesh.corners.ϕ) end @@ -188,19 +195,17 @@ function march_mesh!(mesh::FaceMesh) mesh.corners.r .-= δ * mesh.corners.vr mesh.corners.c .-= δ * mesh.corners.vc - println( - """ + println(""" - March mesh with correction_ratio δ = $(δ) - $(field_summary(mesh.corners.vr, "∇u")) - $(field_summary(mesh.corners.vc, "∇v")) - $(field_summary(mesh_r - mesh.corners.r , "new mesh changes on row")) - $(field_summary(mesh_c - mesh.corners.c, "new mesh changes on col")) - $(field_summary(mesh_r - mesh.corners.rows_numbers , "total mesh changes on row")) - $(field_summary(mesh_c - mesh.corners.cols_numbers, "total mesh changes on col")) + March mesh with correction_ratio δ = $(δ) + $(field_summary(mesh.corners.vr, "∇u")) + $(field_summary(mesh.corners.vc, "∇v")) + $(field_summary(mesh_r - mesh.corners.r , "new mesh changes on row")) + $(field_summary(mesh_c - mesh.corners.c, "new mesh changes on col")) + $(field_summary(mesh_r - mesh.corners.rows_numbers , "total mesh changes on row")) + $(field_summary(mesh_c - mesh.corners.cols_numbers, "total mesh changes on col")) - """, - ) + """) return δ end diff --git a/src/scratchpad.jl b/src/scratchpad.jl index 25deaea..272a82a 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -4,10 +4,9 @@ gr() using CausticsEngineering -image = Images.load("./examples/cat_posing.jpg"); # Check current working directory with pwd() - image = Images.load("./examples/personal/slashdot.jpg"); # Check current working directory with pwd() +image = Images.load("./examples/cat_posing.jpg"); # Check current working directory with pwd() image = Images.load("./examples/personal/goose.jpg"); # Check current working directory with pwd() image = Images.load("./examples/personal/salvador_dali_1.jpg"); # Check current working directory with pwd() From 860904bee77ba6da3aef97c1debbc809a07b40f8 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Sun, 26 Sep 2021 05:34:42 +0200 Subject: [PATCH 52/58] Minor. --- src/create_mesh.jl | 23 +++++---- src/scratchpad.jl | 117 ++++++++++++++++++++++++++++++++++++++++++++- 2 files changed, 129 insertions(+), 11 deletions(-) diff --git a/src/create_mesh.jl b/src/create_mesh.jl index dc2a531..a5390a2 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -23,8 +23,9 @@ function engineer_caustics(source_image) marginal_change = nothing max_update = Inf + list_max_update = [] counter = 0 - while (abs(max_update) > 1e-6 && counter < 10_000) + while (abs(max_update) > 1e-6 && counter < 10) counter += 1 print( @@ -37,7 +38,8 @@ function engineer_caustics(source_image) ) ϕ = mesh.corners.ϕ - ε, max_update = solve_velocity_potential!(mesh, imageBW, "it$(counter)") + ε, max_update, list_new_update = solve_velocity_potential!(mesh, imageBW, "it$(counter)") + append!(list_max_update, list_new_update) marginal_change = mesh.corners.ϕ - ϕ @@ -66,7 +68,7 @@ function engineer_caustics(source_image) # Move the around a nil average. mesh.corners.ϕ .-= average(mesh.corners.ϕ) - return mesh, imageBW + return mesh, imageBW, list_max_update end @@ -112,14 +114,16 @@ function solve_velocity_potential!(mesh, image, prefix) ϕ_b4 = copy(mesh.corners.ϕ) count = 0 min_update = new_update = 10_000 + list_new_update = [] old_update = 2 * new_update while ( - 1e-5 < new_update < 1.5 * min_update && - 1e-4 < (old_update - new_update) / old_update && + 1e-6 < new_update < 1.5 * min_update && + # 1e-4 < (old_update - new_update) / old_update && count < 10_000 ) count += 1 old_update = new_update + push!(list_new_update, new_update) min_update = min(min_update, new_update) new_update, ∇²ϕ_est, δ = propagate_poisson!(mesh.corners.ϕ, ε) @@ -146,7 +150,7 @@ function solve_velocity_potential!(mesh, image, prefix) # Now we need to march the mesh row,col corner locations according to this gradient. δ = march_mesh!(mesh) - return ε, new_update + return ε, new_update, list_new_update end @@ -161,9 +165,10 @@ $(SIGNATURES) function march_mesh!(mesh::FaceMesh) # Calculate the gradient of the velocity potential and reverse its direction. - mesh.corners.vr, mesh.corners.vc = ∇(mesh.corners.ϕ) - mesh.corners.vr .*= -1.0 - mesh.corners.vc .*= -1.0 + ∇ϕᵤ, ∇ϕᵥ = ∇(mesh.corners.ϕ) + mesh.corners.vr = -∇ϕᵤ + mesh.corners.vc = -∇ϕᵥ + # Clean up the mesh borders reset_border_values!(mesh.corners) diff --git a/src/scratchpad.jl b/src/scratchpad.jl index 3aa3ffc..db1a688 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -21,7 +21,12 @@ image = Images.load("./examples/personal/caricature.jpg"); # Check current worki image = Images.load("./examples/personal/portrait.jpg"); # Check current working directory with pwd() image = Images.load("./examples/personal/bilal.jpg"); # Check current working directory with pwd() -mesh, imageBW = engineer_caustics(image); +mesh, imageBW, list_max_updates = engineer_caustics(image); + +length(list_max_updates) +p = plot((log.(clamp01nan.(list_max_updates)))) +p +save("ppp.png", map(clamp01nan, p)) imageBW = Float64.(Gray.(image)); Gray.(imageBW) @@ -314,7 +319,7 @@ CausticsEngineering.field_summary(origerror_luminosity) CausticsEngineering.field_summary(error_luminosity - origerror_luminosity') -######################## Distance to Laplacian & propagate +######################## Propagation max_update, Lϕ, δ = CausticsEngineering.propagate_poisson!(mesh.corners.ϕ, error_luminosity); CausticsEngineering.field_summary(mesh.corners.ϕ) CausticsEngineering.field_summary(Lϕ) @@ -327,6 +332,114 @@ CausticsEngineering.field_summary(origLϕ) CausticsEngineering.field_summary(origδ) +######################## March mesh +dfx, dfy = ∇(mesh.corners.ϕ) +CausticsEngineering.field_summary(dfx) +CausticsEngineering.field_summary(dfy) +mesh.corners.vr = -dfx +mesh.corners.vc = -dfy +CausticsEngineering.field_summary(mesh.corners.vr) +CausticsEngineering.field_summary(mesh.corners.vc) + +dfx2, dfy2 = CausticsEngineering.orig_∇(origϕ) +CausticsEngineering.field_summary(dfx2) +CausticsEngineering.field_summary(dfy2) + + +# Min t +list_triangles = vcat( + [CausticsEngineering.triangle3D(mesh, row, col, :top) for row ∈ 1:h, col ∈ 1:w], + [CausticsEngineering.triangle3D(mesh, row, col, :bottom) for row ∈ 1:h, col ∈ 1:w], +) + +list_maximum_t = [t for t ∈ CausticsEngineering.find_maximum_t.(list_triangles) if !isnothing(t) && t > 0.0] +δ = minimum(list_maximum_t) + +mesh_r = copy(mesh.corners.r) +mesh_c = copy(mesh.corners.c) +δ = minimum(list_maximum_t) / 2.0 +mesh.corners.r .-= δ * mesh.corners.vr +mesh.corners.c .-= δ * mesh.corners.vc + +println( + """ + +March mesh with correction_ratio δ = $(δ) + $(CausticsEngineering.field_summary(mesh.corners.vr, "∇u")) + $(CausticsEngineering.field_summary(mesh.corners.vc, "∇v")) + $(CausticsEngineering.field_summary(mesh_r - mesh.corners.r , "new mesh changes on row")) + $(CausticsEngineering.field_summary(mesh_c - mesh.corners.c, "new mesh changes on col")) + $(CausticsEngineering.field_summary(mesh_r - mesh.corners.rows_numbers , "total mesh changes on row")) + $(CausticsEngineering.field_summary(mesh_c - mesh.corners.cols_numbers, "total mesh changes on col")) + + """, +) + + +velocities = Matrix{CausticsEngineering.Point3D}(undef, w+1, h+1) +fill!(velocities, CausticsEngineering.Point3D(0.0, 0.0, 0.0, 0.0, 0.0)) + +for x ∈ 1:w-1, y ∈ 1:h-1 + velocities[x, y] = CausticsEngineering.Point3D(-dfx2[x, y], -dfy2[x, y], 0.0, 0.0, 0.0) +end + +min_t = 10000 +triangleCount = 1 +p1 = CausticsEngineering.Point3D(0., 0., 0., 0., 0.) +p2 = CausticsEngineering.Point3D(0., 0., 0., 0., 0.) +p3 = CausticsEngineering.Point3D(0., 0., 0., 0., 0.) +v1 = CausticsEngineering.Point3D(0., 0., 0., 0., 0.) +v2 = CausticsEngineering.Point3D(0., 0., 0., 0., 0.) +v3 = CausticsEngineering.Point3D(0., 0., 0., 0., 0.) +for triangle in origmesh.triangles + p1 = origmesh.nodes[triangle.pt1] + p2 = origmesh.nodes[triangle.pt2] + p3 = origmesh.nodes[triangle.pt3] + + v1 = velocities[p1.ix, p1.iy] + v2 = velocities[p2.ix, p2.iy] + v3 = velocities[p3.ix, p3.iy] + + t = CausticsEngineering.findT(p1, p2, p3, v1, v2, v3) + + if !isnothing(t) + min_t = min(min_t, t) + end + + triangleCount += 1 +end + +p1 +p2 +p3 +v1 +v2 +v3 + +min_t + +size(origmesh.nodes) +avgmx = 0. +avgmy = 0. +avgax = 0. +avgay = 0. +for point in origmesh.nodes + v = velocities[point.ix, point.iy] + px = point.x + py = point.y + point.x = v.x * min_t/2 + point.x + point.y = v.y * min_t/2 + point.y + + avgmx += point.x - px + avgmy += point.y - py + avgax += abs(point.x - px) + avgay += abs(point.y - py) +end + +avgmx/length(origmesh.nodes) +avgmy/length(origmesh.nodes) +avgax/length(origmesh.nodes) +avgay/length(origmesh.nodes) From abf06dbce2fc6455780ce82bc4d63ca964ce054e Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Sun, 26 Sep 2021 07:32:38 +0200 Subject: [PATCH 53/58] Done --- src/CausticsEngineering.jl | 4 +- src/CausticsEngineering.jl.orig | 5 -- src/create_mesh.jl | 111 +++++++++++++++++--------------- src/create_mesh.jl.orig | 14 ---- src/math_utilities.jl.orig | 14 ---- src/scratchpad.jl | 1 - src/scratchpad.jl.orig | 9 --- src/utilities.jl | 4 +- 8 files changed, 62 insertions(+), 100 deletions(-) diff --git a/src/CausticsEngineering.jl b/src/CausticsEngineering.jl index e132126..7e3a2bb 100644 --- a/src/CausticsEngineering.jl +++ b/src/CausticsEngineering.jl @@ -62,8 +62,8 @@ export save_obj!, # Main procedures - propagate_poisson!, - march_mesh!, + propagate_poisson, + march_mesh, engineer_caustics, main diff --git a/src/CausticsEngineering.jl.orig b/src/CausticsEngineering.jl.orig index 397806b..e132126 100644 --- a/src/CausticsEngineering.jl.orig +++ b/src/CausticsEngineering.jl.orig @@ -44,16 +44,11 @@ export FieldVertex3D, FaceMesh, -<<<<<<< HEAD - # Math - average, average_absolute, -======= # math average, average_absolute, laplacian, ∇, ->>>>>>> 9473c949cf07d0e9431c75b57947a2304ac33a97 # Mesh create_solid, diff --git a/src/create_mesh.jl b/src/create_mesh.jl index 6905ad7..e7d59e9 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -23,8 +23,9 @@ function engineer_caustics(source_image) marginal_change = nothing max_update = Inf + list_max_update = [] counter = 0 - while (abs(max_update) > 1e-6 && counter < 4) + while (abs(max_update) > 1e-6 && counter < 5) counter += 1 print( @@ -40,7 +41,8 @@ function engineer_caustics(source_image) start_c = deepcopy(mesh.corners.c) start_ϕ = deepcopy(mesh.corners.ϕ) - ε, max_update = solve_velocity_potential!(mesh, imageBW, "it$(counter)") + ε, max_update, list_updates = solve_velocity_potential!(mesh, imageBW, "it$(counter)") + append!(list_max_update, list_updates) marginal_change = mesh.corners.ϕ - start_ϕ print( @@ -50,6 +52,7 @@ function engineer_caustics(source_image) Luminosity error = $(field_summary(ε)) Vertical move max update = $(max_update) Marginal change = $(field_summary(marginal_change)) + end ϕ field = $(field_summary(mesh.corners.ϕ)) $(field_summary(mesh.corners.vr, "∇u")) $(field_summary(mesh.corners.vc, "∇v")) @@ -58,11 +61,9 @@ function engineer_caustics(source_image) $(field_summary(mesh.corners.ϕ - start_ϕ, "new mesh changes on ϕ")) $(field_summary(mesh.corners.r - mesh.corners.rows_numbers, "total mesh changes on row")) $(field_summary(mesh.corners.c - mesh.corners.cols_numbers, "total mesh changes on col")) - - end ϕ field = $(field_summary(mesh.corners.ϕ)) ================================================================================================================ - """, + """, ) plot_as_quiver(mesh, n_steps = 50, scale = height / 10, max_length = height / 20) average_absolute(marginal_change) < 1e-3 && break @@ -70,13 +71,13 @@ function engineer_caustics(source_image) println("\nSTARTING HORIZONTAL ITERATION ---") - max_update = solve_height_potential(mesh, imageBW; f = Focal_Length) + ϕ_next, max_update = solve_height_potential(mesh, imageBW; f = Focal_Length) println("\t Horizontal max update = $(max_update)") # Move the around a nil average. - mesh.corners.ϕ .-= average(mesh.corners.ϕ) + mesh.corners.ϕ .= ϕ_next .- average(ϕ_next) - return mesh, imageBW + return mesh, imageBW, list_max_update end @@ -119,41 +120,45 @@ function solve_velocity_potential!(mesh, image, prefix) # Start with a clean, flat potential field. mesh.corners.ϕ = zeros(Float64, height + 1, width + 1) - ϕ_b4 = copy(mesh.corners.ϕ) + ϕ_next = ϕ_b4 = copy(mesh.corners.ϕ) count = 0 min_update = new_update = 10_000 + list_new_update = [] old_update = 2 * new_update while ( - 1e-6 < new_update < 1.5 * min_update && - 1e-5 < (old_update - new_update) / old_update && - count < 10_000 + 1e-5 < new_update < 1.5 * min_update && + count < 3_000 ) count += 1 old_update = new_update + push!(list_new_update, new_update) min_update = min(min_update, new_update) - new_update, ∇²ϕ_est, δ = propagate_poisson!(mesh.corners.ϕ, ε) + ϕ_next, new_update, ∇²ϕ_est, δ = propagate_poisson(ϕ_next, ε) - count % 1_000 == 1 && println(""" - Iteration $(count) - max_update = $(round(new_update, sigdigits=4)) - $(field_summary(mesh.corners.ϕ, "ϕ")) - $(field_summary(∇²ϕ_est, "∇²ϕ_est")) - $(field_summary(δ, "δ")) - """) + if count % 250 == 1 + println(""" + Iteration $(count) - max_update = $(round(new_update, sigdigits=4)) + $(field_summary(ϕ_next, "ϕ")) + $(field_summary(∇²ϕ_est, "∇²ϕ_est")) + $(field_summary(δ, "δ")) + """) - # Save the loss image as a png. - if count % 1_000 == 1 - save_plot_scalar_field!(∇²ϕ_est, "∇²ϕ_est_$(prefix)") - save_plot_scalar_field!(δ, "delta_$(prefix)") - save_plot_scalar_field!(mesh.corners.ϕ - ϕ_b4, "change_mesh.corners.ϕ_$(prefix)") + save_plot_scalar_field!(∇²ϕ_est, "∇²ϕ_est_$(prefix)_$(count)") + save_plot_scalar_field!(δ, "delta_$(prefix)_$(count)") + save_plot_scalar_field!(ϕ_next- ϕ_b4, "change_mesh.corners.ϕ_$(prefix)_$(count)") - ϕ_b4 = copy(mesh.corners.ϕ) + ϕ_b4 = copy(ϕ_next) end end # Now we need to march the mesh row,col corner locations according to this gradient. - δ = march_mesh!(mesh) - return ε, new_update + r_next, c_next, δ = march_mesh(mesh, ϕ_next) + mesh.corners.r .= r_next + mesh.corners.c .= c_next + mesh.corners.ϕ .= ϕ_next + + return ε, new_update, list_new_update end @@ -163,23 +168,21 @@ $(SIGNATURES) ϕ is the height map. -`march_mesh!` flexes the mesh +`march_mesh` flexes the mesh """ -function march_mesh!(mesh::FaceMesh) +function march_mesh(mesh, mesh_ϕ) # Calculate the gradient of the velocity potential and reverse its direction. - mesh.corners.vr, mesh.corners.vc = ∇(mesh.corners.ϕ) - mesh.corners.vr .*= -1.0 - mesh.corners.vc .*= -1.0 + vr, vc = ∇(mesh_ϕ) + mesh.corners.vr .= -vr + mesh.corners.vc .= -vc # Clean up the mesh borders - reset_border_values!(mesh.corners) + # reset_border_values!(mesh.corners) # For each point in the mesh we need to figure out its velocity # However all the nodes located at a border will never move # I.e. velocity (Vx, Vy) = (0, 0) and the square of acrylate will remain of the same size. - mesh_r = copy(mesh.corners.r) - mesh_c = copy(mesh.corners.c) # Get the time, at that velocity, for the area of the triangle to be nil. # We are only interested by positive values to only move in the direction of the (opposite) gradient @@ -191,23 +194,23 @@ function march_mesh!(mesh::FaceMesh) list_maximum_t = [t for t ∈ find_maximum_t.(list_triangles) if !isnothing(t) && t > 0.0] - δ = minimum(list_maximum_t) / 2.0 - mesh.corners.r .-= δ * mesh.corners.vr - mesh.corners.c .-= δ * mesh.corners.vc + δ = minimum(list_maximum_t) / 1.5 + new_r = mesh.corners.r - δ * vr + new_c = mesh.corners.c - δ * vc println(""" March mesh with correction_ratio δ = $(δ) $(field_summary(mesh.corners.vr, "∇u")) $(field_summary(mesh.corners.vc, "∇v")) - $(field_summary(mesh_r - mesh.corners.r , "new mesh changes on row")) - $(field_summary(mesh_c - mesh.corners.c, "new mesh changes on col")) - $(field_summary(mesh_r - mesh.corners.rows_numbers , "total mesh changes on row")) - $(field_summary(mesh_c - mesh.corners.cols_numbers, "total mesh changes on col")) + $(field_summary(new_r - mesh.corners.r , "new mesh changes on row")) + $(field_summary(new_c - mesh.corners.c, "new mesh changes on col")) + $(field_summary(new_r - mesh.corners.rows_numbers , "total mesh changes on row")) + $(field_summary(new_c - mesh.corners.cols_numbers, "total mesh changes on col")) """) - return δ + return new_r, new_c, δ end @@ -237,27 +240,28 @@ In order of how to think about the flow of the program for the velocity potentia - => Increase the value of ϕ at that point means a positive change when δ > 0. - δ > 0 => correction of the SAME sign. """ -function propagate_poisson!