Microfacet Theory for Non-Uniform Heightfields

We propose new methods for combining NDFs in microfacet theory, enabling a wider range of surface statistics. The new BSDFs that follow allow for independent adjustment of appearance at grazing angles, and can't be represented by linear blends of single-NDF BSDFs. We derive importance sampling for a symmetric operator that blends NDFs uniformly, and introduce a new asymmetric operator that supports NDF variation with elevation. We also extend Smith's model to support piecewise-constant NDF and material variations with elevation, and demonstrate accuracy via Monte Carlo simulations.