GGX

GGX, short for the Generalized Trowbridge-Reitz distribution, is a microfacet normal distribution function used in computer graphics to model the distribution of microscopic surface normals on a rough surface. It is a widely adopted component of physically based rendering (PBR) because it yields realistic specular highlights and good energy conservation across a range of roughness values. The GGX distribution is a form of the Trowbridge-Reitz family and is particularly noted for its heavy tails, which allow more contribution from high-curvature microfacets and produce more natural-looking highlights on rough surfaces.

Mathematically, for a microfacet normal h and macroscopic surface normal n, the GGX distribution function D(h) is often written as D(h) = α^2 / [π ((n·h)^2 (α^2 − 1) + 1)^2], where α ≥ 0 is a roughness parameter controlling the spread of the distribution. In many shading models, α is derived from roughness as α = roughness^2 to achieve perceptual linearity. The GGX distribution is defined over the hemisphere around n and is typically used within the microfacet BRDF framework, combined with a geometric shadowing term G and a Fresnel term F to form the specular component.

Usage and properties: GGX is favored in real-time and offline rendering for its balance of physical plausibility and computational efficiency. It provides plausible reflections across a spectrum of roughness levels and pairs with common geometry terms (such as Schlick-GGX) and Fresnel approximations. It is a standard alternative to other distributions like Beckmann in microfacet-based shading.

See also: Microfacet model, Beckmann distribution, Trowbridge-Reitz distribution, Fresnel equations, BRDF.