(ϕ::Matrix{Float64}, ε::Matrix{Float64}) +function propagate_poisson(ϕ::Matrix{Float64}, ε::Matrix{Float64}) height, width = size(ϕ) ∇²ϕ_est = zeros(Float64, height, width) δ = zeros(Float64, height, width) + new_ϕ = ϕ ω = 1.99 for row = 1:height, col = 1:width - val_up = row == 1 ? 0.0 : ϕ[row-1, col] - val_down = row == height ? 0.0 : ϕ[row+1, col] - val_left = col == 1 ? 0.0 : ϕ[row, col-1] - val_right = col == width ? 0.0 : ϕ[row, col+1] + val_up = row == 1 ? 0.0 : new_ϕ[row-1, col] + val_down = row == height ? 0.0 : new_ϕ[row+1, col] + val_left = col == 1 ? 0.0 : new_ϕ[row, col-1] + val_right = col == width ? 0.0 : new_ϕ[row, col+1] - ∇²ϕ_est[row, col] = val_up + val_down + val_left + val_right - 4 * ϕ[row, col] + ∇²ϕ_est[row, col] = val_up + val_down + val_left + val_right - 4 * new_ϕ[row, col] δ[row, col] = ω / 4.0 * (∇²ϕ_est[row, col] - ε[row, col]) - ϕ[row, col] += δ[row, col] + new_ϕ[row, col] += δ[row, col] end - return maximum(abs.(δ)), ∇²ϕ_est, δ + return new_ϕ, maximum(abs.(δ)), ∇²ϕ_est, δ # # Laplacian @@ -328,11 +332,12 @@ function solve_height_potential(mesh::FaceMesh, image; f = Focal_Length) divergence_direction = div_row + div_col # divergence_direction .-= average(divergence_direction) + ϕ_next = mesh.corners.ϕ max_update = Inf old_update = Inf for i ∈ 1:1e6 old_update = max_update - max_update, _, _ = propagate_poisson!(mesh.corners.ϕ, -divergence_direction) + ϕ_next, max_update, _, _ = propagate_poisson(ϕ_next, -divergence_direction) i % 1_000 == 1 && println("Convergence horiz. Δ at counter = $(i) max update = $(max_update)") @@ -345,5 +350,5 @@ function solve_height_potential(mesh::FaceMesh, image; f = Focal_Length) end end - return max_update + return ϕ_next, max_update end diff --git a/src/create_mesh.jl.orig b/src/create_mesh.jl.orig index 8f76f20..30a84bd 100644 --- a/src/create_mesh.jl.orig +++ b/src/create_mesh.jl.orig @@ -25,11 +25,7 @@ function engineer_caustics(source_image) max_update = Inf list_max_update = [] counter = 0 -<<<<<<< HEAD - while (abs(max_update) > 1e-6 && counter < 10) -======= while (abs(max_update) > 1e-6 && counter < 4) ->>>>>>> 7bf9231000e40055c24642b532cd1017367b28d1 counter += 1 print( @@ -41,15 +37,9 @@ function engineer_caustics(source_image) """, ) -<<<<<<< HEAD - ϕ = mesh.corners.ϕ - ε, max_update, list_new_update = solve_velocity_potential!(mesh, imageBW, "it$(counter)") - append!(list_max_update, list_new_update) -======= start_r = deepcopy(mesh.corners.r) start_c = deepcopy(mesh.corners.c) start_ϕ = deepcopy(mesh.corners.ϕ) ->>>>>>> 7bf9231000e40055c24642b532cd1017367b28d1 ε, max_update = solve_velocity_potential!(mesh, imageBW, "it$(counter)") marginal_change = mesh.corners.ϕ - start_ϕ @@ -137,11 +127,7 @@ function solve_velocity_potential!(mesh, image, prefix) old_update = 2 * new_update while ( 1e-6 < new_update < 1.5 * min_update && -<<<<<<< HEAD - # 1e-4 < (old_update - new_update) / old_update && -======= 1e-5 < (old_update - new_update) / old_update && ->>>>>>> 7bf9231000e40055c24642b532cd1017367b28d1 count < 10_000 ) count += 1 diff --git a/src/math_utilities.jl.orig b/src/math_utilities.jl.orig index a9660ba..148548a 100644 --- a/src/math_utilities.jl.orig +++ b/src/math_utilities.jl.orig @@ -8,27 +8,13 @@ average(m::AbstractMatrix) = (sum(m) / length(m)) """ $(SIGNATURES) """ -<<<<<<< HEAD -average(m::AbstractMatrix) = sum(m) / length(m) -======= average_absolute(m::AbstractMatrix) = (sum(abs.(m)) / length(m)) ->>>>>>> 9473c949cf07d0e9431c75b57947a2304ac33a97 """ $(SIGNATURES) """ -<<<<<<< HEAD -average_absolute(m::AbstractMatrix) = sum(abs.(m)) / length(m) - - -""" -$(SIGNATURES) -""" -test_average_absolute(m::AbstractMatrix) = average_absolute(m) < 1e10 -======= test_average_absolute(m::AbstractMatrix) = (average_absolute(m)) < 1e6 ->>>>>>> 9473c949cf07d0e9431c75b57947a2304ac33a97 """ diff --git a/src/scratchpad.jl b/src/scratchpad.jl index adb85ff..8b6d8f8 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -25,7 +25,6 @@ mesh, imageBW, list_max_updates = engineer_caustics(image); length(list_max_updates) p = plot((log.(clamp01nan.(list_max_updates)))) p -save("ppp.png", map(clamp01nan, p)) imageBW = Float64.(Gray.(image)); Gray.(imageBW) diff --git a/src/scratchpad.jl.orig b/src/scratchpad.jl.orig index a97cacd..9bab967 100644 --- a/src/scratchpad.jl.orig +++ b/src/scratchpad.jl.orig @@ -330,7 +330,6 @@ CausticsEngineering.field_summary(origϕ) CausticsEngineering.field_summary(origLϕ) CausticsEngineering.field_summary(origδ) -<<<<<<< HEAD ######################## March mesh dfx, dfy = ∇(mesh.corners.ϕ) @@ -444,14 +443,6 @@ avgay/length(origmesh.nodes) -======= -CausticsEngineering.field_summary(mesh.corners.ϕ[1:end-1, 1:end-1] - origϕ') -CausticsEngineering.field_summary(mesh.corners.ϕ[2:end, 1:end-1] - origϕ') -CausticsEngineering.field_summary(mesh.corners.ϕ[1:end-1, 2:end] - origϕ') -CausticsEngineering.field_summary(mesh.corners.ϕ[2:end, 2:end] - origϕ') -m = (mesh.corners.ϕ[1:end-1, 1:end-1] + mesh.corners.ϕ[2:end, 1:end-1] + mesh.corners.ϕ[1:end-1, 2:end] + mesh.corners.ϕ[2:end, 2:end]) / 4.; -CausticsEngineering.field_summary(m - origϕ') ->>>>>>> 7bf9231000e40055c24642b532cd1017367b28d1 diff --git a/src/utilities.jl b/src/utilities.jl index 9d23772..17cfa7a 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -358,12 +358,12 @@ $(SIGNATURES) """ function field_summary(field, fieldname) s = round(sum(field), sigdigits = 6) - max = round(maximum(field), sigdigits = 4) min = round(minimum(field), sigdigits = 4) + max = round(maximum(field), sigdigits = 4) avg = round(average(field), sigdigits = 4) abs = round(average_absolute(field), sigdigits = 4) - return """$(fieldname) (Sum/Max/Min/Avg/Avg abs.): $(s) / $(max) / $(min) / $(avg) / $(abs)""" + return """$(fieldname) (Sum/Min/Max/Avg/Avg abs.): $(s) / $(min) / $(max) / $(avg) / $(abs)""" end From 15179af89e8cb2a0947baf85f69d6b314cf5b699 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Sun, 26 Sep 2021 13:17:56 +0200 Subject: [PATCH 54/58] Clean up --- src/create_mesh.jl | 123 ++++++--------------------------------------- 1 file changed, 14 insertions(+), 109 deletions(-) diff --git a/src/create_mesh.jl b/src/create_mesh.jl index e7d59e9..a3d1f4a 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -6,7 +6,6 @@ $(SIGNATURES) function engineer_caustics(source_image) imageBW = Float64.(Gray.(source_image)) - # Set global size parameters height, width = size(imageBW) global N_Pixel_Height = height @@ -37,12 +36,7 @@ function engineer_caustics(source_image) """, ) - start_r = deepcopy(mesh.corners.r) - start_c = deepcopy(mesh.corners.c) - start_ϕ = deepcopy(mesh.corners.ϕ) - - ε, max_update, list_updates = solve_velocity_potential!(mesh, imageBW, "it$(counter)") - append!(list_max_update, list_updates) + ε, max_update = solve_velocity_potential!(mesh, imageBW, "it$(counter)") marginal_change = mesh.corners.ϕ - start_ϕ print( @@ -53,14 +47,6 @@ function engineer_caustics(source_image) Vertical move max update = $(max_update) Marginal change = $(field_summary(marginal_change)) end ϕ field = $(field_summary(mesh.corners.ϕ)) - - $(field_summary(mesh.corners.vr, "∇u")) - $(field_summary(mesh.corners.vc, "∇v")) - $(field_summary(mesh.corners.r - start_r, "new mesh changes on row")) - $(field_summary(mesh.corners.c - start_c, "new mesh changes on col")) - $(field_summary(mesh.corners.ϕ - start_ϕ, "new mesh changes on ϕ")) - $(field_summary(mesh.corners.r - mesh.corners.rows_numbers, "total mesh changes on row")) - $(field_summary(mesh.corners.c - mesh.corners.cols_numbers, "total mesh changes on col")) ================================================================================================================ """, @@ -69,15 +55,13 @@ function engineer_caustics(source_image) average_absolute(marginal_change) < 1e-3 && break end - println("\nSTARTING HORIZONTAL ITERATION ---") - - ϕ_next, max_update = solve_height_potential(mesh, imageBW; f = Focal_Length) - println("\t Horizontal max update = $(max_update)") + println("\nSTARTING HORIZONTAL DISPERSION ---") + ϕ_next, max_update = solve_horizontal_dispersion(mesh, imageBW; f = Focal_Length) # Move the around a nil average. mesh.corners.ϕ .= ϕ_next .- average(ϕ_next) - return mesh, imageBW, list_max_update + return mesh, imageBW end @@ -92,9 +76,9 @@ function solve_velocity_potential!(mesh, image, prefix) # Start with a new clean field height, width = size(mesh) + # Illumination only depends on the position of the corners, not their heights. ϕ is not relevant. # Get the area of each individual pixel as stretch/shrunk on the lens. Area = energy. # _FENCES_SIZED_ - # Illumination only depends on the position of the corners, not their heights. ϕ is not relevant. lens_pixels_area = get_lens_pixels_area(mesh) # Positive error => the triangle needs to shrink (less light). Enforce nil average error. @@ -102,53 +86,13 @@ function solve_velocity_potential!(mesh, image, prefix) ε[1:end-1, 1:end-1] = Float64.(lens_pixels_area - image) ε .-= average(ε) - println(""" - solve_velocity_potential! before loop: - $(field_summary(lens_pixels_area, "Pixel area")) - $(field_summary(ε, "luminosity error")) - """) - - # Save the loss image as a png. - save_plot_scalar_field!(ε, "error_$(prefix)") - - # Save the generated image as a png. - luminosity_ratio = sum(image) / sum(lens_pixels_area) - save( - "./examples/img_$(prefix).png", - Gray.(clamp.(lens_pixels_area * luminosity_ratio, 0.0, 1.0)), - ) - # Start with a clean, flat potential field. - mesh.corners.ϕ = zeros(Float64, height + 1, width + 1) - ϕ_next = ϕ_b4 = copy(mesh.corners.ϕ) + ϕ_next = zeros(Float64, height + 1, width + 1) count = 0 - min_update = new_update = 10_000 - list_new_update = [] - old_update = 2 * new_update - while ( - 1e-5 < new_update < 1.5 * min_update && - count < 3_000 - ) + while 1e-5 < new_update && count < 3_000 count += 1 - old_update = new_update - push!(list_new_update, new_update) - min_update = min(min_update, new_update) - - ϕ_next, new_update, ∇²ϕ_est, δ = propagate_poisson(ϕ_next, ε) - - if count % 250 == 1 - println(""" - Iteration $(count) - max_update = $(round(new_update, sigdigits=4)) - $(field_summary(ϕ_next, "ϕ")) - $(field_summary(∇²ϕ_est, "∇²ϕ_est")) - $(field_summary(δ, "δ")) - """) - save_plot_scalar_field!(∇²ϕ_est, "∇²ϕ_est_$(prefix)_$(count)") - save_plot_scalar_field!(δ, "delta_$(prefix)_$(count)") - save_plot_scalar_field!(ϕ_next- ϕ_b4, "change_mesh.corners.ϕ_$(prefix)_$(count)") - - ϕ_b4 = copy(ϕ_next) + ϕ_next, new_update = propagate_poisson(ϕ_next, ε) end end @@ -158,7 +102,7 @@ function solve_velocity_potential!(mesh, image, prefix) mesh.corners.c .= c_next mesh.corners.ϕ .= ϕ_next - return ε, new_update, list_new_update + return ε, new_update end @@ -198,18 +142,6 @@ function march_mesh(mesh, mesh_ϕ) new_r = mesh.corners.r - δ * vr new_c = mesh.corners.c - δ * vc - println(""" - - March mesh with correction_ratio δ = $(δ) - $(field_summary(mesh.corners.vr, "∇u")) - $(field_summary(mesh.corners.vc, "∇v")) - $(field_summary(new_r - mesh.corners.r , "new mesh changes on row")) - $(field_summary(new_c - mesh.corners.c, "new mesh changes on col")) - $(field_summary(new_r - mesh.corners.rows_numbers , "total mesh changes on row")) - $(field_summary(new_c - mesh.corners.cols_numbers, "total mesh changes on col")) - - """) - return new_r, new_c, δ end @@ -261,33 +193,14 @@ function propagate_poisson(ϕ::Matrix{Float64}, ε::Matrix{Float64}) new_ϕ[row, col] += δ[row, col] end - return new_ϕ, maximum(abs.(δ)), ∇²ϕ_est, δ - - - # # Laplacian - # # ∇²ϕ_est represent the estimate of the Laplacian of ϕ (second-order value) - # ∇²ϕ_est = laplacian(ϕ) - - - # # In the case of the velocity potential, δ is the difference between the divergence of the luminosity error - # # and the current one for the current field ϕ (divergence of its gradient). - # # High luminosity error ∇²ϕ means that the triangles are too bright = too large. - # # The Laplacian Lϕ has to converge towards the ∇²ϕ. Difference to calculate speed of the descent. - - # # Correction ratio to avoid setting the triangle to nothing - # δ = ω / 4.0 * (∇²ϕ_est - ε) - - # # In the case of the velocity potential, if δ > 0, the Laplacian is too high at that point (∇²ϕ is too low). - # ϕ[1:end-1, 1:end-1] .+= δ - - # return ∇²ϕ_est, δ, maximum(abs.(δ)) + return new_ϕ, maximum(abs.(δ)) end """ $(SIGNATURES) """ -function solve_height_potential(mesh::FaceMesh, image; f = Focal_Length) +function solve_horizontal_dispersion(mesh::FaceMesh, image; f = Focal_Length) # height indexes rows, width indexes columns height, width = size(mesh) @@ -315,11 +228,6 @@ function solve_height_potential(mesh::FaceMesh, image; f = Focal_Length) N_row = tan.(atan.(d_row ./ true_H) / (n₁ - n₂)) N_col = tan.(atan.(d_col ./ true_H) / (n₁ - n₂)) - # @. N_row[1:end, 1:end] = - # tan(atan(d_row[1:end, 1:end] / true_H[1:end, 1:end]) / (n₁ - n₂)) - # @. N_col[1:end, 1:end] = - # tan(atan(d_col[1:end, 1:end] / true_H[1:end, 1:end]) / (n₁ - n₂)) - # We need to find the divergence of the Vector field described by Nx and Ny # div_row/div_col are _FENCES_SIZED_ div_row = zeros(Float64, size(true_H)) @@ -330,19 +238,16 @@ function solve_height_potential(mesh::FaceMesh, image; f = Focal_Length) # Normalised divergence # divergence_direction is _FENCES_SIZED_ divergence_direction = div_row + div_col - # divergence_direction .-= average(divergence_direction) ϕ_next = mesh.corners.ϕ max_update = Inf - old_update = Inf for i ∈ 1:1e6 - old_update = max_update - ϕ_next, max_update, _, _ = propagate_poisson(ϕ_next, -divergence_direction) + ϕ_next, max_update = propagate_poisson(ϕ_next, -divergence_direction) - i % 1_000 == 1 && + i % 250 == 1 && println("Convergence horiz. Δ at counter = $(i) max update = $(max_update)") - if abs(old_update - max_update) / old_update < 1e-5 || abs(max_update) <= 1e-6 + if abs(max_update) <= 1e-6 println( "Convergence horiz. Δ stopped at counter = $(i) with max_update of $(max_update)", ) From 5aa5da214f76a36e35a0ab9c66e689a5ed3eb92d Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Sun, 26 Sep 2021 13:33:45 +0200 Subject: [PATCH 55/58] Rebase --- src/CausticsEngineering.jl.orig | 71 ---- src/create_mesh.jl | 59 --- src/create_mesh.jl.orig | 353 ------------------ src/math_utilities.jl.orig | 77 ---- src/scratchpad.jl.orig | 634 -------------------------------- 5 files changed, 1194 deletions(-) delete mode 100644 src/CausticsEngineering.jl.orig delete mode 100644 src/create_mesh.jl.orig delete mode 100644 src/math_utilities.jl.orig delete mode 100644 src/scratchpad.jl.orig diff --git a/src/CausticsEngineering.jl.orig b/src/CausticsEngineering.jl.orig deleted file mode 100644 index e132126..0000000 --- a/src/CausticsEngineering.jl.orig +++ /dev/null @@ -1,71 +0,0 @@ -module CausticsEngineering - -using DocStringExtensions -using Random, Images - -using Plots -gr() - -using Meshes, FileIO, MeshIO - - -include("../examples/personal/original.jl") - - -include("parameters.jl") -include("utilities.jl") -include("math_utilities.jl") -include("mesh.jl") -include("io.jl") -include("plots.jl") - -include("create_mesh.jl") - - - -""" -$(SIGNATURES) -""" -function main() - @assert size(ARGS) == (1,) "Intented usage is: julia create_mesh.jl image.png" - - img = Images.load(ARGS[1]) - return engineer_caustics(img) -end - -export - # Constants - Meters_Per_Pixel, - Bottom_Offset, - Top_Offset, - - # Types - Vertex3D, - FieldVertex3D, - FaceMesh, - - # math - average, - average_absolute, - laplacian, - ∇, - - # Mesh - create_solid, - create_solid_as_dict, - get_lens_pixels_area, - - # Plotting - plot_as_quiver, - - # I/O - save_obj!, - - # Main procedures - propagate_poisson!, - march_mesh!, - engineer_caustics, - main - - -end # End module diff --git a/src/create_mesh.jl b/src/create_mesh.jl index 6d1987b..ac1e784 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -20,40 +20,22 @@ function engineer_caustics(source_image) # imageBW is normalised to have 1 unit per pixel on average. imageBW /= average(imageBW) -<<<<<<< HEAD - marginal_change = nothing - max_update = Inf - list_max_update = [] - counter = 0 - while (abs(max_update) > 1e-6 && counter < 5) -======= marginal_change_top = marginal_change_bot = nothing max_update_top = marginal_change_top = Inf counter = 0 while (abs(max_update_top+marginal_change_bot) > 1e-6 && counter < 10_000) ->>>>>>> fd50f9e13d65a72284ebd37e06443a0c788acb68 counter += 1 print( """ -<<<<<<< HEAD - ================================================================================================================ - STARTING ITERATION $(counter): - starting ϕ field = $(field_summary(mesh.corners.