Integrating Clipped Spherical Harmonics Expansions

  title={Integrating Clipped Spherical Harmonics Expansions},
  author={Laurent Belcour and Guofu Xie and Christophe Hery and Mark Meyer and Wojciech Jarosz and Derek Nowrouzezahrai},
  journal={ACM Trans. Graph.},
Many applications in rendering rely on integrating functions over spherical polygons. We present a new numerical solution for computing the integral of spherical harmonics (SH) expansions clipped to polygonal domains. Our solution, based on zonal decompositions of spherical integrands and discrete contour integration, introduces an important numerical operating for SH expansions in rendering applications. Our method is simple, efficient, and scales linearly in the bandlimited integrand’s… CONTINUE READING


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