Function to calculate 'a' parameter for lambda functions needed in Smith G term This is a version for shape invariant (isotropic) NDFs Note: makse sur

Evaluates G2 for selected configuration (GGX/Beckmann, optimized/non-optimized, separable/height-correlated) Note that some paths aren't optimized too

Attenuates F90 for very low F0 values Source: "An efficient and Physically Plausible Real-Time Shading Model" in ShaderX7 by Schuler Also see section

Converts Beckmann roughness (alpha) to Phong's exponent (shininess) Source: "Microfacet Models for Refraction through Rough Surfaces" by Walter et al.

Precalculates commonly used terms in BRDF evaluation Clamps around dot products prevent NaNs and ensure numerical stability, but make sure to correctl

Optimized point rotation using quaternion Source: https://gamedev.stackexchange.com/questions/28395/rotating-vector3-by-a-quaternion

Smith G1 term (masking function) optimized for GGX distribution (by substituting G_Lambda_GGX into G1)

For derivation see "Phong Normalization Factor derivation" by Giesen

Smith G2 term (masking-shadowing function) Height correlated version - non-optimized, uses G_Lambda functions for selected NDF

Smith G2 term (masking-shadowing function) for GGX distribution Height correlated version - optimized by substituing G_Lambda for G_Lambda_GGX and div

A fraction G2/G1 where G2 is height correlated can be expressed using only G1 terms Source: "Implementing a Simple Anisotropic Rough Diffuse Material

Smith G2 term (masking-shadowing function) Separable version assuming independent (uncorrelated) masking and shadowing, uses G1 functions for selected

Smith G2 term (masking-shadowing function) for GGX distribution Separable version assuming independent (uncorrelated) masking and shadowing - optimize

Converts Beckmann roughness (alpha) to Oren-Nayar roughness (sigma) Source: "Moving Frostbite to Physically Based Rendering" by Lagarde & de Rousiers

Disney's diffuse term Source "Physically-Based Shading at Disney" by Burley

Schlick's approximation to Fresnel term f90 should be 1.0, except for the trick used by Schuler (see 'shadowedF90' function)

Frostbite's version of Disney diffuse with energy normalization. Source: "Moving Frostbite to Physically Based Rendering" by Lagarde & de Rousiers

Calculates rotation quaternion from vector (0, 0, 1) to the input vector Input vector must be normalized!

Calculates rotation quaternion from input vector to the vector (0, 0, 1) Input vector must be normalized!

Returns the quaternion with inverted rotation

Based on Oren-Nayar's qualitative model Source: "Generalization of Lambert's Reflectance Model" by Oren & Nayar

Samples a direction within a hemisphere oriented along +Z axis with a cosine-weighted distribution Source: "Sampling Transformations Zoo" in Ray Traci

Samples a Phong distribution lobe oriented along +Z axis Source: "Sampling Transformations Zoo" in Ray Tracing Gems by Shirley et al.

Smith G1 term (masking function) optimized for Beckmann distribution (by substituting G_Lambda_Beckmann_Walter into G1) Source: "Microfacet Models for

Smith G1 term (masking function) This non-optimized version uses NDF specific lambda function (G_Lambda) resolved bia macro based on selected NDF

Smith G2 term (masking-shadowing function) for GGX distribution Height correlated version - approximation by Hammon Source: "PBR Diffuse Lighting for

Lambda function for Smith G term derived for Beckmann distribution This is Walter's rational approximation (avoids evaluating of error function) Sourc

Lambda function for Smith G term derived for GGX distribution

For sampling of all our diffuse BRDFs we use cosine-weighted hemisphere sampling, with PDF equal to (NdotL/PI)

This is an entry point for evaluation of all other BRDFs based on selected configuration (for direct light)

Schlick's approximation to Fresnel term with Hoffman's improvement using the Lazanyi's error term Source: "Fresnel Equations Considered Harmful" by Ho

Schlick's approximation to Fresnel term calculated using spherical gaussian approximation Source: https://seblagarde.wordpress.com/2012/06/03/spherica

This is an entry point for evaluation of all other BRDFs based on selected configuration (for indirect light)

Evaluates microfacet specular BRDF

Samples a microfacet normal for the Beckmann distribution using walter's method. Source: "Microfacet Models for Refraction through Rough Surfaces" by

Samples a microfacet normal for the GGX distribution using VNDF method. Source: "Sampling the GGX Distribution of Visible Normals" by Heitz Source: "S

PDF of sampling a reflection vector L using 'sampleGGXVNDF'. Note that PDF of sampling given microfacet normal is (G1 * D) when vectors are in local s

Samples a microfacet normal for the GG-X distribution using walter's method. Source: "Microfacet Models for Refraction through Rough Surfaces" by Walt

Samples a reflection ray from the rough surface using selected microfacet distribution and sampling method Resulting weight includes multiplication by

Sampling the specular BRDF based on Phong, includes normalization term

PDF of sampling a reflection vector L using 'sampleBeckmannWalter' or 'sampleGGXWalter'. Note that PDF of sampling given microfacet normal is (D * Ndo

Converts Phong's exponent (shininess) to Beckmann roughness (alpha) Source: "Microfacet Models for Refraction through Rough Surfaces" by Walter et al.

Approximates the directional-hemispherical reflectance of the micriofacet specular BRDF with GG-X distribution Source: "Accurate Real-Time Specular Re

Weight for the reflection ray sampled from Beckmann distribution using Walter's method

Weight for the reflection ray sampled from GGX distribution using VNDF method

Weight for the reflection ray sampled from GGX distribution using Walter's method

"Walter's trick" is an adjustment of alpha value for Walter's sampling to reduce maximal weight of sample to about 4 Source: "Microfacet Models for Re