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Collision Detection

Overview

What is Collision Detection?

Which objects are occupying the same space, partially or fully, at the same time?
- or will in the future?

British pool table pocket

Challenges in Collision Detection 1

Is there a collision between A and B?
Where was the collision?
When was the collision? (or will be?)

Challenges in Collision Detection 2

Computational cost
- Which objects can collide with each other?
- How many collision tests do we need to do?
- How expensive are collision tests?

Challenges in Collision Detection 3

When do run collision detection?
- discrete vs. continuous collision detection
Accuracy of collision detection
- Small objects
- Fast objects
- Complex objects (lots of polygons)

A problem with simulation rate and collision

fastObjects

A problem with simulation rate and collision 2

set a minimum size for objects
set a maximum speed for objects
consider time in collision detection
- do continuous collision detection

Collision objects

Collisions between objects of arbitrarily complex geometry is expensive
- use simpler geometry for objects
- at least until we know we need something better
- i.e. cheat, at least some of the time

Make it work, then make it fast

Important

Make you program work first. Then make if fast

Tip	Ideally, we’d profile our code to see which parts use lots of time and use that for guidance. Your IDE may be able to help you with this.

What types of (simple) geometry are there?

Point
Line / Plane
Circle / Sphere
Rectangle / Cuboid (AKA: Boxes)
- Axis-Aligned
- non-Axis-Aligned
Triangle / ???
Convex Polygon / Convex Polyhedron
Concave Polygon / Concave Polyhedron

What types of geometry are easy to collide with what other types?

Circle-Circle / Sphere-Sphere
Circle-Line / Sphere-Plane
Axis-Aligned-Box vs Axis-Aligned-Box
non-Axis-Aligned vs non-Axis-Aligned
Convex polygon / Convex polyhedron
Concave polygon / Concave polyhedron

Convex polygon vs. Concave polyhedron

1083px Convex polygon illustration1

1024px non Convex polygon illustration2

What types of geometry are easy to collide with what other types?

	Point	Line	Circle	AAB	Box	Convex	Concave
Point	???	-	-	-	-	-	-
Line	???	???	-	-	-	-	-
Circle	???	???	???	-	-	-	-
AAB	???	???	???	???	-	-	-
Box	???	???	???	???	???	-	-
Convex	???	???	???	???	???	???	-
Concave	???	???	???	???	???	???	???

What types of geometry are easy to collide with what other types?

	Point	Line	Circle	AAB	Box	Convex	Concave
Point	:-)	-	-	-	-	-	-
Line	:-)	:-)	-	-	-	-	-
Circle	:-)	:-)	:-)	-	-	-	-
AAB	:-)	:-)	:-)	:-)	-	-	-
Box	OK	OK	:-(	OK	OK	-	-
Convex	OK	OK	:-(	:-(	:-(	:-(	-
Concave	:-(	:-(	HARD	HARD	HARD	HARD	HARD

Circle-Circle / Sphere-Sphere

Distance between centers is less than the sum of the radii

Distance between centers

Distance between two points
Square-root of the sum of the squares (Pythagoras, again)

Sum of the radii

Radius A plus Radius B

Circle-Line / Sphere-Plane

For axis-aligned line/plane, non collision if:
- ???

Circle-Line / Sphere-Plane 2

For axis-aligned line/plane, non collision if:
- Circle center + radius < axisValue
- Circle center - radius > axisValue

Circle-Line / Sphere-Plane 3

Generically, use dot-product
- look up "Circle-Line" intersection

Axis-Aligned-Box vs Axis-Aligned-Box

For each box, for each axis, have a minimum and a maximum value
- AKA an interval
non-collision on ANY axis ⇒ non-collision
test for each axis (X, Y, Z):
- ???

Test for each axis (X, Y, Z)

All of A is lower than B
— or —
All of B is lower than A

Test for each axis (X, Y, Z) 2

All of A is lower than B
- ⇒ Amax < Bmin
— or —
All of B is lower than A
- ⇒ Bmax < Amin

Collision resolution

What to do when we find a Collision
Various options, including:
1. calculate next positions, for collisions apply forces
2. calculate next positions, for collisions change velocities
  - physically (real-world) unrealistic
3. calculate next positions, for collisions change positions
  - very physically (real-world) unrealistic
4. store present position, calculate next positions, for collisions revert to stored

Collision non-resolution

Many "collisions" don’t result in physical changes, but game logic changes. e.g.
- pick ups
- deaths
- hits (bullets hit things and disappear)

Coordinate System

Warning

SDL’s draw functions (e.g. SDL_RenderCopy, SDL_RenderFillRect) work in Window Coordinates

Tip	You DON’T want to. You WANT to work in something independent of the resolution, and less discrete. i.e. some floating point system.

Tip	You’ll need (WANT) to convert from your coordinate system to Window coordinates (remember linear transformations and matrices …).

Tip	You can choose where your origin is. Where makes most sense to you?

Tip	You can choose which way is positive - e.g. does the y-value increase as you go DOWN the Window, or increase as you go UP the window

Coordinates for our sprites

SDL’s draw functions use a position (top-left) and a height and width
- these may not be the most useful/natural for us
We may want to make our sprite interface talk about sprite centers, and translate that when we draw

Debug Draw

Tip	Collision detection can be difficult to debug. Have a mode where you render the collision bounds can be really helpful.

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