Atanasov, AsenKoylazov, VladimirDimov, RossenWilkie, AlexanderGhosh, AbhijeetWei, Li-Yi2022-07-012022-07-0120221467-8659https://doi.org/10.1111/cgf.14590https://diglib.eg.org:443/handle/10.1111/cgf14590We derive a general result in microfacet theory: given an arbitrary microsurface defined via standard microfacet statistics, we show how to construct the statistics of its linearly transformed counterparts. A common use case of such transformations is to generate anisotropic versions of a given surface. Traditional anisotropic derivations based on varying the roughness of an isotropic distribution in an ellipse have a general closed-form formula only for the subclass of shape-invariant distributions. While our formulation is equivalent to these specific constructs, it is more general in two aspects: it leads to simple closedform solutions for all distributions, including shape-variant ones, and works for all invertible 2D transform matrices. The latter is of particular importance in case of deformation of the macrosurface, since it can be approximated locally by a linear transformation in the tangent plane. We demonstrate our results using the Generalized Trowbridge-Reitz (GTR) distribution which is shape-invariant only in the special case of the popular Trowbridge-Reitz (GGX) distribution.CCS Concepts: Computing methodologies --> Rendering; Reflectance modelingComputing methodologiesRenderingReflectance modeling10.1111/cgf.14590105-11612 pages