Spherical Light Integration over Spherical Caps via Spherical Harmonics

Abstract

Spherical area light sources are widely used in synthetic rendering. However, traditional Monte Carlo methods can require an excessive number of samples for sufficient accuracy. We propose a Spherical Harmonics (SH) based method to provide a trade-off between performance and accuracy. Our key idea is an analytical integration of SH over spherical caps. The SH integration is first decomposed into a weighted sum of Zonal Harmonics (ZH) integration, which could be evaluated using recurrence formulae. The resulting integration could then be used for rendering spherical area lights efficiently, saving 50% light samples at best while maintaining competitive accuracy. Our method can easily fit into an existing SH based rendering framework to support near-field sphere lighting.