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#ifndef UNITY_BSDF_INCLUDED
#define UNITY_BSDF_INCLUDED
// Note: All NDF and diffuse term have a version with and without divide by PI.
// Version with divide by PI are use for direct lighting.
// Version without divide by PI are use for image based lighting where often the PI cancel during importance sampling
//-----------------------------------------------------------------------------
// Fresnel term
//-----------------------------------------------------------------------------
float F_Schlick(float f0, float f90, float u)
{
float x = 1.0 - u;
float x5 = x * x;
x5 = x5 * x5 * x;
return (f90 - f0) * x5 + f0; // sub mul mul mul sub mad
}
float F_Schlick(float f0, float u)
{
return F_Schlick(f0, 1.0, u);
}
float3 F_Schlick(float3 f0, float f90, float u)
{
float x = 1.0 - u;
float x5 = x * x;
x5 = x5 * x5 * x;
return (float3(f90, f90, f90) - f0) * x5 + f0; // sub mul mul mul sub mad
}
float3 F_Schlick(float3 f0, float u)
{
return F_Schlick(f0, 1.0, u);
}
//-----------------------------------------------------------------------------
// Specular BRDF
//-----------------------------------------------------------------------------
// With analytical light (not image based light) we clamp the minimun roughness in the NDF to avoid numerical instability.
#define UNITY_MIN_ROUGHNESS 0.002
float ClampRoughnessForAnalyticalLights(float roughness)
{
return max(roughness, UNITY_MIN_ROUGHNESS);
}
float D_GGXNoPI(float NdotH, float roughness)
{
float a2 = roughness * roughness;
float f = (NdotH * a2 - NdotH) * NdotH + 1.0;
return a2 / (f * f);
}
float D_GGX(float NdotH, float roughness)
{
return INV_PI * D_GGXNoPI(NdotH, roughness);
}
float D_GGX_Inverse(float NdotH, float roughness)
{
float a2 = roughness * roughness;
float f = (NdotH * a2 - NdotH) * NdotH + 1.0;
float g = (f * f) / a2;
return PI * g;
}
// Ref: Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs, p. 19, 29.
float G_MaskingSmithGGX(float NdotV, float VdotH, float roughness)
{
// G1(V, H) = HeavisideStep(VdotH) / (1 + Λ(V)).
// Λ(V) = -0.5 + 0.5 * sqrt(1 + 1 / a²).
// a = 1 / (roughness * tan(theta)).
// 1 + Λ(V) = 0.5 + 0.5 * sqrt(1 + roughness² * tan²(theta)).
// tan²(theta) = (1 - cos²(theta)) / cos²(theta) = 1 / cos²(theta) - 1.
float hs = VdotH > 0.0 ? 1.0 : 0.0;
float a2 = roughness * roughness;
float z2 = NdotV * NdotV;
return hs / (0.5 + 0.5 * sqrt(1.0 + a2 * (1.0 / z2 - 1.0)));
}
// Ref: Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs, p. 12.
float D_GGX_Visible(float NdotH, float NdotV, float VdotH, float roughness)
{
// Note that we pass 1.0 instead of 'VdotH' since the multiplication will already clamp.
return D_GGX(NdotH, roughness) * G_MaskingSmithGGX(NdotV, 1.0, roughness) * VdotH / NdotV;
}
// Ref: http://jcgt.org/published/0003/02/03/paper.pdf
float V_SmithJointGGX(float NdotL, float NdotV, float roughness)
{
// Original formulation:
// lambda_v = (-1 + sqrt(a2 * (1 - NdotL2) / NdotL2 + 1)) * 0.5f;
// lambda_l = (-1 + sqrt(a2 * (1 - NdotV2) / NdotV2 + 1)) * 0.5f;
// G = 1 / (1 + lambda_v + lambda_l);
float a = roughness;
float a2 = a * a;
// Reorder code to be more optimal
float lambdaV = NdotL * sqrt((-NdotV * a2 + NdotV) * NdotV + a2);
float lambdaL = NdotV * sqrt((-NdotL * a2 + NdotL) * NdotL + a2);
// Simplify visibility term: (2.0f * NdotL * NdotV) / ((4.0f * NdotL * NdotV) * (lambda_v + lambda_l));
return 0.5 / (lambdaV + lambdaL);
}
// Precompute part of lambdaV
float GetSmithJointGGXLambdaV(float NdotV, float roughness)
{
float a = roughness;
float a2 = a * a;
return sqrt((-NdotV * a2 + NdotV) * NdotV + a2);
}
float V_SmithJointGGX(float NdotL, float NdotV, float roughness, float lambdaV)
