Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs

Abstract

We provide a new presentation of the masking-shadowing functions (or geometric attenu-ation factors) in microfacet-based BRDFs and answer some common questions about their applications. Our main motivation is to define a correct (geometrically indicated), physically based masking function for application in microfacet models, as well as the properties that function should exhibit. Indeed, several different masking functions are often presented in the literature and making the right choice is not always obvious. We start by showing that physically based masking functions are constrained by the projected area of the visible micro-surface onto the outgoing direction. We use this property to derive the distribution of visible normals from the microsurface, whose normalization factor is the masking function. We then show how the common form of microfacet-based BRDFs emerges from this distribution. As a consequence, the masking function is related to the correct normalization of microfacet-based BRDFs. However, while the correct masking function satisfies these normalization constraints, its explicit form is can only be determined for a given microsurface profile. Our derivation emphasizes that under the assumptions of their respective microsurface