ϕ)) -======= ================================================================================================================ STARTING ITERATION $(counter): starting ϕ TOP field = $(field_summary(mesh.corners.ϕ_top)) starting ϕ BOT field = $(field_summary(mesh.corners.ϕ_bot)) ->>>>>>> fd50f9e13d65a72284ebd37e06443a0c788acb68 """, ) -<<<<<<< HEAD - ε, max_update = solve_velocity_potential!(mesh, imageBW, "it$(counter)") - marginal_change = mesh.corners.ϕ - start_ϕ -======= ϕ_top = mesh.corners.ϕ_top ε_top, max_update_top = solve_velocity_potential!(mesh.corners.ϕ_top, imageBW/2., "it$(counter)_top") marginal_change_top = mesh.corners.ϕ_top - ϕ_top @@ -61,21 +43,11 @@ function engineer_caustics(source_image) ϕ_bot = mesh.corners.ϕ_bot ε_bot, max_update_bot = solve_velocity_potential!(mesh.corners.ϕ_bot, imageBW/2., "it$(counter)_bot") marginal_change_bot = mesh.corners.ϕ_bot - ϕ_bot ->>>>>>> fd50f9e13d65a72284ebd37e06443a0c788acb68 print( """ RESULT AT ITERATION $(counter): -<<<<<<< HEAD - Luminosity error = $(field_summary(ε)) - Vertical move max update = $(max_update) - Marginal change = $(field_summary(marginal_change)) - end ϕ field = $(field_summary(mesh.corners.ϕ)) - ================================================================================================================ - - """, -======= TOP Luminosity error = $(field_summary(ε_top)) Vertical move max update = $(max_update_top) @@ -92,19 +64,11 @@ function engineer_caustics(source_image) ================================================================================================================ """, ->>>>>>> fd50f9e13d65a72284ebd37e06443a0c788acb68 ) plot_as_quiver(mesh.corners.ϕ_top, n_steps = 50, scale = height / 10, max_length = height / 20) average_absolute(marginal_change_top + marginal_change_bot) < 1e-4 && break end -<<<<<<< HEAD - println("\nSTARTING HORIZONTAL DISPERSION ---") - ϕ_next, max_update = solve_horizontal_dispersion(mesh, imageBW; f = Focal_Length) - - # Move the around a nil average. - mesh.corners.ϕ .= ϕ_next .- average(ϕ_next) -======= println("\nSTARTING HORIZONTAL ITERATION ---") println("\t Horizontal max update TOP = $(max_update_top) / BOT = $(max_update_bot)") @@ -112,7 +76,6 @@ function engineer_caustics(source_image) # Move the around a nil average. mesh.corners.ϕ_top .-= average(mesh.corners.ϕ_top) mesh.corners.ϕ_bot .-= average(mesh.corners.ϕ_bot) ->>>>>>> fd50f9e13d65a72284ebd37e06443a0c788acb68 return mesh, imageBW end @@ -132,12 +95,8 @@ function solve_velocity_potential!(mesh, image, prefix) # Illumination only depends on the position of the corners, not their heights. ϕ is not relevant. # Get the area of each individual pixel as stretch/shrunk on the lens. Area = energy. # _FENCES_SIZED_ -<<<<<<< HEAD - lens_pixels_area = get_lens_pixels_area(mesh) -======= # Illumination only depends on the position of the corners, not their heights. ϕ is not relevant. lens_pixels_area_top, lens_pixels_area_bot = get_lens_pixels_area(mesh) ->>>>>>> fd50f9e13d65a72284ebd37e06443a0c788acb68 # Positive error => the triangle needs to shrink (less light). Enforce nil average error. ε_top = zeros(Float64, height, width) @@ -150,15 +109,6 @@ function solve_velocity_potential!(mesh, image, prefix) ε_bot[1:end-1, 1:end-1] = Float64.(lens_pixels_area_bot - image/2.) ε_bot .-= average(ε_bot) -<<<<<<< HEAD - # Start with a clean, flat potential field. - ϕ_next = zeros(Float64, height + 1, width + 1) - count = 0 - while 1e-5 < new_update && count < 3_000 - count += 1 - - ϕ_next, new_update = propagate_poisson(ϕ_next, ε) -======= println(""" solve_velocity_potential! before loop: $(field_summary(lens_pixels_area_top, "Pixel area")) @@ -261,21 +211,12 @@ function solve_velocity_potential!(mesh, image, prefix) ϕ_b4_top = copy(mesh.corners.ϕ_top) ϕ_b4_bot = copy(mesh.corners.ϕ_bot) ->>>>>>> fd50f9e13d65a72284ebd37e06443a0c788acb68 end end # Now we need to march the mesh row,col corner locations according to this gradient. -<<<<<<< HEAD - r_next, c_next, δ = march_mesh(mesh, ϕ_next) - mesh.corners.r .= r_next - mesh.corners.c .= c_next - mesh.corners.ϕ .= ϕ_next - -======= δ_top = march_mesh!(mesh, :top) δ_bot = march_mesh!(mesh, :bottom) ->>>>>>> fd50f9e13d65a72284ebd37e06443a0c788acb68 return ε, new_update end diff --git a/src/create_mesh.jl.orig b/src/create_mesh.jl.orig deleted file mode 100644 index 30a84bd..0000000 --- a/src/create_mesh.jl.orig +++ /dev/null @@ -1,353 +0,0 @@ - -""" -$(SIGNATURES) - -""" -function engineer_caustics(source_image) - imageBW = Float64.(Gray.(source_image)) - - - # Set global size parameters - height, width = size(imageBW) - global N_Pixel_Height = height - global N_Pixel_Width = width - global Meters_Per_Pixel = Caustics_Long_Side / N_Pixel_Height - println("Image size: $(N_Pixel_Height) x $(N_Pixel_Width)") - - # mesh is the same size as the image with an extra row/column to have coordinates to - # cover each image corner with a triangle. - mesh = FaceMesh(N_Pixel_Height, N_Pixel_Width) - - # imageBW is normalised to have 1 unit per pixel on average. - imageBW /= average(imageBW) - - marginal_change = nothing - max_update = Inf - list_max_update = [] - counter = 0 - while (abs(max_update) > 1e-6 && counter < 4) - counter += 1 - - print( - """ - ================================================================================================================ - STARTING ITERATION $(counter): - starting ϕ field = $(field_summary(mesh.corners.ϕ)) - - """, - ) - - start_r = deepcopy(mesh.corners.r) - start_c = deepcopy(mesh.corners.c) - start_ϕ = deepcopy(mesh.corners.ϕ) - - ε, max_update = solve_velocity_potential!(mesh, imageBW, "it$(counter)") - marginal_change = mesh.corners.ϕ - start_ϕ - - print( - """ - - RESULT AT ITERATION $(counter): - Luminosity error = $(field_summary(ε)) - Vertical move max update = $(max_update) - Marginal change = $(field_summary(marginal_change)) - - $(field_summary(mesh.corners.vr, "∇u")) - $(field_summary(mesh.corners.vc, "∇v")) - $(field_summary(mesh.corners.r - start_r, "new mesh changes on row")) - $(field_summary(mesh.corners.c - start_c, "new mesh changes on col")) - $(field_summary(mesh.corners.ϕ - start_ϕ, "new mesh changes on ϕ")) - $(field_summary(mesh.corners.r - mesh.corners.rows_numbers, "total mesh changes on row")) - $(field_summary(mesh.corners.c - mesh.corners.cols_numbers, "total mesh changes on col")) - - end ϕ field = $(field_summary(mesh.corners.ϕ)) - ================================================================================================================ - - """, - ) - plot_as_quiver(mesh, n_steps = 50, scale = height / 10, max_length = height / 20) - average_absolute(marginal_change) < 1e-3 && break - end - - println("\nSTARTING HORIZONTAL ITERATION ---") - - max_update = solve_height_potential(mesh, imageBW; f = Focal_Length) - println("\t Horizontal max update = $(max_update)") - - # Move the around a nil average. - mesh.corners.ϕ .-= average(mesh.corners.ϕ) - - return mesh, imageBW, list_max_update -end - - - -""" -$(SIGNATURES) - -ϕ is the _velocity potential_. The velocity represents the direction towards which the mesh vertices should move. -Zones of high luminosity should be covered with more triangles and should attract more vertices. -""" -function solve_velocity_potential!(mesh, image, prefix) - # Start with a new clean field - height, width = size(mesh) - - # Get the area of each individual pixel as stretch/shrunk on the lens. Area = energy. - # _FENCES_SIZED_ - # Illumination only depends on the position of the corners, not their heights. ϕ is not relevant. - lens_pixels_area = get_lens_pixels_area(mesh) - - # Positive error => the triangle needs to shrink (less light). Enforce nil average error. - ε = zeros(Float64, height + 1, width + 1) - ε[1:end-1, 1:end-1] = Float64.(lens_pixels_area - image) - ε .-= average(ε) - - println(""" - solve_velocity_potential! before loop: - $(field_summary(lens_pixels_area, "Pixel area")) - $(field_summary(ε, "luminosity error")) - """) - - # Save the loss image as a png. - save_plot_scalar_field!(ε, "error_$(prefix)") - - # Save the generated image as a png. - luminosity_ratio = sum(image) / sum(lens_pixels_area) - save( - "./examples/img_$(prefix).png", - Gray.(clamp.(lens_pixels_area * luminosity_ratio, 0.0, 1.0)), - ) - - # Start with a clean, flat potential field. - mesh.corners.ϕ = zeros(Float64, height + 1, width + 1) - ϕ_b4 = copy(mesh.corners.ϕ) - count = 0 - min_update = new_update = 10_000 - list_new_update = [] - old_update = 2 * new_update - while ( - 1e-6 < new_update < 1.5 * min_update && - 1e-5 < (old_update - new_update) / old_update && - count < 10_000 - ) - count += 1 - old_update = new_update - push!(list_new_update, new_update) - min_update = min(min_update, new_update) - - new_update, ∇²ϕ_est, δ = propagate_poisson!(mesh.corners.ϕ, ε) - - count % 1_000 == 1 && println(""" - Iteration $(count) - max_update = $(round(new_update, sigdigits=4)) - $(field_summary(mesh.corners.ϕ, "ϕ")) - $(field_summary(∇²ϕ_est, "∇²ϕ_est")) - $(field_summary(δ, "δ")) - """) - - # Save the loss image as a png. - if count % 1_000 == 1 - save_plot_scalar_field!(∇²ϕ_est, "∇²ϕ_est_$(prefix)") - save_plot_scalar_field!(δ, "delta_$(prefix)") - save_plot_scalar_field!(mesh.corners.ϕ - ϕ_b4, "change_mesh.corners.ϕ_$(prefix)") - - ϕ_b4 = copy(mesh.corners.ϕ) - end - end - - # Now we need to march the mesh row,col corner locations according to this gradient. - δ = march_mesh!(mesh) - return ε, new_update, list_new_update -end - - - -""" -$(SIGNATURES) - -ϕ is the height map. - -`march_mesh!` flexes the mesh -""" -function march_mesh!(mesh::FaceMesh) - - # Calculate the gradient of the velocity potential and reverse its direction. - ∇ϕᵤ, ∇ϕᵥ = ∇(mesh.corners.ϕ) - mesh.corners.vr = -∇ϕᵤ - mesh.corners.vc = -∇ϕᵥ - - - # Clean up the mesh borders - reset_border_values!(mesh.corners) - - # For each point in the mesh we need to figure out its velocity - # However all the nodes located at a border will never move - # I.e. velocity (Vx, Vy) = (0, 0) and the square of acrylate will remain of the same size. - mesh_r = copy(mesh.corners.r) - mesh_c = copy(mesh.corners.c) - - # Get the time, at that velocity, for the area of the triangle to be nil. - # We are only interested by positive values to only move in the direction of the (opposite) gradient - height, width = size(mesh) - list_triangles = vcat( - [triangle3D(mesh, row, col, :top) for row ∈ 1:height, col ∈ 1:width], - [triangle3D(mesh, row, col, :bottom) for row ∈ 1:height, col ∈ 1:width], - ) - - list_maximum_t = [t for t ∈ find_maximum_t.(list_triangles) if !isnothing(t) && t > 0.0] - - δ = minimum(list_maximum_t) / 2.0 - mesh.corners.r .-= δ * mesh.corners.vr - mesh.corners.c .-= δ * mesh.corners.vc - - println(""" - - March mesh with correction_ratio δ = $(δ) - $(field_summary(mesh.corners.vr, "∇u")) - $(field_summary(mesh.corners.vc, "∇v")) - $(field_summary(mesh_r - mesh.corners.r , "new mesh changes on row")) - $(field_summary(mesh_c - mesh.corners.c, "new mesh changes on col")) - $(field_summary(mesh_r - mesh.corners.rows_numbers , "total mesh changes on row")) - $(field_summary(mesh_c - mesh.corners.cols_numbers, "total mesh changes on col")) - - """) - - return δ -end - - - -""" -$(SIGNATURES) - -This function implements successive over relaxation for a matrix and its associated error matrix -There is a hardcoded assumption of Neumann boundary conditions -- that the derivative across the -boundary must be zero in all cases. See: -https://math.stackexchange.com/questions/3790299/how-to-iteratively-solve-poissons-equation-with-no-boundary-conditions - -- ϕ is the potential to be solved subject to the Poisson equation and is the same size as the corners (_POSTS_SIZED_) -- target is ∇ϕ and is of the size in pixels (_FENCES_SIZED_) - -In order of how to think about the flow of the program for the velocity potential, - - if δ > 0, the Laplacian is too high at that point (∇²ϕ is too low). - - To decrease the Laplacian ∇²ϕ, note that ∇² is a divergence (of a gradient) that represents net flow going outside. - - - Decrease the Laplacian - - => decrease a divergence - - => decrease flow towards outside - - - The flow is a gradient of the potential ϕ. - - => decrease flow towards outside - - => either decrease the values of the potential around that point, or increase the value of the potential at that point. - - => Increase the value of ϕ at that point means a positive change when δ > 0. - - δ > 0 => correction of the SAME sign. -""" -function propagate_poisson!(ϕ::Matrix{Float64}, ε::Matrix{Float64}) - - height, width = size(ϕ) - - ∇²ϕ_est = zeros(Float64, height, width) - δ = zeros(Float64, height, width) - - ω = 1.99 - - for row = 1:height, col = 1:width - val_up = row == 1 ? 0.0 : ϕ[row-1, col] - val_down = row == height ? 0.0 : ϕ[row+1, col] - val_left = col == 1 ? 0.0 : ϕ[row, col-1] - val_right = col == width ? 0.0 : ϕ[row, col+1] - - ∇²ϕ_est[row, col] = val_up + val_down + val_left + val_right - 4 * ϕ[row, col] - δ[row, col] = ω / 4.0 * (∇²ϕ_est[row, col] - ε[row, col]) - ϕ[row, col] += δ[row, col] - end - - return maximum(abs.(δ)), ∇²ϕ_est, δ - - - # # Laplacian - # # ∇²ϕ_est represent the estimate of the Laplacian of ϕ (second-order value) - # ∇²ϕ_est = laplacian(ϕ) - - - # # In the case of the velocity potential, δ is the difference between the divergence of the luminosity error - # # and the current one for the current field ϕ (divergence of its gradient). - # # High luminosity error ∇²ϕ means that the triangles are too bright = too large. - # # The Laplacian Lϕ has to converge towards the ∇²ϕ. Difference to calculate speed of the descent. - - # # Correction ratio to avoid setting the triangle to nothing - # δ = ω / 4.0 * (∇²ϕ_est - ε) - - # # In the case of the velocity potential, if δ > 0, the Laplacian is too high at that point (∇²ϕ is too low). - # ϕ[1:end-1, 1:end-1] .+= δ - - # return ∇²ϕ_est, δ, maximum(abs.(δ)) -end - - -""" -$(SIGNATURES) -""" -function solve_height_potential(mesh::FaceMesh, image; f = Focal_Length) - # height indexes rows, width indexes columns - height, width = size(mesh) - - # Coordinates on the caustics = simple rectangular values in corners. - # Coordinates on the lens face comes from corner field. - # d_row/d_col are _POSTS-SIZED_ - d_row = mesh.corners.rows_numbers - mesh.corners.r - d_col = mesh.corners.cols_numbers - mesh.corners.c - - # The focal length is in meters. H is in corners. - H = f / Meters_Per_Pixel - - # true_H is the real distance beteen the surface of the lens and the projection - # H is the initial distance from the surface of the carved face to the projection screen. - # H is constant and does not account for the change in heights due to carving. - # Note: Higher location means closer to the caustics => negative sign - # true_H is _POSTS_SIZED_ - true_H = zeros(Float64, height + 1, width + 1) - true_H = -mesh.corners.ϕ .+ H - - # Normals. - # N_row/N_col are _POSTS_SIZED_ - N_row = zeros(Float64, size(true_H)) - N_col = zeros(Float64, size(true_H)) - N_row = tan.(atan.(d_row ./ true_H) / (n₁ - n₂)) - N_col = tan.(atan.(d_col ./ true_H) / (n₁ - n₂)) - - # @. N_row[1:end, 1:end] = - # tan(atan(d_row[1:end, 1:end] / true_H[1:end, 1:end]) / (n₁ - n₂)) - # @. N_col[1:end, 1:end] = - # tan(atan(d_col[1:end, 1:end] / true_H[1:end, 1:end]) / (n₁ - n₂)) - - # We need to find the divergence of the Vector field described by Nx and Ny - # div_row/div_col are _FENCES_SIZED_ - div_row = zeros(Float64, size(true_H)) - div_col = zeros(Float64, size(true_H)) - div_row[1:end-1, 1:end-1] = N_row[2:end, 1:end-1] .- N_row[1:end-1, 1:end-1] - div_col[1:end-1, 1:end-1] = N_col[1:end-1, 2:end] .