Microsurface Transformations

Abstract

We 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 closed‐form 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.

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