geometric

Some geometric calculations

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