Raytracing, Math,, Graphics,

Mappings between Sphere, Disc, and Square

A variety of mappings between a sphere and a disc and between a disc and a square, as well as combinations of both, are used in computer graphics applications, resulting in mappings between spheres and squares. Many options exist for each type of mapping; to pick the right methods for a given application requires knowledge about the nature and magnitude of mapping distortions. This paper provides an overview of forward and inverse mappings between a unit sphere, a unit disc, and a unit square. Quality measurements relevant for computer graphics applications are derived from tools used in the field of map projection, and a comparative analysis of the mapping methods is given.