A practical algorithm for rendering interreflections with all-frequency BRDFs

Algorithms for rendering interreflection (or indirect illumination) effects often make assumptions about the frequency range of the materials' reflectance properties. For example, methods based on Virtual Point Lights (VPLs) perform well for diffuse and semi-glossy materials but not so for highly glossy or specular materials; the situation is reversed for methods based on ray tracing. In this article, we present a practical algorithm for rendering interreflection effects with all-frequency BRDFs. Our method builds upon a spherical Gaussian representation of the BRDF, based on which a novel mathematical development of the interreflection equation is made. This allows us to efficiently compute one-bounce interreflection from a triangle to a shading point, by using an analytic formula combined with a piecewise linear approximation. We show through evaluation that this method is accurate for a wide range of BRDFs. We further introduce a hierarchical integration method to handle complex scenes (i.e., many triangles) with bounded errors. Finally, we have implemented the present algorithm on the GPU, achieving rendering performance ranging from near interactive to a few seconds per frame for various scenes with different complexity.