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 : We give a new presentation of the masking-shadowing functions in microfacet-based BRDFs and answer some common questions about their applications. We use the fact that the masking function (or geometric attenuation factor) is constrained by the visible projected area of the microsurface onto the outgoing direction to derive the properties of 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 ensure correct normalization of microfacet-based BRDFs. However, the exact masking function that satisfies these properties can be determined only if a microsurface profile is chosen. Our derivation emphasizes that under the assumptions of their respective microsurface profiles, Smith's and the historical V-cavity masking functions are both exact. However, we show that the V-cavity microsurface 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. 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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Eric Heitz. Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs. [Research Report] RR-8468, INRIA. 2014. ⟨hal-00942452v2⟩

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