A Multiscale Microfacet Model Based On Inverse Bin Mapping

Accurately controllable shading detail is a crucial aspect of realistic appearance modelling. Two fundamental building blocks for this are microfacet BRDFs, which describe the statistical behaviour of infinitely small facets, and normal maps, which provide user-controllable spatio-directional surface features. We analyse the filtering of the combined effect of a microfacet BRDF and a normal map. By partitioning the half-vector domain into bins we show that the filtering problem can be reduced to evaluation of an integral histogram (IH), a generalization of a summed-area table (SAT). Integral histograms are known for their large memory requirements, which are usually proportional to the number of bins. To alleviate this, we introduce Inverse Bin Maps, a specialised form of IH with a memory footprint that is practically independent of the number of bins. Based on these, we present a memory-efficient, production-ready approach for filtering of high resolution normal maps with arbitrary Beckmann flake roughness. In the corner case of specular normal maps (zero, or very small roughness values) our method shows similar convergence rates to the current state of the art, and is also more memory efficient.