Representation

2D

• Line

  • [a, b, c] for $ax+by+c=0$, where $\sqrt{a^2+b^2}=1$

• Circle

  • [[a, b], r, [0.0, 0.0, 1.0, 0.0]] for $(x-a)^2+(y-b)^2=r^2$
  • The last term, [0.0, 0.0, 1.0, 0.0]], means that the circle lies in the plane $z=0$, which is ignorable

3D

• Line
  • [[a, b, c], [r, s, t]] for $x=a+rk$, $y=b+sk$, $z=c+tk$, where $\sqrt{r^2+s^2+t^2}=1,k\in\mathbb{R}$
• Plane
  • [a, b, c, d] for $ax+by+cz+d=0$, where $\sqrt{a^2+b^2+c^2}=1$
• Circle
  • [[x_c, y_c, z_c], r, [a, b, c, d]] for circle lies in plane [a, b, c, d], center at [x_c, y_c, z_c] and with radius r
• Sphere
  • [[a, b, c], r] for sphere center at [a, b, c] and with radius r
• Cylinder
  • [[a, b, c], h, r, [nx, ny, nz]] where
    • [a, b, c] is the center of the base circle in 3D space
    • h and r are the height and the radius of the cylinder, respectively
    • [nx, ny, nz] is the direction vector of the cylinder's direction axis