Points on a sphere's surface are computed from two angles using nested sin and cos

While a 2D circle requires one angle to locate points on its perimeter, a 3D sphere requires two angles (s and t). The formulas: x = centX + (radius * cos(s) * sin(t)); y = centY + (radius * sin(s) * sin(t)); z = centZ + (radius * cos(t)). To draw a sphere surface manually, iterate both angles: t from 0° to 180° (polar angle), s cycling multiple times per t increment to spiral around the surface. This gives the artist control over how the sphere is traversed — creating spirals, latitude bands, or other non-standard distributions of points. Adding Perlin noise to the radius at each point creates organic deformation (as in Pearson’s Frosti video piece).

Examples

Spiraling around a sphere: while (t < 180) { s += 18; t += 1; float x = 0 + (radius * cos(radians(s)) * sin(radians(t))); ...} Frosti (2010) applies Perlin noise to the radius at each spherical point to create an organic deformed-sphere video work.

Assessment

Given the sphere coordinate formulas, explain why uniform random s and t gives denser points at the poles, and describe one approach to achieve a more uniform distribution.