An Elementary Expression for Multiple Scattering in Homogeneous Microflake Media

arXiv cs.GR details Jonathan Dupuy’s new BRDF construction for homogeneous microflake media, aimed at solving a long-standing gap in microfacet theory: an exact multiple-scattering model that is still elementary to evaluate and sample. The key claim is that it handles all scattering orders under the Smith shadowing assumption without falling back to stochastic approximations.

For game and film rendering work, that matters because multiple scattering is where many “physically based” materials start to get expensive or awkward to approximate. A closed-form model can simplify implementation, reduce variance in importance sampling, and make it easier to ship stable looks for rough diffuse-like surfaces, especially when artists need predictable energy behavior across view angles.

The model behaves like Lambertian reflectance at normal incidence, then concentrates reflected energy toward the mirror direction as the view moves toward grazing. Dupuy compares the result against Lambertian shading and state-of-the-art stochastic microfacet BRDFs, positioning the new formulation as both a theoretical answer and a potentially practical shading tool.

The paper was submitted on 17 Sep 2026 and is currently available through arXiv. The exact production use cases haven’t been demonstrated yet, but the combination of exact multi-bounce handling and elementary sampling is the sort of result that can influence future material libraries, offline renderers, and real-time research prototypes.