Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs

Eric Heitz 1, *
* Corresponding author
1 MAVERICK - Models and Algorithms for Visualization and Rendering
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : This document is dedicated to answering common questions regarding the masking-shadowing functions in microfacet-based BRDFs. We use the fact that the masking function (or geometric attenuation factor) is constrained by the visible projected area of the microsurface onto the view direction to derive the exact masking function. We introduce the distribution of visible normals from the microsurface, whose normalization factor is the masking function, and we show how the common form of microfacet-based BRDFs emerges from this distribution. The consequence of this is that only exact masking functions ensures correct normalization of microfacet-based BRDFs. Our derivation emphasizes that under the assumptions of common microfacet-based BRDF models, the exact masking function is the generalized form of Smith's masking function. We also discuss the properties of Smith's function used for shadowing and the consequences for the normalization of the BRDF. We review the historical V-cavity model and we show that the underlying surface profile is closer to a normal map than a displacement map. This intuition explains why this non-realistic model is responsible for wrong specular highlights at grazing view angles. Finally, we argue that the insights gained from these observations motivate new research directions in the field of microfacet theory. For instance, we show that masking functions are stretching invariant and we show how this property can be used to derive the masking function for anisotropic microsurface in a straightforward way. We discuss future work such as the incorporation of multiple scattering on the microsurface into BRDF models.
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Contributor : Eric Heitz <>
Submitted on : Wednesday, February 5, 2014 - 6:19:46 PM
Last modification on : Monday, April 9, 2018 - 12:22:29 PM
Long-term archiving on: Sunday, April 9, 2017 - 9:23:56 AM


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  • HAL Id : hal-00942452, version 1



Eric Heitz. Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs. [Research Report] RR-8468, 2014. ⟨hal-00942452v1⟩



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