Sphere Maps with the Near-Equal Solid-Angle Property

Liang Wan and Tien-Tsin Wong ,
Game Developers Conference (GDC2007), March 2007.


Unlike the common spherical maps that sample the sphere unevenly, three sphere maps that own the near-equal solid-angle property are introduced. The first is HEALPix, adopted from astrophysics, which partitions the sphere into equal-area quadrilateral elements. It allows fast integration over the sphere and is especially useful in environment sampling. The second is one of our newly designed maps. It subdivides the sphere with a set of simple equations. Unlike HEALPix, it fits naturally into the six-face cube structure and can fully utilize the hardware operators tailored for traditional cubemap. It samples the sphere in a more balanced fashion than cubemap. The third one uses a family of skew great circles as the subdivision strategy. All texels are distorted similarly. Besides the mathematics, we present the real-time demos to demonstrate their applicabilities to real-time application.

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Related Publications

isocube: HEALPix:
  • "Real-Time Environment Mapping with Equal Solid-Angle Spherical Quad-Map",
    T. T. Wong, L. Wan, C. S. Leung and P. M. Lam,
    Shader X4: Advanced Rendering Techniques, Edited by W. Engel, Charles River Media, 2006, pp. 221-233.