Understanding the Masking-Shadowing Function
in Microfacet-Based BRDFs

Author: Eric Heitz
INRIA; CNRS; Univ. Grenoble Alpes

Editors: Stephen Hill
Ubisoft Montreal

Naty Hoffman
2K

Editor-in-Chief: Morgan McGuire
NVIDIA & Williams College

Abstract

We provide a new presentation of the masking-shadowing functions (or geometric attenuation 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 profiles, both Smith's function and the V-cavity masking function are correct. However, we show that the V-cavity microsurface yields results that miss the effect of occlusion, making it analogous to the shading of a normal map instead of a displacement map. This observation explains why the V-cavity model yields incorrect glossy highlights at grazing view angles.

We also review other common masking functions, which are not associated with a micro-surface profile and thus are not physically based. The insights gained from these observations motivate new research directions in the field of microfacet theory. For instance, we show that masking functions are stretch invariant and we show how this property can be used to derive the masking function for anisotropic microsurfaces in a straightforward way. We also discuss future work such as the incorporation of multiple scattering on the microsurface into BRDF models.


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Citation: Eric Heitz, Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs, Journal of Computer Graphics Techniques (JCGT), vol. 3, no. 2, 48-107, 2014
Available online http://jcgt.org/published/0003/02/03/

Copyright: © 2014 Heitz

Received: 2014-01-24; Recommended: 2014-05-14; Published: 2014-06-30