- N_col[1:end-1, 1:end-1] - - # Normalised divergence - # divergence_direction is _FENCES_SIZED_ - divergence_direction = div_row + div_col - # divergence_direction .-= average(divergence_direction) - - max_update = Inf - old_update = Inf - for i ∈ 1:1e6 - old_update = max_update - max_update, _, _ = propagate_poisson!(mesh.corners.ϕ, -divergence_direction) - - i % 1_000 == 1 && - println("Convergence horiz. Δ at counter = $(i) max update = $(max_update)") - - if abs(old_update - max_update) / old_update < 1e-5 || abs(max_update) <= 1e-6 - println( - "Convergence horiz. Δ stopped at counter = $(i) with max_update of $(max_update)", - ) - break - end - end - - return max_update -end diff --git a/src/math_utilities.jl.orig b/src/math_utilities.jl.orig deleted file mode 100644 index 148548a..0000000 --- a/src/math_utilities.jl.orig +++ /dev/null @@ -1,77 +0,0 @@ - -""" -$(SIGNATURES) -""" -average(m::AbstractMatrix) = (sum(m) / length(m)) - - -""" -$(SIGNATURES) -""" -average_absolute(m::AbstractMatrix) = (sum(abs.(m)) / length(m)) - - -""" -$(SIGNATURES) -""" -test_average_absolute(m::AbstractMatrix) = (average_absolute(m)) < 1e6 - - -""" -$(SIGNATURES) -""" -function smallest_positive(x1::Float64, x2::Float64) - (x1 > 0.0 && x2 < 0.0) && return x1 - (x1 < 0.0 && x2 > 0.0) && return x2 - (x1 > 0.0 && x2 > 0.0) && return min(x1, x2) - return nothing -end - - -""" -$(SIGNATURES) - -Approximates the gradient of a scalar field. -""" -function ∇(ϕ::AbstractMatrix{Float64}) - height, width = size(ϕ) - - # x, y only represents the first and the second variables. No reference to graphical representations. - ∇ϕx = zeros(Float64, height, width) # divergence on the right edge will be filled with zeros - ∇ϕy = zeros(Float64, height, width) # divergence on bottom edge will be filled with zeros - - ∇ϕx[begin:end-1, :] = ϕ[begin+1:end, :] - ϕ[begin:end-1, :] - ∇ϕy[:, begin:end-1] = ϕ[:, begin+1:end] - ϕ[:, begin:end-1] - - fill_borders!(∇ϕx, 0.0) - fill_borders!(∇ϕy, 0.0) - - return ∇ϕx, ∇ϕy -end - - -""" -$(SIGNATURES) - -Calculate the second-order Laplace operator by convolution of a kernel. -""" -function laplacian(ϕ::AbstractMatrix{Float64}) - height, width = size(ϕ) - - # Embed matrix within a larger matrix for better vectorization and avoid duplicated code - # Padded matrix adds 1 row/col after the size of ϕ. - # ϕ is inserted in padded matrix within 1:1+height+1 x 1:1+width+1. - # The rest of the padded matrix (its borders) are set at 0.0. - padded_ϕ = zeros(Float64, 1 + height + 1, 1 + width + 1) - padded_ϕ[begin+1:end-1, begin+1:end-1] .= ϕ[1:end, 1:end] - - # Convolution = up + down + left + right - ∇²ϕ = - padded_ϕ[begin+1-1:end-1-1, begin+1:end-1] + - padded_ϕ[begin+1+1:end-1+1, begin+1:end-1] + - padded_ϕ[begin+1:end-1, begin+1-1:end-1-1] + - padded_ϕ[begin+1:end-1, begin+1+1:end-1+1] - - 4.0 * padded_ϕ[begin+1:end-1, begin+1:end-1] - - return ∇²ϕ[1:end-1, 1:end-1] -end diff --git a/src/scratchpad.jl.orig b/src/scratchpad.jl.orig deleted file mode 100644 index 9bab967..0000000 --- a/src/scratchpad.jl.orig +++ /dev/null @@ -1,634 +0,0 @@ -using Revise, Debugger -using Images, Plots -gr() - -using CausticsEngineering - -image = Images.load("./examples/personal/slashdot.jpg"); # Check current working directory with pwd() - -image = Images.load("./examples/cat_posing.jpg"); # Check current working directory with pwd() -image = Images.load("./examples/personal/goose.jpg"); # Check current working directory with pwd() - -image = Images.load("./examples/personal/salvador_dali_1.jpg"); # Check current working directory with pwd() -image = Images.load("./examples/personal/salvador_dali_2.jpg"); # Check current working directory with pwd() - -image = Images.load("./examples/personal/statue_of_liberty_1.jpg"); # Check current working directory with pwd() -image = Images.load("./examples/personal/statue_of_liberty_2.jpg"); # Check current working directory with pwd() -image = Images.load("./examples/personal/statue_of_liberty_3.jpg"); # Check current working directory with pwd() - -image = Images.load("./examples/personal/caricature.jpg"); # Check current working directory with pwd() -image = Images.load("./examples/personal/portrait.jpg"); # Check current working directory with pwd() -image = Images.load("./examples/personal/bilal.jpg"); # Check current working directory with pwd() - -mesh, imageBW, list_max_updates = engineer_caustics(image); - -length(list_max_updates) -p = plot((log.(clamp01nan.(list_max_updates)))) -p -save("ppp.png", map(clamp01nan, p)) - -imageBW = Float64.(Gray.(image)); -Gray.(imageBW) -sum(imageBW) -sum(imageBW) / length(imageBW) - -CausticsEngineering.average(imageBW) - - -new_img = CausticsEngineering.get_lens_pixels_area(mesh); -luminosity_ratio = sum(imageBW) / sum(new_img) -Gray.(new_img * luminosity_ratio) - - -ε = Float64.(lens_pixels_area - image) -ε .-= average(ε) - -# Save the loss image as a png -save_plot_scalar_field!(ε, "loss_" * prefix) - - - -mesh, imageBW = CausticsEngineering.original_engineer_caustics(image); -imageBW = Float64.(Gray.(image)) -Gray.(imageBW) - -new_img = CausticsEngineering.get_lens_pixels_area(mesh) -luminosity_ratio = sum(imageBW) / sum(new_img) -Gray.(new_img * luminosity_ratio) - - - - -imageBW = Float64.(Gray.(image)); -average_energy_caustics = CausticsEngineering.average(imageBW) -imageBW = imageBW / average_energy_caustics; - -(sum(imageBW) / length(imageBW) - 1.0) * 1e12 - - -# Check a few values to make sure they make sense -mesh.corners.r -mesh.corners.vr -minimum(mesh.corners.vr) -maximum(mesh.corners.vr) - -mesh.corners.c -mesh.corners.vc -minimum(mesh.corners.vc) -maximum(mesh.corners.vc) - -mesh.corners.ϕ -minimum(mesh.corners.ϕ) -maximum(mesh.corners.ϕ) -mean_ϕ = sum(mesh.corners.ϕ) / length(mesh.corners.ϕ) - -# Plot the last vector field -p = plot_as_quiver(mesh, n_steps = 60, scale = 5.0, max_length = 20) - - - -# Generate dictionaries and arrays containing the vertices and triangles. -triangle_dict, vertex_dict, triangle_index, vertex_index = - create_solid(mesh; bottom_distance = Bottom_Offset, top_distance = Top_Offset) - - -# Can be done in 2 steps -# -# triangle_dict, vertex_dict = create_solid_as_dict( -# mesh; -# bottom_distance = Bottom_Offset, -# top_distance = Top_Offset -# ) -# -# # Generate array or coordinates and indices usable to create traditional mesh objects -# _, _, triangle_index, vertex_index = create_solid( -# triangle_dict, -# vertex_dict; -# bottom_distance = Bottom_Offset, -# top_distance = Top_Offset, -# ) - -# Area of all the distorted pixels -am = CausticsEngineering.get_area_corners(mesh) -maximum(am) -minimum(am) - -# Save as an obj file -save_obj!( - triangle_index, - vertex_index, - "./examples/result_cat_mesh.obj", - scale = Float64(Meters_Per_Pixel), - scaleh = Float64(Meters_Per_Pixel), -) - - -# Convert to a mesh structure -using Meshes - -# Zone to plot -row_min = 100.0 -row_max = 200.0 -col_min = 100.0 -col_max = 200.0 - -function clip_trangle_index( - triangle_index, - vertex_index; - row_min = 100.0, - row_max = 200.0, - col_min = 100.0, - col_max = 200.0, -) - - function is_in_zone(t)::Bool - p1, p2, p3 = t - v1_r, v1_c = vertex_index[p1] - v2_r, v2_c = vertex_index[p2] - v3_r, v3_c = vertex_index[p3] - - return row_min <= v1_r <= row_max && - col_min <= v1_c <= col_max && - row_min <= v2_r <= row_max && - col_min <= v2_c <= col_max && - row_min <= v3_r <= row_max && - col_min <= v3_c <= col_max - end - - return [t for t ∈ triangle_index if is_in_zone(t)] -end - -# Select relevant triangles -triangle_index3D = clip_trangle_index(triangle_index, vertex_index) -connections = Meshes.connect.(triangle_index3D) - -# 3D Mesh -vertices3D = Meshes.Point3.(vertex_index) -cat_mesh3D = Meshes.SimpleMesh(vertices3D, connections) - -# 2D Mesh -vertex_index2D = [(v[1], v[2]) for v ∈ vertex_index] -vertices2D = Meshes.Point2.(vertex_index2D) -cat_mesh2D = Meshes.SimpleMesh(vertices2D, connections) - - -# NOT WORKING... -using MeshViz - -# Explicitly import the preferred backend (depending on use case) -import GLMakie -MeshViz.viz(cat_mesh3D) -MeshViz.viz(cat_mesh2D) - - - - - - - - - -imageBW = Float64.(Gray.(image)) - -# Set global size parameters -height, width = size(imageBW) -global N_Pixel_Height = height -global N_Pixel_Width = width -global Meters_Per_Pixel = Caustics_Long_Side / N_Pixel_Height -println("Image size: $(N_Pixel_Height) x $(N_Pixel_Width)") - -# mesh is the same size as the image with an extra row/column to have coordinates to -# cover each image corner with a triangle. -mesh = FaceMesh(N_Pixel_Height, N_Pixel_Width) - -# The total energy going through the lens is equal to the amount of energy on the caustics -total_energy_lens = N_Pixel_Height * N_Pixel_Width * 1.0 # 1 unit of energy per pixel -total_energy_caustics = sum(imageBW) -average_energy_per_pixel = average(imageBW) - -# imageBW is normalised to the same (sort of) _energy_ as the original image. -imageBW = imageBW / average_energy_per_pixel - -lens_pixels_area = get_lens_pixels_area(mesh) - -# Positive error => the triangle needs to shrink (less light) -error_luminosity = Float64.(lens_pixels_area - imageBW) -error_luminosity = error_luminosity .- average(error_luminosity) - -# Save the loss image as a png -println( - """ -Luminosity: - Max/min pixel areas: $(maximum(lens_pixels_area)) / $(minimum(lens_pixels_area)) - Average pixel areas: $(average_absolute(lens_pixels_area)) - Average pixel areas: $(average(lens_pixels_area)) - - Max/min luminosity error: $(maximum(error_luminosity)) / $(minimum(error_luminosity)) - Average abs error: $(average_absolute(error_luminosity)) - Average error: $(average(error_luminosity)) - """, -) - - - -#################################################################################################################### -## STEPPING - -using Revise, Debugger, Images, Plots; -gr() - -using CausticsEngineering - - -######################## Load image -image = Images.load("./examples/personal/slashdot.jpg"); # Check current working directory with pwd() -imageBW = Float64.(Gray.(image)); -imageBW /= average(imageBW); -sum(imageBW) - -h, w = size(imageBW) - - -######################## Create mesh -mesh = CausticsEngineering.FaceMesh(h, w); -CausticsEngineering.field_summary(mesh.corners.ϕ) - -origmesh = CausticsEngineering.OriginalMesh(w + 1, h + 1); -origϕ = zeros(w, h); -CausticsEngineering.field_summary(origϕ) - - -######################## Lens luminosity -area_distorted_corners = CausticsEngineering.get_lens_pixels_area(mesh); -CausticsEngineering.field_summary(area_distorted_corners) - -origarea_distorted_corners = CausticsEngineering.getPixelArea(origmesh); -CausticsEngineering.field_summary(origarea_distorted_corners) - -CausticsEngineering.field_summary(area_distorted_corners - origarea_distorted_corners') - - -######################## Laplacian -Lϕ = CausticsEngineering.laplacian(mesh.corners.ϕ); -CausticsEngineering.field_summary(Lϕ) - -function orig_laplacian(ϕ) - width, height = size(ϕ) - Lϕ = zeros(Float64, size(ϕ)) - - for x = 1:width, y = 1:height - val_up = (y == 1) ? 0.0 : ϕ[x, y-1] - val_down = (y == height) ? 0.0 : ϕ[x, y+1] - val_left = (x == 1) ? 0.0 : ϕ[max(1, x - 1), y] - val_right = (x == width) ? 0.0 : ϕ[x+1, y] - - Lϕ[x, y] = val_up + val_down + val_left + val_right - 4 * ϕ[x, y] - - # if Lϕ[x, y] != 0.0 - # println(val_up, val_down, val_left, val_right, ϕ[x, y], x, y) - # break - # end - end - return Lϕ -end - -origLϕ = orig_laplacian(origϕ); -CausticsEngineering.field_summary(origLϕ) - - -######################## Error luminosity -error_luminosity = zeros(Float64, h + 1, w + 1); -error_luminosity[1:end-1, 1:end-1] = Float64.(area_distorted_corners - imageBW); -CausticsEngineering.field_summary(error_luminosity) - -origerror_luminosity = zeros(Float64, w + 1, h + 1); -origerror_luminosity[1:end-1, 1:end-1] = Float64.(origarea_distorted_corners - imageBW'); -CausticsEngineering.field_summary(origerror_luminosity) - -CausticsEngineering.field_summary(error_luminosity - origerror_luminosity') - - -######################## Normalised error luminosity -error_luminosity = error_luminosity .- average(error_luminosity); -CausticsEngineering.field_summary(error_luminosity) - -origerror_luminosity = origerror_luminosity .- average(origerror_luminosity); -CausticsEngineering.field_summary(origerror_luminosity) - -CausticsEngineering.field_summary(error_luminosity - origerror_luminosity') - - -######################## Propagation -max_update, Lϕ, δ = CausticsEngineering.propagate_poisson!(mesh.corners.ϕ, error_luminosity); -CausticsEngineering.field_summary(mesh.corners.ϕ) -CausticsEngineering.field_summary(Lϕ) -CausticsEngineering.field_summary(δ) - -max_update, origLϕ, origδ = - CausticsEngineering.orig_propagate_poisson!(origϕ, origerror_luminosity); -CausticsEngineering.field_summary(origϕ) -CausticsEngineering.field_summary(origLϕ) -CausticsEngineering.field_summary(origδ) - - -######################## March mesh -dfx, dfy = ∇(mesh.corners.ϕ) -CausticsEngineering.field_summary(dfx) -CausticsEngineering.field_summary(dfy) -mesh.corners.vr = -dfx -mesh.corners.vc = -dfy -CausticsEngineering.field_summary(mesh.corners.vr) -CausticsEngineering.field_summary(mesh.corners.vc) - -dfx2, dfy2 = CausticsEngineering.orig_∇(origϕ) -CausticsEngineering.field_summary(dfx2) -CausticsEngineering.field_summary(dfy2) - - -# Min t -list_triangles = vcat( - [CausticsEngineering.triangle3D(mesh, row, col, :top) for row ∈ 1:h, col ∈ 1:w], - [CausticsEngineering.triangle3D(mesh, row, col, :bottom) for row ∈ 1:h, col ∈ 1:w], -) - -list_maximum_t = [t for t ∈ CausticsEngineering.find_maximum_t.(list_triangles) if !isnothing(t) && t > 0.0] -δ = minimum(list_maximum_t) - -mesh_r = copy(mesh.corners.r) -mesh_c = copy(mesh.corners.c) -δ = minimum(list_maximum_t) / 2.0 -mesh.corners.r .-= δ * mesh.corners.vr -mesh.corners.c .-= δ * mesh.corners.vc - -println( - """ - -March mesh with correction_ratio δ = $(δ) - $(CausticsEngineering.field_summary(mesh.corners.vr, "∇u")) - $(CausticsEngineering.field_summary(mesh.corners.vc, "∇v")) - $(CausticsEngineering.field_summary(mesh_r - mesh.corners.r , "new mesh changes on row")) - $(CausticsEngineering.field_summary(mesh_c - mesh.corners.c, "new mesh changes on col")) - $(CausticsEngineering.field_summary(mesh_r - mesh.corners.rows_numbers , "total mesh changes on row")) - $(CausticsEngineering.field_summary(mesh_c - mesh.corners.cols_numbers, "total mesh changes on col")) - - """, -) - - -velocities = Matrix{CausticsEngineering.Point3D}(undef, w+1, h+1) -fill!(velocities, CausticsEngineering.Point3D(0.0, 0.0, 0.0, 0.0, 0.0)) - -for x ∈ 1:w-1, y ∈ 1:h-1 - velocities[x, y] = CausticsEngineering.Point3D(-dfx2[x, y], -dfy2[x, y], 0.0, 0.0, 0.0) -end - -min_t = 10000 -triangleCount = 1 -p1 = CausticsEngineering.Point3D(0., 0., 0., 0., 0.) -p2 = CausticsEngineering.Point3D(0., 0., 0., 0., 0.) -p3 = CausticsEngineering.Point3D(0., 0., 0., 0., 0.) -v1 = CausticsEngineering.Point3D(0., 0., 0., 0., 0.) -v2 = CausticsEngineering.Point3D(0., 0., 0., 0., 0.) -v3 = CausticsEngineering.Point3D(0., 0., 0., 0., 0.) -for triangle in origmesh.triangles - p1 = origmesh.nodes[triangle.pt1] - p2 = origmesh.nodes[triangle.pt2] - p3 = origmesh.nodes[triangle.pt3] - - v1 = velocities[p1.ix, p1.iy] - v2 = velocities[p2.ix, p2.iy] - v3 = velocities[p3.ix, p3.iy] - - t = CausticsEngineering.findT(p1, p2, p3, v1, v2, v3) - - if !isnothing(t) - min_t = min(min_t, t) - end - - triangleCount += 1 -end - -p1 -p2 -p3 -v1 -v2 -v3 - -min_t - -size(origmesh.nodes) -avgmx = 0. -avgmy = 0. -avgax = 0. -avgay = 0. -for point in origmesh.nodes - v = velocities[point.ix, point.iy] - px = point.x - py = point.y - point.x = v.x * min_t/2 + point.x - point.y = v.y * min_t/2 + point.y - - avgmx += point.x - px - avgmy += point.y - py - avgax += abs(point.x - px) - avgay += abs(point.y - py) -end - -avgmx/length(origmesh.nodes) -avgmy/length(origmesh.nodes) -avgax/length(origmesh.nodes) -avgay/length(origmesh.nodes) - - - - - - - -δ = Lϕ - error_luminosity; -CausticsEngineering.field_summary(δ) - -δ .*= 0.50; -ϕ = mesh.corners.ϕ[1:end-1, 1:end-1]; -ϕ .+= δ; -mesh.corners.ϕ[1:end-1, 1:end-1] .= ϕ .- average(ϕ); -CausticsEngineering.field_summary(mesh.corners.