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.
We present triple sphere, a method to integrate spherical lights over spherical caps via spherical harmonics for rendering applications.