Computer Graphics

Materials and BSDFs

Models for what a surface does to light that hits it.

Colour is the family; a dashed line is the second member of it.

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G artist-friendly-fresnel Artist-Friendly Metallic Fresnel fresnel Fresnel Equations artist-friendly-fresnel->fresnel reflectivity and edge tint, not unauthorable complex IOR beckmann Beckmann Distribution microfacet-model Microfacet Model beckmann->microfacet-model supplies a Gaussian slope distribution as D blinn-phong Blinn-Phong phong Phong blinn-phong->phong the half vector is cheaper and behaves at grazing angles bssrdf BSSRDF bsdf BSDF bssrdf->bsdf light can leave far from where it entered cook-torrance Cook-Torrance cook-torrance->microfacet-model first graphics-side instance of the framework correlated-smith Height-Correlated Smith smith-masking Smith Masking- Shadowing correlated-smith->smith-masking incident and exitant masks are related, not independent diffuse-layering Layering with Diffuse Interfaces statistical-operators-layering Statistical Operators Layering diffuse-layering->statistical-operators-layering diffuse interfaces, not just rough specular ones diffuse-reflection Diffuse Reflection reflection Reflection diffuse-reflection->reflection dipole-diffusion Dipole Diffusion Approximation dipole-diffusion->bssrdf a closed-form falloff instead of volumetric transport disney-principled-brdf Disney Principled BRDF merl-database MERL BRDF Database disney-principled-brdf->merl-database the lobes were fitted against measured materials disney-principled-brdf->microfacet-model wraps it in parameters artists can actually author fresnel->reflection refraction Refraction fresnel->refraction the split between the two is what it computes ggx GGX / Trowbridge- Reitz ggx->beckmann longer tail fits measured materials better ggx->microfacet-model supplies a long-tailed slope distribution as D hair-bsdf Hair Scattering Model hair-bsdf->bsdf a fibre scatters around its axis, not a normal kulla-conty Kulla-Conty Energy Compensation multiple-scattering-microfacet Multiple-Scattering Microfacet BSDF kulla-conty->multiple-scattering-microfacet adds lost energy back from a table instead of walking lambert Lambertian Diffuse lambert->diffuse-reflection the simplest case, a constant BRDF layering Coated Layer Model layering->microfacet-model microfacet layers stacked into a single BSDF brdf BRDF merl-database->brdf measured ground truth to fit analytic models against microfacet-model->fresnel each microfacet is a mirror, so needs its reflectance microfacet-model->smith-masking microfacets occlude each other at grazing angles microfacet-model->bsdf derives the BSDF from a statistical surface model multiple-scattering-microfacet->smith-masking some hits are lost in scatter, never re-emitted normalized-diffusion Normalized Diffusion normalized-diffusion->dipole-diffusion the dipole fits poorly close to the entry point oren-nayar Oren-Nayar oren-nayar->lambert V-cavity distribution: rough surfaces flatten at grazing angles specular-reflection Specular Reflection phong->specular-reflection an ad hoc cosine-power lobe with no physical basis schlick Schlick's Approximation schlick->fresnel a fifth-power curve instead of the full equations smith-masking->microfacet-model specular-reflection->reflection statistical-operators-layering->layering scattering between interfaces, tracked as variance thin-film-iridescence Thin-Film Iridescence thin-film-iridescence->fresnel interference in a thin coat makes reflectance shift torrance-sparrow Torrance-Sparrow torrance-sparrow->microfacet-model vndf Visible Normal Distribution Sampling vndf->ggx can't hit back-facing normals ward-anisotropic Ward Anisotropic Model ward-anisotropic->specular-reflection roughness differs along two tangent directions

30 nodes

Smith Masking-Shadowing

Derives the fraction of microfacets visible from a given direction from the normal distribution itself, rather than being an independent invented fun… · 1967

Torrance-Sparrow

The optics paper that introduced the microfacet formulation, developed to explain off-specular peaks in measured reflectance that mirror models could… · 1967

Phong

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

Blinn-Phong

Replaces Phong's reflection vector with the half vector between light and view. Cheaper, and the resulting highlight elongates at grazing angles the… · 1977

Cook-Torrance

Brought microfacet theory into graphics, with spectral Fresnel and a proper distinction between metals and dielectrics. The direct ancestor of every… · 1982

Ward Anisotropic Model

An early reflectance model with separate roughness along two tangent directions, capturing brushed metal and other surfaces whose highlight stretches… · 1992

Oren-Nayar

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

Schlick's Approximation

Approximates Fresnel reflectance as a fifth-power interpolation between normal incidence reflectance and one. Accurate enough for dielectrics and che… · 1994

BSSRDF

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

Dipole Diffusion Approximation

Approximates subsurface transport with a pair of virtual light sources straddling the surface, reducing a volumetric simulation to a closed- form fal… · 2001

Hair Scattering Model

Models a hair as a dielectric cylinder with a tilted cuticle, splitting scattering into reflection, transmission and internal reflection lobes. Expla… · 2003

MERL BRDF Database

Densely measured reflectance for a hundred real materials. The de facto ground truth that analytic models are fitted and compared against. · 2003

GGX / Trowbridge-Reitz

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

Coated Layer Model

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

Microfacet Model

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

Disney Principled BRDF

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

Artist-Friendly Metallic Fresnel

Reparameterizes conductor Fresnel from complex indices of refraction, which nobody can author, into reflectivity and edge tint, which can be picked f… · 2014

Height-Correlated Smith

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

Normalized Diffusion

Replaces the dipole's physically derived profile with a two-exponential curve fitted directly to Monte Carlo ground truth, which matches measured ski… · 2015

Multiple-Scattering Microfacet BSDF

Random-walks light between microfacets instead of discarding whatever the masking term blocks. Rough metals stop going dark, which is the visible sym… · 2016

Kulla-Conty Energy Compensation

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

Thin-Film Iridescence

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

Statistical Operators Layering

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

Visible Normal Distribution Sampling

Samples the distribution of microfacet normals actually visible from the view direction, rather than the full distribution. Every sample is usable, a… · 2018

Layering with Diffuse Interfaces

Extends statistical layering to stacks containing diffuse interfaces, which the lobe-variance formulation could not represent. · 2022

Beckmann Distribution

A Gaussian distribution of microfacet slopes, derived from physical optics. Its tail falls off quickly, so highlights end more abruptly than measured…

Diffuse Reflection

Light that enters a surface, scatters under it and re-emerges in a broad distribution largely independent of the incoming direction.

Fresnel Equations

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…

Lambertian Diffuse

A constant BRDF: outgoing radiance is the same in every direction, so the surface looks equally bright from any viewpoint. Cheap, reciprocal, and the…

Specular Reflection

Light reflected about the surface normal, concentrated in a lobe whose width is set by how rough the interface is.