ϕ) - - - - -mesh = CausticsEngineering.FaceMesh(height, width); -CausticsEngineering.field_summary( - CausticsEngineering.laplacian(mesh.corners.ϕ) - error_luminosity, -) - - - -origϕ = zeros(w, h); - - - - - - - -mesh = CausticsEngineering.FaceMesh(height, width); -new_update = 10_000 -old_update = 2 * new_update -for i ∈ 1:1_000 - old_update = new_update - new_update, Lϕ, δ = - CausticsEngineering.propagate_poisson!(mesh.corners.ϕ, error_luminosity) - i % 50 == 0 && println(""" - $(i) => $(max_update) - $(CausticsEngineering.field_summary(mesh.corners.ϕ)) - $(CausticsEngineering.field_summary(Lϕ)) - $(CausticsEngineering.field_summary(δ)) - """) - if new_update > old_update || i == 5_000 - new_update, Lϕ, δ = - CausticsEngineering.orig_propagate_poisson!(origϕ, origerror_luminosity) - println(""" - $(i) => $(new_update) - $(CausticsEngineering.field_summary(mesh.corners.ϕ)) - $(CausticsEngineering.field_summary(Lϕ)) - $(CausticsEngineering.field_summary(δ)) - """) - break - end -end - -origϕ = zeros(width, height); -for i ∈ 1:5_000 - max_update, origLϕ, origδ = - CausticsEngineering.orig_propagate_poisson!(origϕ, origerror_luminosity) - i % 500 == 0 && println(""" - $(i) => $(max_update) - $(CausticsEngineering.field_summary(origϕ)) - $(CausticsEngineering.field_summary(origLϕ)) - $(CausticsEngineering.field_summary(origδ)) - """) - if max_update <= 1e-3 - max_update, origLϕ, origδ = - CausticsEngineering.orig_propagate_poisson!(origϕ, origerror_luminosity) - println(CausticsEngineering.field_summary(origϕ)) - println(CausticsEngineering.field_summary(origLϕ)) - println(CausticsEngineering.field_summary(origδ)) - break - end -end - - - - - - - - - - -CausticsEngineering.save_plot_scalar_field!(error_luminosity, "trace_1", imageBW) - -max_update = Inf -old_update = Inf - -any(isnan.(error_luminosity)) - -any(isnan.(mesh.corners.r)) -any(isnan.(mesh.corners.c)) -any(isnan.(mesh.corners.vr)) -any(isnan.(mesh.corners.vc)) - -any(isnan.(mesh.corners.ϕ)) - -i = 0 -begin - i += 1 - old_update = max_update - max_update = CausticsEngineering.propagate_poisson!(mesh.corners.ϕ, error_luminosity) - # i % 100 == 0 && println(max_update) - # (abs(old_update - max_update) <= 1e-6 || abs(max_update) <= 1e-4) && break -end - -max_update -old_update - - -f() - - -∇ϕᵤ, ∇ϕᵥ = CausticsEngineering.∇(mesh.corners.ϕ) - -sum(∇ϕᵤ) -average(∇ϕᵤ) -average_absolute(∇ϕᵤ) - - -height, width = size(imageBW) -mesh.corners.vr .= -∇ϕᵤ -mesh.corners.vc .= -∇ϕᵥ -list_triangles = vcat( - [ - CausticsEngineering.triangle3D(mesh, row, col, :top) for row ∈ 1:height, - col ∈ 1:width - ], - [ - CausticsEngineering.triangle3D(mesh, row, col, :bottom) for row ∈ 1:height, - col ∈ 1:width - ], -) - -list_maximum_t = [ - time for time ∈ CausticsEngineering.find_maximum_t.(list_triangles) if - !isnothing(time) && time > 0.0 -] -minimum(list_maximum_t) -maximum(list_maximum_t) - -δ = minimum(list_maximum_t) / 2.0 - -mesh.corners.r += δ * ∇ϕᵤ -mesh.corners.c += δ * ∇ϕᵥ - -nothing; - - -function my_laplacian(ϕ::AbstractMatrix{Float64}) - height, width = size(ϕ) - - # Embed matrix within a larger matrix for better vectorization and avoid duplicated code - # Padded matrix adds 1 row/col after the size of ϕ. - # ϕ is inserted in padded matrix within 1:1+height+1 x 1:1+width+1. - # The rest of the padded matrix (its borders) are set at 0.0. - padded_ϕ = zeros(Float64, 1 + height + 1, 1 + width + 1) - padded_ϕ[begin+1:end-1, begin+1:end-1] .= ϕ[1:end, 1:end] - - # Convolution = up + down + left + right - ∇²ϕ = - padded_ϕ[begin+1-1:end-1-1, begin+1:end-1] + - padded_ϕ[begin+1+1:end-1+1, begin+1:end-1] + - padded_ϕ[begin+1:end-1, begin+1-1:end-1-1] + - padded_ϕ[begin+1:end-1, begin+1+1:end-1+1] - - 4.0 * padded_ϕ[begin+1:end-1, begin+1:end-1] - - return ∇²ϕ[1:end-1, 1:end-1] -end - - - - -m = [[1.0 2.0 3.0 2.0]; [4.0 5.0 6.0 5.0]; [7.0 8.0 9.0 8.0]; [10.0 11.0 12.0 11.0]] -h, w = size(m) -padded_m = zeros(Float64, 1 + h + 1, 1 + w + 1) -padded_m[begin+1:end-1, begin+1:end-1] .= m[1:end, 1:end] -padded_m - -padded_m[begin+1-1:end-1-1, begin+1:end-1] + -padded_m[begin+1+1:end-1+1, begin+1:end-1] + -padded_m[begin+1:end-1, begin+1-1:end-1-1] + -padded_m[begin+1:end-1, begin+1+1:end-1+1] - 4.0 * padded_m[begin+1:end-1, begin+1:end-1] - - -sum(CausticsEngineering.laplacian(m)) -sum(orig_laplacian(m)) From 485873b5e6de8ab4b428f724607f7190fdbec92f Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Thu, 30 Sep 2021 20:11:36 +0200 Subject: [PATCH 56/58] Minor --- src/create_mesh.jl | 17 ++++++++--------- src/scratch2.jl | 29 +++++++++++++++++++++++++++++ 2 files changed, 37 insertions(+), 9 deletions(-) create mode 100644 src/scratch2.jl diff --git a/src/create_mesh.jl b/src/create_mesh.jl index ac1e784..0e5c650 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -299,15 +299,14 @@ function march_mesh!(mesh::FaceMesh, side::Union{:top, :bottom}) println( """ - March mesh with correction_ratio δ = $(δ) - $(field_summary(mesh.corners.vr, "∇u")) - $(field_summary(mesh.corners.vc, "∇v")) - $(field_summary(mesh_r - mesh.corners.r , "new mesh changes on row")) - $(field_summary(mesh_c - mesh.corners.c, "new mesh changes on col")) - $(field_summary(mesh_r - mesh.corners.rows_numbers , "total mesh changes on row")) - $(field_summary(mesh_c - mesh.corners.cols_numbers, "total mesh changes on col")) - - """, + March mesh with correction_ratio δ = $(δ) + $(field_summary(mesh.corners.vr, "∇u")) + $(field_summary(mesh.corners.vc, "∇v")) + $(field_summary(mesh_r - mesh.corners.r , "new mesh changes on row")) + $(field_summary(mesh_c - mesh.corners.c, "new mesh changes on col")) + $(field_summary(mesh_r - mesh.corners.rows_numbers , "total mesh changes on row")) + $(field_summary(mesh_c - mesh.corners.cols_numbers, "total mesh changes on col")) + """, ) return δ diff --git a/src/scratch2.jl b/src/scratch2.jl new file mode 100644 index 0000000..0951fb2 --- /dev/null +++ b/src/scratch2.jl @@ -0,0 +1,29 @@ +struct P2D + x::AbstractMatrix{Real} + y::AbstractMatrix{Real} + + function P2D(dim1, dim2) + x = Matrix{Float64}(undef, dim1, dim2) + fill!(x, 0.) + y = Matrix{Float64}(undef, dim1, dim2) + fill!(y, 0.) + + return new(x, y) + end +end + + + +m = P2D(2, 3) + +m.x +m.y + +m.x .+= 2.0 + +function f1(v::P2D, a) + v.x .+= a +end + +f1(m, 3.) + From 24ce62b77700c0ffb5c700593e57ff4e6ae4c20e Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Sun, 3 Oct 2021 11:34:10 +0200 Subject: [PATCH 57/58] Documenter signatures --- .gitignore | 10 +- src/CausticsEngineering.jl | 4 +- src/create_mesh.jl | 450 ++++++++++++++++--------------------- src/mesh.jl | 3 +- src/scratchpad.jl | 131 ++--------- src/utilities.jl | 37 +-- 6 files changed, 219 insertions(+), 416 deletions(-) diff --git a/.gitignore b/.gitignore index e86dd5f..a31e38d 100644 --- a/.gitignore +++ b/.gitignore @@ -1,20 +1,12 @@ # Editors .vscode -.orig # Files generated by invoking Julia with --code-coverage *.jl.cov *.jl.*.cov *.obj -it*.png -loss*.png -change*.png -delta*.png -error*.png -img*.png -orig*.png - +examples/**.png # Files generated by invoking Julia with --track-allocation *.jl.mem diff --git a/src/CausticsEngineering.jl b/src/CausticsEngineering.jl index 7e3a2bb..e132126 100644 --- a/src/CausticsEngineering.jl +++ b/src/CausticsEngineering.jl @@ -62,8 +62,8 @@ export save_obj!, # Main procedures - propagate_poisson, - march_mesh, + propagate_poisson!, + march_mesh!, engineer_caustics, main diff --git a/src/create_mesh.jl b/src/create_mesh.jl index 0e5c650..fb5bff7 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -6,6 +6,7 @@ $(SIGNATURES) function engineer_caustics(source_image) imageBW = Float64.(Gray.(source_image)) + # Set global size parameters height, width = size(imageBW) global N_Pixel_Height = height @@ -17,65 +18,56 @@ function engineer_caustics(source_image) # cover each image corner with a triangle. mesh = FaceMesh(N_Pixel_Height, N_Pixel_Width) + # Create a pre-allocated solver + solve_velocity_potential! = solver_potential!(mesh) + # imageBW is normalised to have 1 unit per pixel on average. imageBW /= average(imageBW) - marginal_change_top = marginal_change_bot = nothing - max_update_top = marginal_change_top = Inf + marginal_change = nothing + max_update = Inf counter = 0 - while (abs(max_update_top+marginal_change_bot) > 1e-6 && counter < 10_000) + while (abs(max_update) > 1e-6 && counter < 4) counter += 1 print( """ - ================================================================================================================ - STARTING ITERATION $(counter): - starting ϕ TOP field = $(field_summary(mesh.corners.ϕ_top)) - starting ϕ BOT field = $(field_summary(mesh.corners.ϕ_bot)) + ================================================================================================================ + STARTING ITERATION $(counter): + starting ϕ field = $(field_summary(mesh.corners.ϕ)) """, ) - ϕ_top = mesh.corners.ϕ_top - ε_top, max_update_top = solve_velocity_potential!(mesh.corners.ϕ_top, imageBW/2., "it$(counter)_top") - marginal_change_top = mesh.corners.ϕ_top - ϕ_top - - ϕ_bot = mesh.corners.ϕ_bot - ε_bot, max_update_bot = solve_velocity_potential!(mesh.corners.ϕ_bot, imageBW/2., "it$(counter)_bot") - marginal_change_bot = mesh.corners.ϕ_bot - ϕ_bot + ε, max_update = solve_velocity_potential!(imageBW, "it$(counter)") print( """ RESULT AT ITERATION $(counter): - TOP - Luminosity error = $(field_summary(ε_top)) - Vertical move max update = $(max_update_top) - Marginal change = $(field_summary(marginal_change_top)) - end ϕ field = $(field_summary(mesh.corners.ϕ_top)) - - BOT - end ϕ field = $(field_summary(mesh.corners.ϕ_bot)) - Luminosity error = $(field_summary(ε_bot)) - Vertical move max update = $(max_update_bot) - Marginal change = $(field_summary(marginal_change_bot)) - end ϕ field = $(field_summary(mesh.corners.ϕ_bot)) + Luminosity error = $(field_summary(ε)) + Vertical move max update = $(max_update) + $(field_summary(mesh.corners.vr, "∇u")) + $(field_summary(mesh.corners.vc, "∇v")) + $(field_summary(mesh.corners.r - mesh.corners.rows_numbers, "total mesh changes on row")) + $(field_summary(mesh.corners.c - mesh.corners.cols_numbers, "total mesh changes on col")) + + end ϕ field = $(field_summary(mesh.corners.ϕ)) ================================================================================================================ """, ) - plot_as_quiver(mesh.corners.ϕ_top, n_steps = 50, scale = height / 10, max_length = height / 20) - average_absolute(marginal_change_top + marginal_change_bot) < 1e-4 && break + plot_as_quiver(mesh, n_steps = 50, scale = height / 10, max_length = height / 20) end println("\nSTARTING HORIZONTAL ITERATION ---") - println("\t Horizontal max update TOP = $(max_update_top) / BOT = $(max_update_bot)") + max_update = solve_height_potential(mesh, imageBW; f = Focal_Length) + println("\t Horizontal max update = $(max_update)") # Move the around a nil average. - mesh.corners.ϕ_top .-= average(mesh.corners.ϕ_top) - mesh.corners.ϕ_bot .-= average(mesh.corners.ϕ_bot) + mesh.corners.ϕ .-= average(mesh.corners.ϕ) return mesh, imageBW end @@ -88,138 +80,84 @@ $(SIGNATURES) ϕ is the _velocity potential_. The velocity represents the direction towards which the mesh vertices should move. Zones of high luminosity should be covered with more triangles and should attract more vertices. """ -function solve_velocity_potential!(mesh, image, prefix) - # Start with a new clean field - height, width = size(mesh) - - # Illumination only depends on the position of the corners, not their heights. ϕ is not relevant. - # Get the area of each individual pixel as stretch/shrunk on the lens. Area = energy. - # _FENCES_SIZED_ - # Illumination only depends on the position of the corners, not their heights. ϕ is not relevant. - lens_pixels_area_top, lens_pixels_area_bot = get_lens_pixels_area(mesh) - - # Positive error => the triangle needs to shrink (less light). Enforce nil average error. - ε_top = zeros(Float64, height, width) - ε_bot = zeros(Float64, height, width) +function solver_potential!(mesh) - # Each triangle should have the luminosity of half a pixel - ε_top[1:end-1, 1:end-1] = Float64.(lens_pixels_area_top - image/2.) - ε_top .-= average(ε_top) + # Start with a new clean field + (height, width) = size(mesh) + ε = zeros(Float64, height + 1, width + 1) + lens_pixels_area = zeros(Float64, height, width) - ε_bot[1:end-1, 1:end-1] = Float64.(lens_pixels_area_bot - image/2.) - ε_bot .-= average(ε_bot) + # Preallocate the Poisson solver + propagate_poisson! = poisson_propagator!(height + 1, width + 1) - println(""" - solve_velocity_potential! before loop: - $(field_summary(lens_pixels_area_top, "Pixel area")) - $(field_summary(ε_top, "luminosity error")) - $(field_summary(lens_pixels_area_bot, "Pixel area")) - $(field_summary(ε_bot, "luminosity error")) - """) - - # Save the loss image as a png. - save_plot_scalar_field!(ε_top+ε_bot, "error_ε_$(prefix)") - save_plot_scalar_field!(ε_top, "error_εtop_$(prefix)") - save_plot_scalar_field!(ε_bot, "error_εbot_$(prefix)") - - # Save the generated image as a png. - lens_pixels_area = lens_pixels_area_top + lens_pixels_area_bot - save( - "./examples/img_noluminosityratio_$(prefix).png", - Gray.(clamp.(lens_pixels_area, 0.0, 1.0)), - ) + return (image, prefix) -> begin - luminosity_ratio = sum(image) / sum(lens_pixels_area) - save( - "./examples/img_$(prefix).png", - Gray.(clamp.(lens_pixels_area * luminosity_ratio, 0.0, 1.0)), - ) + # Reset at each call + fill!(ε, 0.0) + fill!(lens_pixels_area, 0.0) - luminosity_ratio = sum(image/2.) / sum(lens_pixels_area_top) - save( - "./examples/img_$(prefix)_top.png", - Gray.(clamp.(lens_pixels_area_top * luminosity_ratio, 0.0, 1.0)), - ) + # Get the area of each individual pixel as stretch/shrunk on the lens. Area = energy. + # _FENCES_SIZED_ + # Illumination only depends on the position of the corners, not their heights. ϕ is not relevant. + lens_pixels_area .= get_lens_pixels_area(mesh) - luminosity_ratio = sum(image/2.) / sum(lens_pixels_area_bot) - save( - "./examples/img_$(prefix)_bot.png", - Gray.(clamp.(lens_pixels_area * lens_pixels_area_bot, 0.0, 1.0)), - ) + # Positive error => the triangle needs to shrink (less light). Enforce nil average error. + ε[1:end-1, 1:end-1] = Float64.(lens_pixels_area - image) + ε .-= average(ε) - # Start with a clean, flat potential field. - mesh.corners.ϕ_top = zeros(Float64, height, width) - mesh.corners.ϕ_bot = zeros(Float64, height, width) - - ϕ_b4_top = copy(mesh.corners.ϕ_top) - ϕ_b4_bot = copy(mesh.corners.ϕ_bot) - - count = 0 - min_update_top = min_update_bot = new_update_top = new_update_bot = 10_000 - old_update_top = 2 * new_update_top - old_update_bot = 2 * new_update_bot - while ( - 1e-5 < new_update_top + new_update_bot < 1.5 * min_update_top + 1.5 * min_update_bot && - 1e-4 < (old_update_top - new_update_top) / old_update_top && - 1e-4 < (old_update_bot - new_update_bot) / old_update_bot && - count < 10_000 - ) - count += 1 - old_update_top = new_update_top - old_update_bot = new_update_bot - min_update_top = min(min_update_top, new_update_top) - min_update_bot = min(min_update_bot, new_update_bot) - - new_update_top, ∇²ϕ_est_top, δ_top = propagate_poisson!(mesh.corners.ϕ_top,ε_top) - new_update_bot, ∇²ϕ_est_bot, δ_bot = propagate_poisson!(mesh.corners.ϕ_bot,ε_bot) - - count % 1_000 == 1 && println(""" - TOP - Iteration $(count) - max_update = $(round(new_update_top, sigdigits=4)) - $(field_summary(mesh.corners.ϕ_top, "ϕ")) - $(field_summary(∇²ϕ_est_top, "∇²ϕ_est")) - $(field_summary(δ_top, "δ")) - BOTTOM - Iteration $(count) - max_update = $(round(new_update_bot, sigdigits=4)) - $(field_summary(mesh.corners.ϕ_bot, "ϕ")) - $(field_summary(∇²ϕ_est_bot, "∇²ϕ_est")) - $(field_summary(δ_bot, "δ")) - """) + println(""" + solve_velocity_potential! before loop: + $(field_summary(lens_pixels_area, "Pixel area")) + $(field_summary(ε, "luminosity error")) + """) # Save the loss image as a png. - if count % 1_000 == 1 - save_plot_scalar_field!(∇²ϕ_est_top, "∇²ϕ_est_$(prefix)") - save_plot_scalar_field!(δ_top, "delta_$(prefix)") - save_plot_scalar_field!( - mesh.corners.ϕ_bot + mesh.corners.ϕ_top -ϕ_b4_top -ϕ_b4_bot , - "change_mesh.corners.ϕ_$(prefix)", - ) + save_plot_scalar_field!(ε, "error_$(prefix)") - save_plot_scalar_field!