Indirection mapping for quasi-conformal relief texturing

Heightfield terrain and parallax occlusion mapping (POM) are popular rendering techniques in games. They can be thought of as per-vertex and per-pixel relief methods, which both create texture stretch artifacts at steep slopes. To ameliorate stretching artifacts, we describe how to precompute an indirection map that transforms traditional texture coordinates into a quasi-conformal parameterization on the relief surface. The map arises from iteratively relaxing a spring network. Because it is independent of the resolution of the base geometry, indirection mapping can be used with POM, heightfields, and any other displacement effect. Noisy textures like grass and stucco can be used with indirection mapped (which is convenient when texturing terrain.) We pre-warp structured textures by the inverse of the indirection map to maintain their appearance. Our process gives approximately uniform texture resolution on all surfaces. During rendering, the time and space overhead are one texture fetch and one texture map.