Models for what a surface does to light that hits it.
Colour is the family; a dashed line is the second member of it.
Derives the fraction of microfacets visible from a given direction from the normal distribution itself, rather than being an independent invented fun… · 1967
The optics paper that introduced the microfacet formulation, developed to explain off-specular peaks in measured reflectance that mirror models could… · 1967
An empirical specular lobe: the cosine between the reflection vector and the view, raised to a power. No physical basis, but it was the first shading… · 1975
Replaces Phong's reflection vector with the half vector between light and view. Cheaper, and the resulting highlight elongates at grazing angles the… · 1977
Brought microfacet theory into graphics, with spectral Fresnel and a proper distinction between metals and dielectrics. The direct ancestor of every… · 1982
An early reflectance model with separate roughness along two tangent directions, capturing brushed metal and other surfaces whose highlight stretches… · 1992
Models a diffuse surface as a distribution of Lambertian V-cavities, which produces the flat, backscattering look of rough materials such as clay, co… · 1994
Approximates Fresnel reflectance as a fifth-power interpolation between normal incidence reflectance and one. Accurate enough for dielectrics and che… · 1994
Relates light entering at one point to light leaving at another, rather than assuming both happen at the same place. Necessary for skin, marble and m… · 2001
Approximates subsurface transport with a pair of virtual light sources straddling the surface, reducing a volumetric simulation to a closed- form fal… · 2001
Models a hair as a dielectric cylinder with a tilted cuticle, splitting scattering into reflection, transmission and internal reflection lobes. Expla… · 2003
Densely measured reflectance for a hundred real materials. The de facto ground truth that analytic models are fitted and compared against. · 2003
A microfacet normal distribution with a much longer tail than Beckmann. The tail is the whole point: it reproduces the soft, wide falloff around high… · 2007
Composes a stack of smooth or rough interfaces into a single BSDF by tracking attenuation between them, giving car paint and lacquered wood without s… · 2007
Treats a rough surface as a statistical field of tiny perfect mirrors. The BSDF factors into a normal distribution D, a Fresnel term F and a masking-… · 2007
A single artist-facing parameter set, all normalized to zero-to-one, fitted against measured data. Its influence is mostly social: it made one vocabu… · 2012
Reparameterizes conductor Fresnel from complex indices of refraction, which nobody can author, into reflectivity and edge tint, which can be picked f… · 2014
Accounts for the fact that a microfacet hidden from the light is likely to be hidden from the view as well, since both depend on the same height fiel… · 2014
Replaces the dipole's physically derived profile with a two-exponential curve fitted directly to Monte Carlo ground truth, which matches measured ski… · 2015
Random-walks light between microfacets instead of discarding whatever the masking term blocks. Rough metals stop going dark, which is the visible sym… · 2016
Precomputes the directional albedo a single-scattering microfacet BRDF loses and adds a fitted lobe back to make up the difference. Far cheaper than… · 2017
Models wave interference in a coating a few wavelengths thick, which makes reflectance shift with angle and produces the colours of soap films, oil s… · 2017
Represents each layer's effect as an operator on the mean and variance of a lobe, so light scattering between interfaces is carried through the stack… · 2018
Samples the distribution of microfacet normals actually visible from the view direction, rather than the full distribution. Every sample is usable, a… · 2018
Extends statistical layering to stacks containing diffuse interfaces, which the lobe-variance formulation could not represent. · 2022
A Gaussian distribution of microfacet slopes, derived from physical optics. Its tail falls off quickly, so highlights end more abruptly than measured…
Light that enters a surface, scatters under it and re-emerges in a broad distribution largely independent of the incoming direction.
Give the fraction of light reflected rather than transmitted at an interface, as a function of angle and the two indices of refraction. Reflectance r…
A constant BRDF: outgoing radiance is the same in every direction, so the surface looks equally bright from any viewpoint. Cheap, reciprocal, and the…
Light reflected about the surface normal, concentrated in a lobe whose width is set by how rough the interface is.