The Layer Laboratory: A Calculus for Additive and Subtractive Composition of Anisotropic Surface Reflectance

We present a versatile computational framework for modeling the reflective and transmissive properties of arbitrarily layered anisotropic material structures. Given a set of input layers, our model synthesizes an effective BSDF of the entire structure, which accounts for all orders of internal scattering and is efficient to sample and evaluate in modern rendering systems. Our technique builds on the insight that reflectance data is sparse when expanded into a suitable frequency-space representation, and that this property extends to the class of anisotropic materials. This sparsity enables an efficient matrix calculus that admits the entire space of BSDFs and considerably expands the scope of prior work on layered material modeling. We show how both measured data and the popular class of microfacet models can be expressed in our representation, and how the presence of anisotropy leads to a weak coupling between Fourier orders in frequency space. In addition to additive composition, our models supports subtractive composition, a fascinating new operation that reconstructs the BSDF of a material that can only be observed indirectly through another layer with known reflectance properties. The operation produces a new BSDF of the desired layer as if measured in isolation. Subtractive composition can be interpreted as a type of deconvolution that removes both internal scattering and blurring due to transmission through the known layer. We experimentally demonstrate the accuracy and scope of our model and validate both additive and subtractive composition using measurements of real-world layered materials. Both implementation and data will be released to ensure full reproducibility of all of our results.(1)