(∇²ϕ_est_top, "∇²ϕ_est_$(prefix)_top") - save_plot_scalar_field!(δ_top, "delta_$(prefix)_top") - save_plot_scalar_field!( - mesh.corners.ϕ_top - ϕ_b4_top, - "change_mesh.corners.ϕ_$(prefix)_top", - ) - - save_plot_scalar_field!(∇²ϕ_est_bot, "∇²ϕ_est_$(prefix)_bot") - save_plot_scalar_field!(δ_bot, "delta_$(prefix)_bot") - save_plot_scalar_field!( - mesh.corners.ϕ_bot - ϕ_b4_bot, - "change_mesh.corners.ϕ_$(prefix)_bot", - ) + # Save the generated image as a png. + luminosity_ratio = sum(image) / sum(lens_pixels_area) + save( + "./examples/img_$(prefix).png", + Gray.(clamp.(lens_pixels_area * luminosity_ratio, 0.0, 1.0)), + ) - ϕ_b4_top = copy(mesh.corners.ϕ_top) - ϕ_b4_bot = copy(mesh.corners.ϕ_bot) + # Start with a clean, flat potential field. + mesh.corners.ϕ = zeros(Float64, height + 1, width + 1) + count = 0 + max_update = Inf + ∇²ϕ_est = δ = nothing + while (1e-6 < max_update && count < 10_000) + count += 1 + max_update, ∇²ϕ_est, δ = propagate_poisson!(mesh.corners.ϕ, ε) + + # Save the loss image as a png. + if count % 1_000 == 1 + println(""" + Iteration $(count) - max_update = $(round(max_update, sigdigits=4)) + $(field_summary(mesh.corners.ϕ, "ϕ")) + $(field_summary(∇²ϕ_est, "∇²ϕ_est")) + $(field_summary(δ, "δ")) + """) + save_plot_scalar_field!(∇²ϕ_est, "∇²ϕ_est_$(prefix)") + save_plot_scalar_field!(δ, "delta_$(prefix)") + save_plot_scalar_field!(mesh.corners.ϕ, "change_mesh.corners.ϕ_$(prefix)") + end end - end - # Now we need to march the mesh row,col corner locations according to this gradient. - δ_top = march_mesh!(mesh, :top) - δ_bot = march_mesh!(mesh, :bottom) - return ε, new_update -end + println( + """ + Finished iteration at count $(count) - max_update = $(round(max_update, sigdigits=4)) + $(field_summary(mesh.corners.ϕ, "ϕ")) + $(field_summary(∇²ϕ_est, "∇²ϕ_est")) + $(field_summary(δ, "δ")) + """, + ) + # Now we need to march the mesh row,col corner locations according to this gradient. + δ = march_mesh!(mesh) + return ε, max_update + end +end """ @@ -227,22 +165,21 @@ $(SIGNATURES) ϕ is the height map. -`march_mesh` flexes the mesh +`march_mesh!` flexes the mesh """ -function march_mesh(mesh, mesh_ϕ) +function march_mesh!(mesh::FaceMesh) # Calculate the gradient of the velocity potential and reverse its direction. - vr, vc = ∇(mesh_ϕ) - mesh.corners.vr .= -vr - mesh.corners.vc .= -vc + mesh.corners.vr, mesh.corners.vc = ∇(mesh.corners.ϕ) + mesh.corners.vr .*= -1.0 + mesh.corners.vc .*= -1.0 # Clean up the mesh borders - # reset_border_values!(mesh.corners) + reset_border_values!(mesh.corners) # For each point in the mesh we need to figure out its velocity # However all the nodes located at a border will never move # I.e. velocity (Vx, Vy) = (0, 0) and the square of acrylate will remain of the same size. - # Get the time, at that velocity, for the area of the triangle to be nil. # We are only interested by positive values to only move in the direction of the (opposite) gradient height, width = size(mesh) @@ -253,124 +190,34 @@ function march_mesh(mesh, mesh_ϕ) list_maximum_t = [t for t ∈ find_maximum_t.(list_triangles) if !isnothing(t) && t > 0.0] - δ = minimum(list_maximum_t) / 1.5 - new_r = mesh.corners.r - δ * vr - new_c = mesh.corners.c - δ * vc - - return new_r, new_c, δ -end - - -function march_mesh!(mesh::FaceMesh, side::Union{:top, :bottom}) - - # Calculate the gradient of the velocity potential and reverse its direction. - if side == :top - mesh.corners.vr, mesh.corners.vc = ∇(mesh.corners.ϕ_top) - elseif side == :bottom - mesh.corners.vr, mesh.corners.vc = ∇(mesh.corners.ϕ_bot) - end - mesh.corners.vr .*= -1.0 - mesh.corners.vc .*= -1.0 - - # Clean up the mesh borders - reset_border_values!(mesh.corners) - - # For each point in the mesh we need to figure out its velocity - # However all the nodes located at a border will never move - # I.e. velocity (Vx, Vy) = (0, 0) and the square of acrylate will remain of the same size. - mesh_r = copy(mesh.corners.r) - mesh_c = copy(mesh.corners.c) - - # Get the time, at that velocity, for the area of the triangle to be nil. - # We are only interested by positive values to only move in the direction of the (opposite) gradient - height, width = size(mesh) - list_triangles = [triangle3D(mesh, row, col, side) for row ∈ 1:height, col ∈ 1:width] - list_maximum_t = [t for t ∈ find_maximum_t.(list_triangles) if !isnothing(t) && t > 0.0] - δ = minimum(list_maximum_t) / 2.0 - if side == :top - mesh.corners.r[1:end-1, 1:end-1] .-= δ * mesh.corners.vr[1:end-1, 1:end-1] - mesh.corners.c[1:end-1, 1:end-1] .-= δ * mesh.corners.vc[1:end-1, 1:end-1] - elseif - mesh.corners.r[2:end, 2:end] .-= δ * mesh.corners.vr[1:end-1, 1:end-1] - mesh.corners.c[2:end, 2:end] .-= δ * mesh.corners.vc[1:end-1, 1:end-1] - end + mesh.corners.r .-= δ * mesh.corners.vr + mesh.corners.c .-= δ * mesh.corners.vc - println( - """ + println(""" March mesh with correction_ratio δ = $(δ) $(field_summary(mesh.corners.vr, "∇u")) $(field_summary(mesh.corners.vc, "∇v")) - $(field_summary(mesh_r - mesh.corners.r , "new mesh changes on row")) - $(field_summary(mesh_c - mesh.corners.c, "new mesh changes on col")) - $(field_summary(mesh_r - mesh.corners.rows_numbers , "total mesh changes on row")) - $(field_summary(mesh_c - mesh.corners.cols_numbers, "total mesh changes on col")) - """, - ) + + """) return δ end -""" -$(SIGNATURES) - -This function implements successive over relaxation for a matrix and its associated error matrix -There is a hardcoded assumption of Neumann boundary conditions -- that the derivative across the -boundary must be zero in all cases. See: -https://math.stackexchange.com/questions/3790299/how-to-iteratively-solve-poissons-equation-with-no-boundary-conditions - -- ϕ is the potential to be solved subject to the Poisson equation and is the same size as the corners (_POSTS_SIZED_) -- target is ∇ϕ and is of the size in pixels (_FENCES_SIZED_) - -In order of how to think about the flow of the program for the velocity potential, - - if δ > 0, the Laplacian is too high at that point (∇²ϕ is too low). - - To decrease the Laplacian ∇²ϕ, note that ∇² is a divergence (of a gradient) that represents net flow going outside. - - - Decrease the Laplacian - - => decrease a divergence - - => decrease flow towards outside - - - The flow is a gradient of the potential ϕ. - - => decrease flow towards outside - - => either decrease the values of the potential around that point, or increase the value of the potential at that point. - - => Increase the value of ϕ at that point means a positive change when δ > 0. - - δ > 0 => correction of the SAME sign. -""" -function propagate_poisson(ϕ::Matrix{Float64}, ε::Matrix{Float64}) - - height, width = size(ϕ) - - ∇²ϕ_est = zeros(Float64, height, width) - δ = zeros(Float64, height, width) - new_ϕ = ϕ - - ω = 1.99 - - for row = 1:height, col = 1:width - val_up = row == 1 ? 0.0 : new_ϕ[row-1, col] - val_down = row == height ? 0.0 : new_ϕ[row+1, col] - val_left = col == 1 ? 0.0 : new_ϕ[row, col-1] - val_right = col == width ? 0.0 : new_ϕ[row, col+1] - - ∇²ϕ_est[row, col] = val_up + val_down + val_left + val_right - 4 * new_ϕ[row, col] - δ[row, col] = ω / 4.0 * (∇²ϕ_est[row, col] - ε[row, col]) - new_ϕ[row, col] += δ[row, col] - end - - return new_ϕ, maximum(abs.(δ)) -end - - """ $(SIGNATURES) """ -function solve_horizontal_dispersion(mesh::FaceMesh, image; f = Focal_Length) +function solve_height_potential(mesh::FaceMesh, image; f = Focal_Length) # height indexes rows, width indexes columns height, width = size(mesh) + # Preallocate the Poisson solver + propagate_poisson! = poisson_propagator!(height + 1, width + 1) + + # Coordinates on the caustics = simple rectangular values in corners. # Coordinates on the lens face comes from corner field. # d_row/d_col are _POSTS-SIZED_ @@ -395,6 +242,11 @@ function solve_horizontal_dispersion(mesh::FaceMesh, image; f = Focal_Length) N_row = tan.(atan.(d_row ./ true_H) / (n₁ - n₂)) N_col = tan.(atan.(d_col ./ true_H) / (n₁ - n₂)) + # @. N_row[1:end, 1:end] = + # tan(atan(d_row[1:end, 1:end] / true_H[1:end, 1:end]) / (n₁ - n₂)) + # @. N_col[1:end, 1:end] = + # tan(atan(d_col[1:end, 1:end] / true_H[1:end, 1:end]) / (n₁ - n₂)) + # We need to find the divergence of the Vector field described by Nx and Ny # div_row/div_col are _FENCES_SIZED_ div_row = zeros(Float64, size(true_H)) @@ -405,13 +257,15 @@ function solve_horizontal_dispersion(mesh::FaceMesh, image; f = Focal_Length) # Normalised divergence # divergence_direction is _FENCES_SIZED_ divergence_direction = div_row + div_col + # divergence_direction .-= average(divergence_direction) - ϕ_next = mesh.corners.ϕ max_update = Inf + old_update = Inf for i ∈ 1:1e6 - ϕ_next, max_update = propagate_poisson(ϕ_next, -divergence_direction) + old_update = max_update + max_update, _, _ = propagate_poisson!(mesh.corners.ϕ, -divergence_direction) - i % 250 == 1 && + i % 1_000 == 1 && println("Convergence horiz. Δ at counter = $(i) max update = $(max_update)") if abs(max_update) <= 1e-6 @@ -422,5 +276,81 @@ function solve_horizontal_dispersion(mesh::FaceMesh, image; f = Focal_Length) end end - return ϕ_next, max_update + return max_update +end + + + + +""" +$(SIGNATURES) + +This function implements successive over relaxation for a matrix and its associated error matrix +There is a hardcoded assumption of Neumann boundary conditions -- that the derivative across the +boundary must be zero in all cases. See: +https://math.stackexchange.com/questions/3790299/how-to-iteratively-solve-poissons-equation-with-no-boundary-conditions + +- ϕ is the potential to be solved subject to the Poisson equation and is the same size as the corners (_POSTS_SIZED_) +- target is ∇ϕ and is of the size in pixels (_FENCES_SIZED_) + +In order of how to think about the flow of the program for the velocity potential, + - if δ > 0, the Laplacian is too high at that point (∇²ϕ is too low). + - To decrease the Laplacian ∇²ϕ, note that ∇² is a divergence (of a gradient) that represents net flow going outside. + + - Decrease the Laplacian + - => decrease a divergence + - => decrease flow towards outside + + - The flow is a gradient of the potential ϕ. + - => decrease flow towards outside + - => either decrease the values of the potential around that point, or increase the value of the potential at that point. + - => Increase the value of ϕ at that point means a positive change when δ > 0. + - δ > 0 => correction of the SAME sign. +""" +function poisson_propagator!(height, width) + + ∇²ϕ_est = zeros(Float64, height, width) + δ = zeros(Float64, height, width) + + # Return a closure over preallocaed arrays + return (ϕ::Matrix{Float64}, ε::Matrix{Float64}) -> begin + ω = 1.99 + + # Reset at each call + fill!(∇²ϕ_est, 0.0) + fill!(δ, 0.0) + + for row = 1:height, col = 1:width + val_up = row == 1 ? 0.0 : ϕ[row-1, col] + val_down = row == height ? 0.0 : ϕ[row+1, col] + val_left = col == 1 ? 0.0 : ϕ[row, col-1] + val_right = col == width ? 0.0 : ϕ[row, col+1] + + ∇²ϕ_est[row, col] = + val_up + val_down + val_left + val_right - 4 * ϕ[row, col] + δ[row, col] = ω / 4.0 * (∇²ϕ_est[row, col] - ε[row, col]) + ϕ[row, col] += δ[row, col] + end + + return maximum(abs.(δ)), ∇²ϕ_est, δ + + # Problem with the in-place updates if using the followng. + # # Laplacian + # # ∇²ϕ_est represent the estimate of the Laplacian of ϕ (second-order value) + # ∇²ϕ_est = laplacian(ϕ) + + + # # In the case of the velocity potential, δ is the difference between the divergence of the luminosity error + # # and the current one for the current field ϕ (divergence of its gradient). + # # High luminosity error ∇²ϕ means that the triangles are too bright = too large. + # # The Laplacian Lϕ has to converge towards the ∇²ϕ. Difference to calculate speed of the descent. + + # # Correction ratio to avoid setting the triangle to nothing + # δ = ω / 4.0 * (∇²ϕ_est - ε) + + # # In the case of the velocity potential, if δ > 0, the Laplacian is too high at that point (∇²ϕ is too low). + # ϕ[1:end-1, 1:end-1] .+= δ + + # return ∇²ϕ_est, δ, maximum(abs.(δ)) + end end diff --git a/src/mesh.jl b/src/mesh.jl index c79161e..12e8e98 100644 --- a/src/mesh.jl +++ b/src/mesh.jl @@ -265,8 +265,7 @@ function create_solid( # The connections are listed as a tuple of 3 arrays. # First array contains the first point of a triangle, and so on triangle_index = [ - (index_dict[v[1]], index_dict[v[2]], index_dict[v[3]]) for - v ∈ values(triangle_dict) + (index_dict[v[1]], index_dict[v[2]], index_dict[v[3]]) for v ∈ values(triangle_dict) ] return triangle_dict, vertex_dict, triangle_index, vertex_index diff --git a/src/scratchpad.jl b/src/scratchpad.jl index 8b6d8f8..049175c 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -20,11 +20,7 @@ image = Images.load("./examples/personal/caricature.jpg"); # Check current worki image = Images.load("./examples/personal/portrait.jpg"); # Check current working directory with pwd() image = Images.load("./examples/personal/bilal.jpg"); # Check current working directory with pwd() -mesh, imageBW, list_max_updates = engineer_caustics(image); - -length(list_max_updates) -p = plot((log.(clamp01nan.(list_max_updates)))) -p +mesh, imageBW = engineer_caustics(image); imageBW = Float64.(Gray.(image)); Gray.(imageBW) @@ -317,7 +313,7 @@ CausticsEngineering.field_summary(origerror_luminosity) CausticsEngineering.field_summary(error_luminosity - origerror_luminosity') -######################## Propagation +######################## Distance to Laplacian & propagate max_update, Lϕ, δ = CausticsEngineering.propagate_poisson!(mesh.corners.ϕ, error_luminosity); CausticsEngineering.field_summary(mesh.corners.ϕ) CausticsEngineering.field_summary(Lϕ) @@ -330,118 +326,17 @@ CausticsEngineering.field_summary(origLϕ) CausticsEngineering.field_summary(origδ) CausticsEngineering.field_summary(mesh.corners.ϕ[1:end-1, 1:end-1] - origϕ') -######################## March mesh -dfx, dfy = ∇(mesh.corners.ϕ) -CausticsEngineering.field_summary(dfx) -CausticsEngineering.field_summary(dfy) -mesh.corners.vr = -dfx -mesh.corners.vc = -dfy -CausticsEngineering.field_summary(mesh.corners.vr) -CausticsEngineering.field_summary(mesh.corners.vc) - -dfx2, dfy2 = CausticsEngineering.orig_∇(origϕ) -CausticsEngineering.field_summary(dfx2) -CausticsEngineering.field_summary(dfy2) - - -# Min t -list_triangles = vcat( - [CausticsEngineering.triangle3D(mesh, row, col, :top) for row ∈ 1:h, col ∈ 1:w], - [CausticsEngineering.triangle3D(mesh, row, col, :bottom) for row ∈ 1:h, col ∈ 1:w], -) - -list_maximum_t = [t for t ∈ CausticsEngineering.find_maximum_t.(list_triangles) if !isnothing(t) && t > 0.0] -δ = minimum(list_maximum_t) - -mesh_r = copy(mesh.corners.r) -mesh_c = copy(mesh.corners.c) -δ = minimum(list_maximum_t) / 2.0 -mesh.corners.r .-= δ * mesh.corners.vr -mesh.corners.c .-= δ * mesh.corners.vc - -println( - """ - -March mesh with correction_ratio δ = $(δ) - $(CausticsEngineering.field_summary(mesh.corners.vr, "∇u")) - $(CausticsEngineering.field_summary(mesh.corners.vc, "∇v")) - $(CausticsEngineering.field_summary(mesh_r - mesh.corners.r , "new mesh changes on row")) - $(CausticsEngineering.field_summary(mesh_c - mesh.corners.c, "new mesh changes on col")) - $(CausticsEngineering.field_summary(mesh_r - mesh.corners.rows_numbers , "total mesh changes on row")) - $(CausticsEngineering.field_summary(mesh_c - mesh.corners.cols_numbers, "total mesh changes on col")) - - """, -) - - -velocities = Matrix{CausticsEngineering.Point3D}(undef, w+1, h+1) -fill!(velocities, CausticsEngineering.Point3D(0.0, 0.0, 0.0, 0.0, 0.0)) - -for x ∈ 1:w-1, y ∈ 1:h-1 - velocities[x, y] = CausticsEngineering.Point3D(-dfx2[x, y], -dfy2[x, y], 0.0, 0.0, 0.0) -end - -min_t = 10000 -triangleCount = 1 -p1 = CausticsEngineering.Point3D(0., 0., 0., 0., 0.) -p2 = CausticsEngineering.Point3D(0., 0., 0., 0., 0.) -p3 = CausticsEngineering.Point3D(0., 0., 0., 0., 0.) -v1 = CausticsEngineering.Point3D(0., 0., 0., 0., 0.) -v2 = CausticsEngineering.Point3D(0., 0., 0., 0., 0.) -v3 = CausticsEngineering.Point3D(0., 0., 0., 0., 0.) -for triangle in origmesh.triangles - p1 = origmesh.nodes[triangle.pt1] - p2 = origmesh.nodes[triangle.pt2] - p3 = origmesh.nodes[triangle.pt3] - - v1 = velocities[p1.ix, p1.iy] - v2 = velocities[p2.ix, p2.iy] - v3 = velocities[p3.ix, p3.iy] - - t = CausticsEngineering.findT(p1, p2, p3, v1, v2, v3) - - if !isnothing(t) - min_t = min(min_t, t) - end - - triangleCount += 1 -end - -p1 -p2 -p3 -v1 -v2 -v3 - -min_t - -size(origmesh.nodes) -avgmx = 0. -avgmy = 0. -avgax = 0. -avgay = 0. -for point in origmesh.nodes - v = velocities[point.ix, point.iy] - px = point.x - py = point.y - point.x = v.x * min_t/2 + point.x - point.y = v.y * min_t/2 + point.y - - avgmx += point.x - px - avgmy += point.y - py - avgax += abs(point.x - px) - avgay += abs(point.y - py) -end - -avgmx/length(origmesh.nodes) -avgmy/length(origmesh.nodes) -avgax/length(origmesh.nodes) -avgay/length(origmesh.nodes) - - - - +CausticsEngineering.field_summary(mesh.corners.