5.1.1 Sphere

The syntax of the sphere object is:

SPHERE:
  sphere { CENTER, RADIUS [SPHERE_MODIFIERS] }

SPHERE_MODIFIERS:
  [UV_MAPPING] & [OBJECT_MODIFIERS]

Figure: Spheres

See also:

• [pov:6.5.1.9]Sphere
• [pov:3.1.4]Sphere Object
• www.f-lohmueller.de/.../sphere1e.htm

The object described is a sphere (or more correctly a ball, and not just the surface) with the 3d-vector CENTER $(=\langle c_1,c_2,c_3\rangle)$ as center and with the scalar RADIUS$(=r)$ as radius:

$$\{\langle x_1,x_2,x_3 \rangle: (x_1-c_1)^2+(x_2-c_2)^2+(x_3-c_3)^2\leq r^2\}.$$

Each object may contain transformations as part of the OBJECT_MODIFIERS, so a general sphere may be described by the default sphere with CENTER=0 and RADIUS=1 as follows:

sphere { c, r } = sphere { 0, 1 scale r translate c }