Interactive Rendering with Bidirectional Texture Functions

We propose a new technique for efficiently rendering bidirectional texture functions (BTFs). A 6D BTF describes the appearance of a material as a texture that depends on the lighting and viewing directions. As such, a BTF accommodates self-shadowing, interreflection, and masking effects of a complex material without needing an explicit representation of the small scale geometry. Our method represents the BTF as a set of spatially varying apparent BRDFs, that each encode the reflectance field of a single pixel in the BTF. Each apparent BRDF is decomposed into a product of three or more two-dimensional positive factors using a novel factorization technique, which we call chained matrix factorization (CMF). The proposed factorization technique is fully automatic and suitable for both BRDFs and apparent BRDFs (which typically exhibit off-specular peaks and non-reciprocity). The main benefit of CMF is that it delivers factors well suited for the limited dynamic range of conventional texture maps. After factorization, an efficient representation of the BTF is obtained by clustering the factors into a compact set of 2D textures. With this compact representation, BTFs can be rendered on recent consumer level hardware with arbitrary viewing and lighting directions at interactive rates.