Multiple scattering from distributions of specular v-grooves

Microfacet-based reflection models are the most common way to represent reflection from rough surfaces. However, a major current limitation of these models is that they only account for single scattering. Unfortunately, single scattering models do not preserve energy. In this paper, we develop a microfacet BRDF for specular v-grooves that includes multiple scattering. Our approach is based on previous work by Zipin, who showed that the number of reflections inside a specular v-groove is bounded and analytically computable. Using his insight, we present a closed form solution for the BRDF and its probability density function (PDF); we also present a method for importance sampling the BRDF. As a result, our BRDF can be easily used within a path-traced rendering system such as PBRT. The model supports any microfacet distribution function, and spatially-varying surface roughness. The images produced by the model have a pleasing appearance compared to traditional single-scattering models.