real F_Schlick(real f0, real f90, real u)
{
real x = 1.0 - u;
real x = 1.0 - u;
real x2 = x * x;
real x5 = x * x2 * x2;
return (f90 - f0) * x5 + f0; // sub mul mul mul sub mad
real3 F_Schlick(real3 f0, real f90, real u)
{
real x = 1.0 - u;
real x = 1.0 - u;
real x2 = x * x;
real x5 = x * x2 * x2;
return f0 * (1.0 - x5) + (f90 * x5); // sub mul mul mul sub mul mad*3
// Does not handle TIR.
real F_Transm_Schlick(real f0, real f90, real u)
{
real x = 1.0 - u;
real x = 1.0 - u;
real x2 = x * x;
real x5 = x * x2 * x2;
return (1.0 - f90 * x5) - f0 * (1.0 - x5); // sub mul mul mul mad sub mad
// Does not handle TIR.
real3 F_Transm_Schlick(real3 f0, real f90, real u)
{
real x = 1.0 - u;
real x = 1.0 - u;
real x2 = x * x;
real x5 = x * x2 * x2;
return (1.0 - f90 * x5) - f0 * (1.0 - x5); // sub mul mul mul mad sub mad*3
}
// Fresnel dieletric / conductor
real3 F_FresnelConductor(real3 eta, real3 etak, real cosTheta)
// Note: etak2 = etak * etak (optimization for Artist Friendly Metallic Fresnel below)
// eta = eta_t / eta_i and etak = k_t / n_i
real3 F_FresnelConductor(real3 eta, real3 etak2, real cosTheta)
real3 etak2 = etak * etak;
real3 t0 = eta2 - etak2 - sinTheta2;
real3 a2plusb2 = sqrt(t0 * t0 + 4.0 * eta2 * etak2);
return 0.5 * (Rp + Rs);
}
// Conversion FO/IOR
// ior is a value between 1.0 and 3.0. 1.0 is air interface
real IorToFresnel0(real transmittedIor, real incidentIor = 1.0)
{
return Sq((transmittedIor - incidentIor) / (transmittedIor + incidentIor));
}
// Assume air interface for top
// Note: Don't handle the case fresnel0 == 1
real Fresnel0ToIor(real fresnel0)
{
real sqrtF0 = sqrt(fresnel0);
return (1.0 + sqrtF0) / (1.0 - sqrtF0);
}
// This function is a coarse approximation of computing fresnel0 for a different top than air (here clear coat of IOR 1.5) when we only have fresnel0 with air interface
// This function is equivalent to IorToFresnel0(Fresnel0ToIor(fresnel0), 1.5)
// mean
// real sqrtF0 = sqrt(fresnel0);
// return Sq(1.0 - 5.0 * sqrtF0) / Sq(5.0 - sqrtF0);
// Optimization: Fit of the function (3 mad) for range [0.04 (should return 0), 1 (should return 1)]
TEMPLATE_1_REAL(ConvertF0ForAirInterfaceToF0ForClearCoat15, fresnel0, return saturate(-0.0256868 + fresnel0 * (0.326846 + (0.978946 - 0.283835 * fresnel0) * fresnel0)))
// Artist Friendly Metallic Fresnel Ref: http://jcgt.org/published/0003/04/03/paper.pdf
real3 GetIorN(real3 f0, real3 edgeTint)
{
real3 sqrtF0 = sqrt(f0);
return lerp((1.0 - f0) / (1.0 + f0), (1.0 + sqrtF0) / (1.0 - sqrt(f0)), edgeTint);
}
real3 getIorK2(real3 f0, real3 n)
{
real3 nf0 = Sq(n + 1.0) * f0 - Sq(f0 - 1.0);
return nf0 / (1.0 - f0);
}
//-----------------------------------------------------------------------------
// Specular BRDF
//-----------------------------------------------------------------------------
real a2 = Sq(roughness);
real s = (NdotH * a2 - NdotH) * NdotH + 1.0;
real s = (NdotH * a2 - NdotH) * NdotH + 1.0;
return a2 / (s * s);
}
real DV_SmithJointGGX(real NdotH, real NdotL, real NdotV, real roughness, real partLambdaV)
{
real a2 = Sq(roughness);
real s = (NdotH * a2 - NdotH) * NdotH + 1.0;
real s = (NdotH * a2 - NdotH) * NdotH + 1.0;
real lambdaV = NdotL * partLambdaV;
real lambdaL = NdotV * sqrt((-NdotL * a2 + NdotL) * NdotL + a2);
// Inline D_GGXAniso() * V_SmithJointGGXAniso() together for better code generation.