ϕ[2:end, 1:end-1] - origϕ') +CausticsEngineering.field_summary(mesh.corners.ϕ[1:end-1, 2:end] - origϕ') +CausticsEngineering.field_summary(mesh.corners.ϕ[2:end, 2:end] - origϕ') +m = + ( + mesh.corners.ϕ[1:end-1, 1:end-1] + + mesh.corners.ϕ[2:end, 1:end-1] + + mesh.corners.ϕ[1:end-1, 2:end] + + mesh.corners.ϕ[2:end, 2:end] + ) / 4.0; +CausticsEngineering.field_summary(m - origϕ') diff --git a/src/utilities.jl b/src/utilities.jl index 1b2e72f..9d23772 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -1,8 +1,7 @@ """ $(TYPEDEF) -Coordinates as row (vertical), columns (horizontal). Represent the data of each top corner of a pixel. -Topleft for top triangle, bottomleft for bottom triangle +Coordinates as row (vertical), columns (horizontal). Represent the data of each topleft corner of a pixel. vr, vc: velocity vector of that corner. Warning: posts/fences: One more corner than number of pixels. """ @@ -96,8 +95,7 @@ mutable struct FieldVertex3D vc::AbstractMatrix{Float64} # Velocity potential at each corner - ϕ_top::AbstractMatrix{Float64} - ϕ_bot::AbstractMatrix{Float64} + ϕ::AbstractMatrix{Float64} rows_numbers::AbstractMatrix{Float64} cols_numbers::AbstractMatrix{Float64} @@ -114,10 +112,9 @@ function FieldVertex3D(height, width) mvr = zeros(Float64, height + 1, width + 1) mvc = zeros(Float64, height + 1, width + 1) - mϕ_top = zeros(Float64, height , width ) - mϕ_bot = zeros(Float64, height , width ) + mϕ = zeros(Float64, height + 1, width + 1) - fv = FieldVertex3D((height, width), mr, mc, mvr, mvc, mϕ_top, mϕ_bot, rows_numbers, cols_numbers) + fv = FieldVertex3D((height, width), mr, mc, mvr, mvc, mϕ, rows_numbers, cols_numbers) reset_border_values!(fv) return fv end @@ -155,14 +152,13 @@ $(SIGNATURES) function Vertex3D(fv::FieldVertex3D, row, col) height, width = size(fv) - if (1 <= row <= height ) && (1 <= col <= width) + if (1 <= row <= height + 1) && (1 <= col <= width + 1) Vertex3D( fv.r[row, col], fv.c[row, col], fv.vr[row, col], fv.vc[row, col], - fv.ϕ_top[min(height, row), col(width, col)], - fv.ϕ_bot[min(height, row), col(width, col)], + fv.ϕ[row, col], ) else missing @@ -340,8 +336,10 @@ has been shifted and flexed around. function get_lens_pixels_area(mesh::FaceMesh) height, width = size(mesh) - top_tri_area = get_lens_pixels_area(mesh, :top) - bot_tri_area =get_lens_pixels_area(mesh, :bottom) + top_tri_area = + area.([triangle3D(mesh, row, col, :top) for row ∈ 1:height, col ∈ 1:width]) + bot_tri_area = + area.([triangle3D(mesh, row, col, :bottom) for row ∈ 1:height, col ∈ 1:width]) total_area = top_tri_area + bot_tri_area @@ -350,21 +348,10 @@ function get_lens_pixels_area(mesh::FaceMesh) @assert abs(sum(luminosity_pixels) - height * width) < 1.0 "Total lens luminosity is incorrect" - # return luminosity_pixels - return top_tri_area, bot_tri_area + return luminosity_pixels end -function get_lens_pixels_area(mesh::FaceMesh, side::Union{:top, :bottom}) - height, width = size(mesh) - - # return luminosity_pixels - return area.([triangle3D(mesh, row, col, side) for row ∈ 1:height, col ∈ 1:width]) -end - - - - """ $(SIGNATURES) @@ -376,7 +363,7 @@ function field_summary(field, fieldname) avg = round(average(field), sigdigits = 4) abs = round(average_absolute(field), sigdigits = 4) - return """$(fieldname) (Sum/Min/Max/Avg/Avg abs.): $(s) / $(min) / $(max) / $(avg) / $(abs)""" + return """$(fieldname) (Sum/Max/Min/Avg/Avg abs.): $(s) / $(max) / $(min) / $(avg) / $(abs)""" end From 47e0a42054f12190d04666c84a44a320e1f6150d Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Mon, 12 Sep 2022 12:30:30 +0800 Subject: [PATCH 58/58] Change run.jl to use a temporary project --- Project.toml | 4 ++++ docs/make.jl | 2 +- run.jl | 20 +++++++++++++++++--- src/math_utilities.jl | 8 ++++---- src/utilities.jl | 6 +++--- 5 files changed, 29 insertions(+), 11 deletions(-) diff --git a/Project.toml b/Project.toml index f1bd27d..ad64858 100644 --- a/Project.toml +++ b/Project.toml @@ -14,13 +14,17 @@ GLMakie = "e9467ef8-e4e7-5192-8a1a-b1aee30e663a" GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326" Images = "916415d5-f1e6-5110-898d-aaa5f9f070e0" JuliaFormatter = "98e50ef6-434e-11e9-1051-2b60c6c9e899" +LibGit2 = "76f85450-5226-5b5a-8eaa-529ad045b433" MeshIO = "7269a6da-0436-5bbc-96c2-40638cbb6118" MeshViz = "9ecf9c4f-6e5a-4b5e-83ae-06f2c7a661d8" Meshes = "eacbb407-ea5a-433e-ab97-5258b1ca43fa" +OhMyREPL = "5fb14364-9ced-5910-84b2-373655c76a03" +PkgTemplates = "14b8a8f1-9102-5b29-a752-f990bacb7fe1" Plotly = "58dd65bb-95f3-509e-9936-c39a10fdeae7" Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" Revise = "295af30f-e4ad-537b-8983-00126c2a3abe" +Weave = "44d3d7a6-8a23-5bf8-98c5-b353f8df5ec9" [compat] julia = "1" diff --git a/docs/make.jl b/docs/make.jl index f3664cc..b54d21f 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -1,7 +1,7 @@ push!(LOAD_PATH, "../src/") using CausticsEngineering -using Documenter +using Documenter, DocStringExtensions # # HTML docs diff --git a/run.jl b/run.jl index bf33ef8..8a6cd3d 100644 --- a/run.jl +++ b/run.jl @@ -1,7 +1,21 @@ +# Work in a temporary environment using Pkg -Pkg.activate(".") +Pkg.activate(; temp = true) -using Images, CausticsEngineering +# Speed up by avoiding updating the repository when adding packages +Pkg.UPDATED_REGISTRY_THIS_SESSION[] = true -image = Images.load("./examples/cat_posing.jpg") # Check current working directory with pwd() +# Add useful package +Pkg.add([ + "Revise", "Images" +]) + +Pkg.develop(path = @__DIR__) + +using Revise, Images + +using CausticsEngineering + +# Check current working directory with pwd() +image = Images.load("./examples/personal/caricature.jpg") engineer_caustics(image); diff --git a/src/math_utilities.jl b/src/math_utilities.jl index 148548a..863fbda 100644 --- a/src/math_utilities.jl +++ b/src/math_utilities.jl @@ -67,10 +67,10 @@ function laplacian(ϕ::AbstractMatrix{Float64}) # Convolution = up + down + left + right ∇²ϕ = - padded_ϕ[begin+1-1:end-1-1, begin+1:end-1] + - padded_ϕ[begin+1+1:end-1+1, begin+1:end-1] + - padded_ϕ[begin+1:end-1, begin+1-1:end-1-1] + - padded_ϕ[begin+1:end-1, begin+1+1:end-1+1] - + padded_ϕ[begin+1-1:end-1-1, begin+1+0:end-1+0] + + padded_ϕ[begin+1+1:end-1+1, begin+1+0:end-1+0] + + padded_ϕ[begin+1+0:end-1+0, begin+1-1:end-1-1] + + padded_ϕ[begin+1+0:end-1+0, begin+1+1:end-1+1] - 4.0 * padded_ϕ[begin+1:end-1, begin+1:end-1] return ∇²ϕ[1:end-1, 1:end-1] diff --git a/src/utilities.jl b/src/utilities.jl index 9d23772..65af945 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -23,7 +23,7 @@ $(SIGNATURES) function dist(p1::Tuple{Float64,Float64,Float64}, p2::Tuple{Float64,Float64,Float64}) dr = p2[1] - p1[1] dc = p2[2] - p1[2] - return sqrt(dr^2 + dc^2) + return √(dr^2 + dc^2) end """ @@ -32,7 +32,7 @@ $(SIGNATURES) function dist(p1::Vertex3D, p2::Vertex3D) dr = p2.r - p1.r dc = p2.c - p1.c - return sqrt(dr^2 + dc^2) + return √(dr^2 + dc^2) end @@ -47,7 +47,7 @@ function area(v1::Vertex3D, v2::Vertex3D, v3::Vertex3D) # surface_sq = (a + b + c) * (- a + b + c) * (a - b + c) * (a + b - c) / 16.0 surface_sq = s * (s - a) * (s - b) * (s - c) - return surface_sq <= 1e-100 ? 0.0 : sqrt(surface_sq) + return surface_sq <= 1e-100 ? 0.0 : √(surface_sq) end

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KMNUMnLSTYbk^67} diff --git a/src/CausticsEngineering.jl b/src/CausticsEngineering.jl index a533737..b2211d0 100644 --- a/src/CausticsEngineering.jl +++ b/src/CausticsEngineering.jl @@ -2,15 +2,35 @@ module CausticsEngineering using DocStringExtensions -using meshes - -using Images, Plots +using Meshes, Images, Plots gr() include("parameters.jl") include("utilities.jl") +include("plots.jl") +include("io.jl") + include("create_mesh.jl") -export main, engineer_caustics + + +""" +$(SIGNATURES) +""" +function main() + @assert size(ARGS) == (1,) "Intented usage is: julia create_mesh.jl image.png" + + img = Images.load(ARGS[1]) + return engineer_caustics(img) +end + + +""" +$(SIGNATURES) +""" +main() + + +export FaceMesh, main, engineer_caustics end diff --git a/src/create_mesh.jl b/src/create_mesh.jl index 9f3bc57..9d317f6 100644 --- a/src/create_mesh.jl +++ b/src/create_mesh.jl @@ -45,8 +45,6 @@ function find_maximum_t(p1::Vertex3D, p2::Vertex3D, p3::Vertex3D) # There can be no solution if, after translation, B abd C move in parallel direction. # C will never end up on the line AB.result_mesh.rectangles[row, col].z = height_map[row, col] - result_mesh.rectangles[row, col].z = height_map[row, col] - # Very unlikely with Float64. return missing, missing end @@ -60,18 +58,22 @@ find_maximum_t(p::Tuple{Vertex3D,Vertex3D,Vertex3D}) = find_maximum_t(p[1], p[2] $(SIGNATURES) """ function ∇(ϕ::Matrix{Float64}) - width, height = size(f) + height, width = size(ϕ) - ∇ϕᵤ = zeros(Float64, width, height) # the right edge will be filled with zeros - ∇ϕᵥ = zeros(Float64, width, height) # the buttom edge will be filled with zeros + ∇ϕᵤ = zeros(Float64, height, width) # the right edge will be filled with zeros + ∇ϕᵥ = zeros(Float64, height, width) # the buttom edge will be filled with zeros - for ci ∈ CartesianIndex(ϕ) - row = ci[1] - col = ci[2] - ∇ϕᵤ[ci] = ϕ[row+1, col] - ϕ[row, col] - ∇ϕᵥ[ci] = ϕ[row, col+1] - ϕ[row, col] + for row ∈ 1:height-1, col ∈ 1:width-1 + ∇ϕᵤ[row, col] = ϕ[row+1, col] - ϕ[row, col] + ∇ϕᵥ[row, col] = ϕ[row, col+1] - ϕ[row, col] end + ∇ϕᵤ[1:end, end] .= 0.0 + ∇ϕᵤ[end, 1:end] .= 0.0 + + ∇ϕᵥ[1:end, end] .= 0.0 + ∇ϕᵥ[end, 1:end] .= 0.0 + return ∇ϕᵤ, ∇ϕᵥ end @@ -79,14 +81,12 @@ end """ $(SIGNATURES) """ -function get_pixel_area(mesh::RectangleMesh) +function get_pixel_area(mesh::FaceMesh) # A Mesh is a grid of 3D points. The X and Y coordinates are not necessarily aligned or square # The Z coordinate represents the value. brightness is just proportional to area. - height, width = size(mesh) - - pixelAreas = zeros(Float64, height, width) + pixelAreas = zeros(Float64, size(mesh)) - for ci ∈ CartesianIndex + for ci ∈ CartesianIndices(pixelAreas) # # *------* # | TOP/ | @@ -95,7 +95,8 @@ function get_pixel_area(mesh::RectangleMesh) # | /BOT | # *------* # - pixelAreas[ci] = area(top_triangles(mesh, ci)) + area(bottom_triangle(mesh, ci)) + pixelAreas[ci] = + area(top_triangle3D(mesh, ci)...) + area(bot_triangle3D(mesh, ci)...) end return pixelAreas @@ -125,7 +126,7 @@ function relax!(height_map::Matrix{Float64}, divergence::Matrix{Float64}) val_up = container[1:height, 2:width+1] val_down = container[3:height+2, 2:width+1] val_left = container[2:height+1, 1:width] - val_right = embcontaineredding[2:height+1, 3:width+2] + val_right = container[2:height+1, 3:width+2] delta = (val_up + val_down + val_left + val_right - divergence) ./ 4.0 height_map = height_map + ω .* (delta - height_map) @@ -145,14 +146,21 @@ function matrix_to_mesh(height_map::Matrix{Float64}) height, width = size(height_map) mesh = FaceMesh(height, width) - mesh.vertexList[:].z .= height_map[:] - # The borders height is forced at 0. - mesh.topleft[CartesianIndex(:, 1)].z .= 0.0 - mesh.topleft[CartesianIndex(:, end)].z .= 0.0 + for ci ∈ CartesianIndices(height_map) + mesh.topleft[ci].z = height_map[ci] + end + + # The borders' height is forced at 0. + for row ∈ 1:height + mesh.topleft[row, 1].z = 0.0 + mesh.topleft[row, end].z = 0.0 + end - mesh.topleft[CartesianIndex(1, :)].z .= 0.0 - mesh.topleft[CartesianIndex(end, :)].z .= 0.0 + for col ∈ 1:width + mesh.topleft[1, col].z = 0.0 + mesh.topleft[end, col].z = 0.0 + end return mesh end @@ -170,26 +178,31 @@ function march_mesh!(mesh::FaceMesh, ϕ::Matrix{Float64}) # However all the nodes located at a border will never move # I.e. velocity (Vx, Vy) = (0, 0) and the square of acrylate will remain # of the same size. - mesh.topleft[:, :][1].vx .= -∇ϕᵤ[:, :] - mesh.topleft[:, :][1].vy .= -∇ϕᵥ[:, :] + for ci ∈ CartesianIndices(ϕ) + mesh.topleft[ci].vx = -∇ϕᵤ[ci] + mesh.topleft[ci].vy = -∇ϕᵥ[ci] + end # The velocity matrix was initialized with zeros everywhere. We nevertheless ovewrite them just in case... - mesh.topleft[:, 1].vx .= 0.0 - mesh.topleft[:, 1].vy .= 0.0 - mesh.topleft[:, end].vx .= 0.0 - mesh.topleft[:, end].vy .= 0.0 - - mesh.topleft[1, :].vx .= 0.0 - mesh.topleft[1, :].vy .= 0.0 - mesh.topleft[end, :].vx = 0.0 - mesh.topleft[end, :].vy = 0.0 + for row ∈ 1:height + mesh.topleft[row, 1].vx = 0.0 + mesh.topleft[row, 1].vy = 0.0 + mesh.topleft[row, end].vx = 0.0 + mesh.topleft[row, end].vy = 0.0 + end + for col ∈ 1:width + mesh.topleft[1, col].vx = 0.0 + mesh.topleft[1, col].vy = 0.0 + mesh.topleft[end, col].vx = 0.0 + mesh.topleft[end, col].vy = 0.0 + end # Basically infinity time to shrink a triangle to zip. min_t = 10_000.0 for ci ∈ CartesianIndices(ϕ) - top_tri = top_triangles3D(mesh, ci) + top_tri = top_triangle3D(mesh, ci) # Get the time, at that velocity, for the area of the triangle to be nil. # We are only interested in positive times. @@ -219,8 +232,10 @@ function march_mesh!(mesh::FaceMesh, ϕ::Matrix{Float64}) # Modify the mesh triangles but ensuring that we are far from destroying any of them with a nil area. δ = min_t / 2 - mesh.topleft[:, :].x .+= δ * mesh.rectangles[:, :].vx - mesh.topleft[:, :].y .+= δ * mesh.rectangles[:, :].vy + for ci ∈ CartesianIndices(mesh.topleft) + mesh.topleft[ci].x += δ * mesh.topleft[ci].vx + mesh.topleft[ci].y += δ * mesh.topleft[ci].vy + end # saveObj(mesh, "gateau.obj") end @@ -272,16 +287,23 @@ function single_iteration!(mesh, image, suffix) width, height = size(image) - ϕ = Matrix{Float64}(undef, width, height) - - for i = 1:N_Iterations_Convergence - max_update = relax!(ϕ, D) + # ϕ is the heightmap + ϕ = zeros(Float64, width, height) - i % 500 == 0 && println(max_update) + max_update = 100.0 + interaction_count = 0 + while true + interaction_count += 1 + interaction_count % 500 == 0 && println("Converging for intensity: $(max_update)") - max_update < 0.00001 && ( - println("Convergence reached at step $(i) with max_update of $(max_update)"); break - ) + old_max_update = max_update + max_update = relax!(ϕ, D) + if max_update < 1e-6 || abs((max_update - old_max_update) / old_max_update) < 0.01 + println( + "Convergence stopped at step $(interaction_count) with max_update of $(max_update)", + ) + break + end end save_stl!( @@ -310,13 +332,20 @@ function set_heights!( ) width, height = size(height_map) - mesh.rectangles[:, :].z .= height_map[:, :] * height_scale + height_offset + for ci ∈ CartesianIndices(height_map) + mesh.topleft[ci].z = height_map[ci] * height_scale + height_offset + end # Forces the borders at Height_Offset. They will never change because nil velocity. - mesh.rectangles[1, :] .= height_offset - mesh.rectangles[end, :] .= height_offset - mesh.rectangles[:, 1] .= height_offset - mesh.rectangles[:, end] .= height_offset + for row ∈ 1:height + mesh.topleft[row, 1].z = Top_Offset + mesh.topleft[row, end].z = Top_Offset + end + + for col ∈ 1:width + mesh.topleft[1, col].z = Top_Offset + mesh.topleft[end, col].z = Top_Offset + end end @@ -419,11 +448,10 @@ $(SIGNATURES) """ function find_surface( mesh::FaceMesh, - image, + image; f = Focal_Length, picture_width = Caustics_Side, ) - height, width = size(mesh) # H is the initial distance from the surface of the carved face to the projection screen. # H is constant and does not account for the change in heights due to carving. @@ -431,18 +459,27 @@ function find_surface( H = f / Meters_Per_Pixel # h(eight) indexes rows, w(idth) indexes columns + height, width = size(mesh) Nx = zeros(Float64, height + 1, width + 1) Ny = zeros(Float64, height + 1, width + 1) - for ci ∈ CartesianIndices(mesh.nodeArray) - node = mesh.nodeArray[ci] - dx = (node.ix - node.x) - dy = (node.iy - node.y) + for row ∈ 1:height+1, col ∈ 1:width+1 + # Coordinates on the caustics + cx = row + cy = col - true_H = H - node.z + # Coordinates on the lens face + lx = mesh.topleft[row, col].x + ly = mesh.topleft[row, col].y - Nx[ci] = tan(atan(dx / true_H) / (n₁ - n₂)) - Ny[ci] = tan(atan(dy / true_H) / (n₁ - n₂)) + # Coordinates difference + dx = cx - lx + dy = cy - ly + + true_H = H - mesh.topleft[row, col].z + + Nx[row, col] = tan(atan(dx / true_H) / (n₁ - n₂)) + Ny[row, col] = tan(atan(dy / true_H) / (n₁ - n₂)) end # We need to find the divergence of the Vector field described by Nx and Ny @@ -450,19 +487,25 @@ function find_surface( δr = zeros(Float64, width, height) δc = zeros(Float64, width, height) - δr[:, :] .