NVIDIA Research: An Analytic BRDF for Materials with Spherical Lambertian Scatterers

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Researchers at NVIDIA presented a new paper “An Analytic BRDF for Materials with Spherical Lambertian Scatterers” at Eurographics Symposium on Rendering 2021 (EGSR), June 29-July 2, introducing a new BRDF for dusty/diffuse surfaces. 

Our new Lambert-sphere BRDF (right) accurately and efficiently models the reflectance of a porous microstructure consisting of Lambertian spherical particles.

Most rough diffuse BRDFs such as Oren-Nayar are based on a random height-field microsurface, which limits the range of roughnesses that are physically plausible (a height field can only get so spiky before it becomes implausible). To avoid this limitation and extend the usable range of rough diffuse BDRFs, we take a volumetric approach to surface microstructure to derive BRDF for very rough diffuse materials. It is simple and intuitive to control with a single diffuse color parameter and it produces more saturated colors and backscattering than other models.

The intersection of volume and surface representations in computer graphics is seeing a rapid growth with new techniques such as NeRF. Our ability to seamlessly interchange between surface and volume descriptions of the same scene with no noticeable appearance change is an important tool for efficiently authoring and rendering complex scenes. A BRDF is one such form of representation interchange. In this case, we derive the BRDF that simulates a porous volumetric microstructure consisting of Lambertian spherical particles (pictured above). In some sense this results in an infinitely rough version of the Oren-Nayar BRDF. The resulting BRDF can be used to render diffuse porous materials such as foam up to 100 times more efficiently than using stochastic random walk methods.

Our new Lambert-sphere BRDF produces brighter backscattering and more saturated rim lighting than other diffuse BRDFs.

We call our BRDF the Lambert-sphere (LS) BRDF. We present a highly accurate version that is only 30% slower to evaluate than Oren-Nayar, and a faster approximate version for real-time applications. We also include importance sampling for the Lambertian-sphere phase function for use rendering large diffusive smoke and debris particles. Below we compare our BRDF to Lambertian, Oren-Nayar and Chandrasekhar’s BRDF that consists of a thick volumetric layer of mirror spheres in an absorbing matrix.

Learn more: Check out the project website.