5.1.10 Torus

The syntax of the torus object is:

TORUS:
  torus { MAJOR_RADIUS, MINOR_RADIUS [TORUS_MODIFIERS] }

TORUS_MODIFIERS:
  [sturm [BOOL]] & [OBJECT_MODIFIERS]

See also:

• [pov:6.5.1.14]Torus
• [pov:3.2.5]Torus Object
• www.f-lohmueller.de/.../torus1e.htm

This is the particular case of a surface of revolution, where a disk of radius MINOR_RADIUS($=r$) and center at the $x$-axes in distance MAJOR_RADIUS($=R$) from 0 is rotated around the $y$-axes.

Figure: Tori

In parametric form this surface is given by latitude $\th\in[-\pi,\pi]$ and longitude $\varphi \in[0,2\pi]$ as

$$\langle\th ,\varphi \rangle\mapsto \langle (R+r\cos\th )\cos\varphi ,(R+r\cos\th )\sin\varphi ,r\sin\th\rangle$$

or implicitly by

$$(\sqrt{x^2+z^2}-R)^2+y^2=r^2.$$