Efficient multiple scattering in hair using spherical harmonics

Previous research has shown that a global multiple scattering simulation is needed to achieve physically realistic renderings of hair, particularly light-colored hair with low absorption. However, previous methods have either sacrificed accuracy or have been too computationally expensive for practical use. In this paper we describe a physically based, volumetric rendering method that computes multiple scattering solutions, including directional effects, much faster than previous accurate methods. Our two-pass method first traces light paths through a volumetric representation of the hair, contributing power to a 3D grid of spherical harmonic coefficients that store the directional distribution of scattered radiance everywhere in the hair volume. Then, in a ray tracing pass, multiple scattering is computed by integrating the stored radiance against the scattering functions of visible fibers using an efficient matrix multiplication. Single scattering is computed using conventional direct illumination methods. In our comparisons the new method produces quality similar to that of the best previous methods, but computes multiple scattering more than 10 times faster.