Coordinate mapping between sphere, disc and square

This paper, published by Martin Lambers in the Journal of Computer Graphics Techniques, compares different mappings between sphere and disc, and between disc and square. It is worth noting that the source code is available on the publication page.

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.

Capturing and rendering tiny details

Not so long ago I discovered this article presenting the CLEAN mapping technique used in Civilization V to manage how detail gets filtered with distance. I found the side effect of emerging anisotropic surfaces very seducing.

This week Angelo Pesce wrote some thoughts on how the problem of how to represent and render detail in general, how normal maps are not so well suited and what can be done instead.