real DV_SmithJointGGXAniso(real TdotH, real BdotH, real NdotH, real NdotV,
real TdotL, real BdotL, real NdotL,
real roughnessT, real roughnessB, real partLambdaV)
real TdotL, real BdotL, real NdotL,
real roughnessT, real roughnessB, real partLambdaV)
{
real a2 = roughnessT * roughnessB;
real3 v = real3(roughnessB * TdotH, roughnessT * BdotH, a2 * NdotH);
}
real DV_SmithJointGGXAniso(real TdotH, real BdotH, real NdotH,
real TdotV, real BdotV, real NdotV,
real TdotL, real BdotL, real NdotL,
real roughnessT, real roughnessB)
real TdotV, real BdotV, real NdotV,
real TdotL, real BdotL, real NdotL,
real roughnessT, real roughnessB)
roughnessT, roughnessB, partLambdaV);
roughnessT, roughnessB, partLambdaV);
}
//-----------------------------------------------------------------------------
real fd90 = 0.5 + (perceptualRoughness + perceptualRoughness * LdotV);
// Two schlick fresnel term
real lightScatter = F_Schlick(1.0, fd90, NdotL);
real viewScatter = F_Schlick(1.0, fd90, NdotV);
real viewScatter = F_Schlick(1.0, fd90, NdotV);
// Normalize the BRDF for polar view angles of up to (Pi/4).
// We use the worst case of (roughness = albedo = 1), and, for each view angle,
// Ref: Diffuse Lighting for GGX + Smith Microsurfaces, p. 113.
real3 DiffuseGGXNoPI(real3 albedo, real NdotV, real NdotL, real NdotH, real LdotV, real roughness)
{
real facing = 0.5 + 0.5 * LdotV; // (LdotH)^2
real rough = facing * (0.9 - 0.4 * facing) * (0.5 / NdotH + 1);
real facing = 0.5 + 0.5 * LdotV; // (LdotH)^2
real rough = facing * (0.9 - 0.4 * facing) * (0.5 / NdotH + 1);
real smooth = transmitL * transmitV * 1.05; // Normalize F_t over the hemisphere
real single = lerp(smooth, rough, roughness); // Rescaled by PI
real multiple = roughness * (0.1159 * PI); // Rescaled by PI
real smooth = transmitL * transmitV * 1.05; // Normalize F_t over the hemisphere
real single = lerp(smooth, rough, roughness); // Rescaled by PI
real multiple = roughness * (0.1159 * PI); // Rescaled by PI
return single + albedo * multiple;
}
// Note that we could save 2 cycles by inlining the multiplication by INV_PI.
return INV_PI * DiffuseGGXNoPI(albedo, NdotV, NdotL, NdotH, LdotV, roughness);
}
//-----------------------------------------------------------------------------
// Conversion FO/IOR
//-----------------------------------------------------------------------------
// ior is a value between 1.0 and 3.0. 1.0 is air interface
real IorToFresnel0(real transmittedIor, real incidentIor = 1.0)
{
return Sq((transmittedIor - incidentIor) / (transmittedIor + incidentIor));
}
// Assume air interface for top
// Note: Don't handle the case fresnel0 == 1
real Fresnel0ToIor(real fresnel0)
{
real sqrtF0 = sqrt(fresnel0);
return (1.0 + sqrtF0) / (1.0 - sqrtF0);
}
// This function is a coarse approximation of computing fresnel0 for a different top than air (here clear coat of IOR 1.5) when we only have fresnel0 with air interface
// This function is equivalent to IorToFresnel0(Fresnel0ToIor(fresnel0), 1.5)
// mean
// real sqrtF0 = sqrt(fresnel0);
// return Sq(1.0 - 5.0 * sqrtF0) / Sq(5.0 - sqrtF0);
// Optimization: Fit of the function (3 mad) for range [0.04 (should return 0), 1 (should return 1)]
TEMPLATE_1_REAL(ConvertF0ForAirInterfaceToF0ForClearCoat15, fresnel0, return saturate(-0.0256868 + fresnel0 * (0.326846 + (0.978946 - 0.283835 * fresnel0) * fresnel0)))
//-----------------------------------------------------------------------------
// Iridescence