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Specular BRDF Reference

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Brian Karis (Epic Games)

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Description

Brian Karis's comparison page on Graphic Rants, written while building Unreal Engine 4's physically based shading model. It places Cook-Torrance microfacet terms side by side using consistent notation and UE4's roughness parameterization (alpha equals roughness squared).

The page catalogs Normal Distribution Functions (Blinn-Phong, Beckmann, GGX, anisotropic GGX), geometry shadowing terms (Implicit, Neumann, Cook-Torrance, Smith variants), and Fresnel formulations with literature citations. An optimized HLSL block shows how Smith GGX combines with the BRDF denominator for production shaders.

Advanced graphics programmers implementing or auditing PBR specular models should read it. Notation matches Naty Hoffman's SIGGRAPH shading courses. Helpful when porting Disney or UE-style BRDFs to custom engines.

Single long-form blog post from 2013, still cited because it unifies naming across papers. Free; equations render inline on the Blogger page.

Widely cited in the PBR community as the standard notation reference for comparing microfacet BRDF implementations.