“Fast approximation to spherical harmonics rotation” by Křivánek, Konttinen, Pattanaik, Bouatouch and Zara

  • ©Jaroslav Křivánek, Jaakko Konttinen, Sumanta N. Pattanaik, Kadi Bouatouch, and Jiri Zara




    Fast approximation to spherical harmonics rotation



    We present a fast and simple approximation of spherical harmonic rotation which decreases the asymptotic complexity and achieves a speedup of four to six in practical applications. The rotation procedure’s simplicity allows implementation in a pixel shader of standard graphics hardware. The main idea is to replace the general spherical harmonic rotation matrix by its truncated Taylor expansion, resulting in a sparse matrix. We show applications in global illumination (radiance interpolation) and GPU-based real-time shading (normal mapping on surfaces with arbitrary BRDFs illuminated by low-frequency environment lighting). Although the rotation approximation is accurate only for small rotation angles, we show this is not a serious limitation in our applications.


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    2. Křivánek, J., Gautron, P., Pattanaik, S., and Bouatouch, K. 2005. Radiance caching for efficient global illumination computation. IEEE TVCG 11, 5.
    3. Sloan, P.-P., Luna, B., and Snyder, J. 2005. Local, deformable precomputed radiance transfer. ACM Trans. Graph. 24, 3, 1216–1223.

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