public static class Torus
extends java.lang.Object
Let the radius from the center of the hole to the center of the torus tube be R, and the radius of
the tube be r. Then the equation in Cartesian coordinates for a torus azimuthally symmetric about
the z-axis is
(R - sqrt(x^2+y^2))^2 + z^2 = r^2
and the parametric equations are
x = (R + rcos(v)) cos(u)
y = (R + rsin(v)) sin(u)
z = rsin(v)
for u, v in [0, 2PI[
The three different classes of standard tori correspond to the three possible relative sizes of r
and R. When R > r, the surface will be the familiar ring torus. The case R = r corresponds to the
horn torus, which in effect is a torus with no "hole". The case R < r describes the self-intersecting
spindle torus. When R = 0, the torus degenerates to the sphere.
- See Also:
- Serialized Form