= Nx[2:end, 1:end-1] .- Nx[1:end-1, 1:end-1] - δc[:, :] .= Nx[1:end-1, 2:end] .- Ny[1:end-1, 1:end-1] - divergence = δx + δy + δr[1:end, 1:end] .= Nx[2:end, 1:end-1] .- Nx[1:end-1, 1:end-1] + δc[1:end, 1:end] .= Nx[1:end-1, 2:end] .- Ny[1:end-1, 1:end-1] + divergence = δr + δc + println("Have all the divergences") height_map = zeros(Float64, height, width) - max_update = 0.0 - for iter = 1:N_Iterations_Convergence - max_update = relax!(height_map, divergence) + max_update = 1000.0 + iteration_count = 0 + while true + iteration_count += 1 + iteration_count % 100 == 0 && println("Converging for divergence: $(max_update)") - iter % 100 == 0 && println(max_update) - if max_update < 0.00001 - println("Convergence reached at step $(iter) with max_update of $(max_update)") + old_max_update = max_update + max_update = relax!(height_map, divergence) + if max_update < 1e-6 || abs((max_update - old_max_update) / old_max_update) < 0.01 + println( + "Convergence stopped improving at step $(iteration_count) with max_update of $(max_update)", + ) break end end @@ -477,60 +520,44 @@ end """ $(SIGNATURES) """ -function engineer_caustics(img) - img = Gray.(img) - img2 = permutedims(img) * 1.0 - width, height = size(img2) +function engineer_caustics(source_image) + imageBW = Float64.(Gray.(source_image)) + imageBW = permutedims(imageBW) + + width, height = size(imageBW) + println("Image size: $((height, width))") # meshy is the same size as the image with an extra row/column to have coordinates to # cover each image pixel with a triangle. - mesh = FaceMesh(width, height) + mesh = FaceMesh(height, width) # We need to boost the brightness of the image so that its sum and the sum of the area are equal - image_sum = sum(img2) - average_intensity = image_sum / (width * height) + average_intensity = sum(imageBW) / (width * height) # img3 is `grid_definition x grid_definition` and is normalised to the same (sort of) _energy_ as the # original image. - img3 = img2 ./ average_intensity - - single_iteration!(mesh, img3, "it1") - single_iteration!(mesh, img3, "it2") - single_iteration!(mesh, img3, "it3") - - # single_teration(meshy, img3, "it4") - # single_teration(meshy, img3, "it5") - # single_teration(meshy, img3, "it6") + imageBW = imageBW ./ average_intensity + single_iteration!(mesh, imageBW, "it1") + single_iteration!(mesh, imageBW, "it2") + single_iteration!(mesh, imageBW, "it3") - h = find_surface(mesh, img3, 1.0, Artifact_Size) + # single_teration(meshy, imageBW, "it4") + # single_teration(meshy, imageBW, "it5") + # single_teration(meshy, imageBW, "it6") - set_heights!(mesh, h) - solidMesh = create_solid(mesh) - save_stl!( - solidMesh, - "./examples/original_image.obj", - scale = Float64(1 / Grid_Definition * Artifact_Size), - scalez = Float64(1 / Grid_Definition * Artifact_Size), - ) - - return mesh, img3 -end + height_map = find_surface(mesh, imageBW; f = 1.0, picture_width = Caustics_Side) + set_heights!(mesh, height_map) + # solidMesh = create_solid(mesh) -""" -$(SIGNATURES) -""" -function main() - @assert size(ARGS) == (1,) "Intented usage is: julia create_mesh.jl image.png" + # save_stl!( + # solidMesh, + # "./examples/original_image.obj", + # scale = Float64(1 / Grid_Definition * Artifact_Size), + # scalez = Float64(1 / Grid_Definition * Artifact_Size), + # ) - img = Images.load(ARGS[1]) - return engineer_caustics(img) + return mesh, imageBW end - - -""" -$(SIGNATURES) -""" -main() diff --git a/src/io.jl b/src/io.jl index cb3fe68..2fc86b7 100644 --- a/src/io.jl +++ b/src/io.jl @@ -1,5 +1,25 @@ using FileIO, MeshIO + +""" +$(SIGNATURES) + +""" +function convert(::Meshes.SimpleMesh, mesh::FaceMesh) + height, width = size(mesh) + + points = Meshes.Point3.([mesh.topleft[ci] for ci ∈ CartesianIndices(mesh.topleft)]) + + top_connections = + [connect(mesh.toptriangles[ci]) for ci ∈ CartesianIndices(mesh.topleft)] + bot_connections = + [connect(mesh.bottriangles[ci]) for ci ∈ CartesianIndices(mesh.topleft)] + + return SimpleMesh(points, vcat(top_connections, bot_connections)) +end + + + """ $(SIGNATURES) @@ -16,14 +36,14 @@ function save_stl!( flipxy = false, ) + return + height, width = size(mesh) open(filename, "w") do io - println(io, "solid engineered_caustics") for row ∈ 1:height, col ∈ 1:width - # Top triangle top_triangle = top_triangle(mesh, row, col) n = centroid(top_triangle) @@ -40,7 +60,6 @@ function save_stl!( println(io, "v $(n.x * scale) $(n.y * scale) $(n.z * scalez)") end - # Bottom triangle bot_triangle = bottom_triangle(mesh, row, col) n = centroid(bot_triangle) @@ -56,8 +75,6 @@ function save_stl!( else println(io, "v $(n.x * scale) $(n.y * scale) $(n.z * scalez)") end - - end # CHECK what dims exactly represents. Number of triangles? diff --git a/src/parameters.jl b/src/parameters.jl index 349ce06..e72e7c9 100644 --- a/src/parameters.jl +++ b/src/parameters.jl @@ -33,4 +33,4 @@ global Meters_Per_Pixel = Caustics_Height / N_Pixel_Height # calculation const ω = 2 / (1 + π / sqrt(N_Pixel_Height * N_Pixel_Width)) -global n_iterations_convergence = 10_000 # CHECK: What is a reasonable number of iterations? +const N_Iterations_Convergence = 10_000 # CHECK: What is a reasonable number of iterations? diff --git a/src/scratchpad.jl b/src/scratchpad.jl index ea8b4e5..4317fce 100644 --- a/src/scratchpad.jl +++ b/src/scratchpad.jl @@ -1,8 +1,44 @@ -using Images, CausticsEngineering +using Revise +using Images +image = Images.load("./examples/cat_posing.jpg"); # Check current working directory with pwd() -image = Images.load("./examples/cat_posing.jpg") # Check current working directory with pwd() +using CausticsEngineering mesh, image_caustics = engineer_caustics(image); -nothing; -image_caustics' +Gray.(image_caustics') + + +typeof(CartesianIndex(3, 5)[1]) + +t = Matrix{Tuple{CartesianIndex(2),CartesianIndex(2),CartesianIndex(2)}}(undef, 2, 2) + +t[1, 1] = (CartesianIndex(1, 1), CartesianIndex(2, 1), CartesianIndex(1, 2)) +typeof((CartesianIndex(1, 1), CartesianIndex(2, 1), CartesianIndex(1, 2))) + +f = FaceMesh(5, 5); + +f.toptriangles[CartesianIndex(5, 5)] + +f.topleft + + +v3 = CausticsEngineering.top_triangle3D(f, CartesianIndex(5, 5)) +CausticsEngineering.area(v3...) + +v3 = CausticsEngineering.bot_triangle3D(f, CartesianIndex(5, 5)) +CausticsEngineering.area(v3...) + +CausticsEngineering.get_pixel_area(f) + +for _ = 1:100 + h = rand(Float64, (10, 10)) + d = rand(Float64, (10, 10)) + print(CausticsEngineering.relax(h, d)) +end + +c = t[1] + +f.topleft(c) + +t = CausticsEngineering.top_triangle3D(f, CartesianIndex(1, 1)) diff --git a/src/utilities.jl b/src/utilities.jl index f896a94..d4e960d 100644 --- a/src/utilities.jl +++ b/src/utilities.jl @@ -1,3 +1,5 @@ +using StaticArrays + """ $(TYPEDEF) @@ -19,6 +21,7 @@ mutable struct Vertex3D vx::Float64 vy::Float64 + Vertex3D(x, y, z, vx, vy) = new(x, y, z, vx, vy) Vertex3D() = new(0.0, 0.0, Height_Offset, 0.0, 0.0) end @@ -36,11 +39,16 @@ end """ $(SIGNATURES) """ -function dist(p1::Vec3f, p2::Vec3f) - v = p2 .- p1 - return sqrt(sum(v .^ 2)) +function area(v1::Vertex3D, v2::Vertex3D, v3::Vertex3D) + a = dist(v1, v2) + b = dist(v2, v3) + c = dist(v3, v1) + s = (a + b + c) / 2.0 + + return sqrt(s * (s - a) * (s - b) * (s - c)) end + """ $(SIGNATURES) @@ -91,53 +99,64 @@ Rectangle = Nothing $(TYPEDEF) """ struct FaceMesh - size::Tuple{UInt,UInt} + size::Tuple{Int,Int} topleft::AbstractMatrix{Vertex3D} - toptriangles::AbstractMatrix{Tuple{UInt,UInt,UInt}} - bottriangles::AbstractMatrix{Tuple{UInt,UInt,UInt}} + toptriangles::AbstractMatrix{Tuple{CartesianIndex,CartesianIndex,CartesianIndex}} + bottriangles::AbstractMatrix{Tuple{CartesianIndex,CartesianIndex,CartesianIndex}} as_index::Function - function FaceMesh(height::Int, width::Int) - - function as_index(r, c) - if 1 <= r <= height + 1 && 1 <= c <= width - return r + (c - 1) * (width + 1) - else - return nothing - end - end - - m_topleft = Matrix{Vertex3D}(undef, height, width) - t_triangles = Matrix{Tuple{UInt,UInt,UInt}}(undef, height, width) - b_triangles = Matrix{Tuple{UInt,UInt,UInt}}(undef, height, width) - for ci ∈ CartesianIndices(m_topleft) - row = ci[1] - col = ci[2] + FaceMesh(s, tl, tt, bt) = new(s, tl, tt, bt) +end - m_topleft .= (row, col, Top_Offset, 0.0, 0.0) +function FaceMesh(height::Int, width::Int) - t_triangles[ci] = - (as_index(row, col), as_index(row + 1, col), as_index(row, col + 1)) - b_triangles[ci] = - (as_index(row, col + 1), as_index(row + 1, col), as_index(row + 1, col + 1)) + function as_index(r, c) + # Adding "+ 1" since it is the size of the `topleft` matrix + if 1 <= r <= height + 1 && 1 <= c <= width + 1 + return r + (c - 1) * (width + 1) + else + return nothing end - - return new((height, width), m_topleft, t_triangles, b_triangles) end -end - -function convert(Meshes.SimpleMesh, mesh::FaceMesh) - height, width = size(mesh) + as_index(ci::CartesianIndex) = as_index(ci[1], ci[2]) + + m_topleft = Matrix{Vertex3D}(undef, height + 1, width + 1) + t_triangles = Matrix{Tuple{CartesianIndex{2},CartesianIndex{2},CartesianIndex{2}}}( + undef, + height, + width, + ) + b_triangles = Matrix{Tuple{CartesianIndex{2},CartesianIndex{2},CartesianIndex{2}}}( + undef, + height, + width, + ) + + + for ci ∈ CartesianIndices(m_topleft) + row = ci[1] + col = ci[2] + m_topleft[ci] = Vertex3D(row, col, Top_Offset, 0.0, 0.0) + end - points = Meshes.Point3.([mesh.topleft[ci] for ci ∈ CartesianIndices(mesh.topleft)]) + for ci ∈ CartesianIndices(t_triangles) + row = ci[1] + col = ci[2] - top_connections = - [connect(mesh.toptriangles[ci]) for ci ∈ CartesianIndices(mesh.topleft)] - bot_connections = - [connect(mesh.bottriangles[ci]) for ci ∈ CartesianIndices(mesh.topleft)] + t_triangles[ci] = ( + CartesianIndex(row, col), + CartesianIndex(row + 1, col), + CartesianIndex(row, col + 1), + ) + b_triangles[ci] = ( + CartesianIndex(row, col + 1), + CartesianIndex(row + 1, col), + CartesianIndex(row + 1, col + 1), + ) + end - return SimpleMesh(points, vcat(top_connections, bot_connections)) + return FaceMesh((height, width), m_topleft, t_triangles, b_triangles) end @@ -146,7 +165,7 @@ $(TYPEDEF) """ struct Triangle mesh::FaceMesh - points::Tuple{UInt,UInt,UInt} + points::Tuple{Int,Int,Int} function Triangle(mesh::FaceMesh) return Triangle( @@ -157,25 +176,13 @@ struct Triangle end -""" -$(SIGNATURES) -""" -function area(p1::Vec3f, p2::Vec3f, p3::Vec3f) - a = dist(p1, p2) - b = dist(p2, p3) - c = dist(p3, p1) - s = (a + b + c) / 2.0 - - return sqrt(s * (s - a) * (s - b) * (s - c)) -end - """ $(SIGNATURES) Return the dimension of the mesh as the number of rectangles. It does not return the number of corner points. """ -base.size(mesh::FaceMesh) = mesh.size +Base.size(mesh::FaceMesh) = mesh.size """ @@ -183,9 +190,9 @@ $(SIGNATURES) Converts a triangle as a triplet of references to mesh vertices to a triplet of 3D coordinates. """ -function top_triangle3D(mesh::Mesh, ci::CartesianIndex) - if ci ∈ CartesianIndices(mesh.topleft) - t = mesh.top_triangle[ci] +function top_triangle3D(mesh::FaceMesh, ci::CartesianIndex) + if ci ∈ CartesianIndices(mesh.toptriangles) + t = mesh.toptriangles[ci] p1 = mesh.topleft[t[1]] p2 = mesh.topleft[t[2]] p3 = mesh.topleft[t[3]] @@ -195,12 +202,12 @@ function top_triangle3D(mesh::Mesh, ci::CartesianIndex) end end -top_triangle3D(mesh::Mesh, row::UInt, width::UInt) = +top_triangle3D(mesh::FaceMesh, row::Int, width::Int) = top_triangle3D(mesh, CartesianIndex(row, col)) -function bot_triangle3D(mesh::Mesh, ci::CartesianIndex) - if ci ∈ CartesianIndices(mesh.topleft) - t = mesh.bot_triangle[ci] +function bot_triangle3D(mesh::FaceMesh, ci::CartesianIndex) + if ci ∈ CartesianIndices(mesh.bottriangles) + t = mesh.bottriangles[ci] p1 = mesh.topleft[t[1]] p2 = mesh.topleft[t[2]] p3 = mesh.topleft[t[3]] @@ -210,10 +217,11 @@ function bot_triangle3D(mesh::Mesh, ci::CartesianIndex) end end -bot_triangle3D(mesh::Mesh, row::UInt, width::UInt) = +bot_triangle3D(mesh::FaceMesh, row::Int, width::Int) = bot_triangle3D(mesh, CartesianIndex(row, col)) -function triangle3D(mesh::Mesh, ci::CartesianIndex; side = Union{:top,:bottom}) + +function triangle3D(mesh::FaceMesh, ci::CartesianIndex; side = Union{:top,:bottom}) if side == :top return top_triangle3D(mesh, ci) elseif side == :bottom @@ -223,18 +231,18 @@ function triangle3D(mesh::Mesh, ci::CartesianIndex; side = Union{:top,:bottom}) end end -triangle3D(mesh::Mesh, row::Uint, col::UInt; side = Union{:top,:bottom}) = +triangle3D(mesh::FaceMesh, row::Int, col::Int; side = Union{:top,:bottom}) = triangle3D(mesh, CartesianIndex(row, col); side) """ $(SIGNATURES) """ -function centroid(mesh::Mesh, ci::CartesianIndex; side = Union{:top,:bottom}) +function centroid(mesh::FaceMesh, ci::CartesianIndex; side = Union{:top,:bottom}) if side == :top - return centroid(top_triangle3D(mesh, row, col)...) + return centroid(top_triangle3D(mesh, ci)...) elseif side == :bottom - return centroid(bot_triangle3D(mesh, row, col)...) + return centroid(bot_triangle3D(mesh, ci)...) else return missing end @@ -244,7 +252,7 @@ end """ $(SIGNATURES) """ -function area(mesh::Mesh, ci::CartesianIndex; side = Union{:top,:bottom}) +function area(mesh::FaceMesh, ci::CartesianIndex; side = Union{:top,:bottom}) if side == :top return area(top_triangle3D(mesh, ci)...) elseif side == :bottom From c3477a468ccd0285b9c4735b9b7c0e1beceef154 Mon Sep 17 00:00:00 2001 From: Emmanuel-R8 Date: Fri, 3 Sep 2021 16:01:34 +0200 Subject: [PATCH 08/58] Refactoring. Snapshot 6 --- Project.toml | 1 + examples/loss_it10.png | Bin 0 -> 248791 bytes examples/loss_it4.png | Bin 0 -> 248791 bytes examples/loss_it5.png | Bin 0 -> 248791 bytes examples/loss_it6.png | Bin 0 -> 248791 bytes examples/loss_it7.png | Bin 0 -> 248791 bytes examples/loss_it8.png | Bin 0 -> 248791 bytes examples/loss_it9.png | Bin 0 -> 248791 bytes src/CausticsEngineering.jl | 5 ++-- src/create_mesh.jl | 50 ++++++++++++++----------------------- src/scratchpad.jl | 33 +++++++++++++++++++++--- test/runtests.jl | 4 +-- test/triangles.jl | 42 +++++++++++++++++++++++++++++++ 13 files changed, 95 insertions(+), 40 deletions(-) create mode 100644 examples/loss_it10.png create mode 100644 examples/loss_it4.png create mode 100644 examples/loss_it5.png create mode 100644 examples/loss_it6.png create mode 100644 examples/loss_it7.png create mode 100644 examples/loss_it8.png create mode 100644 examples/loss_it9.png create mode 100644 test/triangles.jl diff --git a/Project.toml b/Project.toml index 7596ad2..3bcf539 100644 --- a/Project.toml +++ b/Project.toml @@ -4,6 +4,7 @@ authors = ["Matt Ferraro", "Emmanuel Rialland"] version = "0.1.0" [deps] +Debugger = "31a5f54b-26ea-5ae9-a837-f05ce5417438" DocStringExtensions = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae" Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4" DocumenterTools = "35a29f4d-8980-5a13-9543-d66fff28ecb8" diff --git a/examples/loss_it10.png b/examples/loss_it10.png new file mode 100644 index 0000000000000000000000000000000000000000..2a0709bc5c1476aa8675b8f5dd52c788a96f5fe1 GIT binary patch literal 248791 zcmX`S2UwE(`v=_liH0*5CYl?Z;6idz;Rf6rwQ}Ojow=$bp{1Dv6_s#rvr;tE(-d=% zI4jfgm@7wFj?A>o-pBKQ-xr<>l#A=)%l*CY&w3s*9PF$F`K0)c962J0vo?1+a^!!& zpZ_}oK72}+GP?^rfr7BM*ds?;bNKgtxq<)xigmIwJ#ugO#47NQyuY=R?U5r%%14g; zO*wMpC-BnWD@Tr8)IM_Llh2VOM#V>t9FJoB<7fiB^$5-!>yq%-T6b6uY&B7G^4lp9 z$1&HlYd1X^m8ww6#7`fe)U?xk>tD*>Yo&9)=l|mALDsd+n;*7mBmQehEP+Cx_MPWd zD_m%8ktp=#1;(p`ayx!27B9}ocLyJmCp3Pc?OGLGttrY>w=KvIHigpF)olsv9~cni 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