{
float a = roughness;
float a2 = a * a;
// Reorder code to be more optimal
lambdaV *= NdotL;
float lambdaL = NdotV * sqrt((-NdotL * a2 + NdotL) * NdotL + a2);
// Simplify visibility term: (2.0f * NdotL * NdotV) / ((4.0f * NdotL * NdotV) * (lambda_v + lambda_l));
return 0.5 / (lambdaV + lambdaL);
}
float V_SmithJointGGXApprox(float NdotL, float NdotV, float roughness)
{
float a = roughness;
// Approximation of the above formulation (simplify the sqrt, not mathematically correct but close enough)
float lambdaV = NdotL * (NdotV * (1 - a) + a);
float lambdaL = NdotV * (NdotL * (1 - a) + a);
return 0.5 / (lambdaV + lambdaL);
}
// Precompute part of LambdaV
float GetSmithJointGGXApproxLambdaV(float NdotV, float roughness)
{
float a = roughness;
return NdotV * (1 - a) + a;
}
float V_SmithJointGGXApprox(float NdotL, float NdotV, float roughness, float lambdaV)
{
float a = roughness;
// Approximation of the above formulation (simplify the sqrt, not mathematically correct but close enough)
lambdaV *= NdotL;
float lambdaL = NdotV * (NdotL * (1 - a) + a);
return 0.5 / (lambdaV + lambdaL);
}
// roughnessT -> roughness in tangent direction
// roughnessB -> roughness in bitangent direction
float D_GGXAnisoNoPI(float TdotH, float BdotH, float NdotH, float roughnessT, float roughnessB)
{
float f = TdotH * TdotH / (roughnessT * roughnessT) + BdotH * BdotH / (roughnessB * roughnessB) + NdotH * NdotH;
return 1.0 / (roughnessT * roughnessB * f * f);
}
float D_GGXAniso(float TdotH, float BdotH, float NdotH, float roughnessT, float roughnessB)
{
return INV_PI * D_GGXAnisoNoPI(TdotH, BdotH, NdotH, roughnessT, roughnessB);
}
// Ref: https://cedec.cesa.or.jp/2015/session/ENG/14698.html The Rendering Materials of Far Cry 4
float V_SmithJointGGXAniso(float TdotV, float BdotV, float NdotV, float TdotL, float BdotL, float NdotL, float roughnessT, float roughnessB)
{
float aT = roughnessT;
float aT2 = aT * aT;
float aB = roughnessB;
float aB2 = aB * aB;
float lambdaV = NdotL * sqrt(aT2 * TdotV * TdotV + aB2 * BdotV * BdotV + NdotV * NdotV);
float lambdaL = NdotV * sqrt(aT2 * TdotL * TdotL + aB2 * BdotL * BdotL + NdotL * NdotL);
return 0.5 / (lambdaV + lambdaL);
}
float GetSmithJointGGXAnisoLambdaV(float TdotV, float BdotV, float NdotV, float roughnessT, float roughnessB)
{
float aT = roughnessT;
float aT2 = aT * aT;
float aB = roughnessB;
float aB2 = aB * aB;
return sqrt(aT2 * TdotV * TdotV + aB2 * BdotV * BdotV + NdotV * NdotV);
}
float V_SmithJointGGXAnisoLambdaV(float TdotV, float BdotV, float NdotV, float TdotL, float BdotL, float NdotL, float roughnessT, float roughnessB, float lambdaV)
{
float aT = roughnessT;
float aT2 = aT * aT;
float aB = roughnessB;
float aB2 = aB * aB;
lambdaV *= NdotL;
float lambdaL = NdotV * sqrt(aT2 * TdotL * TdotL + aB2 * BdotL * BdotL + NdotL * NdotL);
return 0.5 / (lambdaV + lambdaL);
}
//-----------------------------------------------------------------------------
// Diffuse BRDF - diffuseColor is expected to be multiply by the caller
//-----------------------------------------------------------------------------
float LambertNoPI()
{
return 1.0;
}
float Lambert()
{
return INV_PI;
}
float DisneyDiffuseNoPI(float NdotV, float NdotL, float LdotH, float perceptualRoughness)
{
float fd90 = 0.5 + 2 * LdotH * LdotH * perceptualRoughness;
// Two schlick fresnel term
float lightScatter = F_Schlick(1.0, fd90, NdotL);
float viewScatter = F_Schlick(1.0, fd90, NdotV);
return lightScatter * viewScatter;
}
float DisneyDiffuse(float NdotV, float NdotL, float LdotH, float perceptualRoughness)
{
return INV_PI * DisneyDiffuseNoPI(NdotV, NdotL, LdotH, perceptualRoughness);
}
#endif // UNITY_BSDF_INCLUDED