ScriptableRenderPipeline/ScriptableRenderPipeline/Core/CoreRP/ShaderLibrary/BSDF.hlsl

#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
//-----------------------------------------------------------------------------

real F_Schlick(real f0, real f90, real 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
}

real F_Schlick(real f0, real u)
{
    return F_Schlick(f0, 1.0, u);               // sub mul mul mul sub mad
}

real3 F_Schlick(real3 f0, real f90, real 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
}

real3 F_Schlick(real3 f0, real u)
{
    return F_Schlick(f0, 1.0, u);               // sub mul mul mul sub mad*3
}

// Does not handle TIR.
real F_Transm_Schlick(real f0, real f90, real 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.
real F_Transm_Schlick(real f0, real u)
{
    return F_Transm_Schlick(f0, 1.0, u);        // sub mul mul mad mad
}

// Does not handle TIR.
real3 F_Transm_Schlick(real3 f0, real f90, real 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
}

// Does not handle TIR.
real3 F_Transm_Schlick(real3 f0, real u)
{
    return F_Transm_Schlick(f0, 1.0, u);        // sub mul mul mad mad*3
}

// Ref: https://seblagarde.wordpress.com/2013/04/29/memo-on-fresnel-equations/
// Fresnel dieletric / dielectric
real F_FresnelDieletric(real ior, real u)
{
    real g = sqrt(Sq(ior) + Sq(u) - 1.0);
    return 0.5 * Sq((g - u) / (g + u)) * (1.0 + Sq(((g + u) * u - 1.0) / ((g - u) * u + 1.0)));
}

// Fresnel dieletric / conductor
// 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)
{
    real cosTheta2 = cosTheta * cosTheta;
    real sinTheta2 = 1.0 - cosTheta2;
    real3 eta2 = eta * eta;

    real3 t0 = eta2 - etak2 - sinTheta2;
    real3 a2plusb2 = sqrt(t0 * t0 + 4.0 * eta2 * etak2);
    real3 t1 = a2plusb2 + cosTheta2;
    real3 a = sqrt(0.5 * (a2plusb2 + t0));
    real3 t2 = 2.0 * a * cosTheta;
    real3 Rs = (t1 - t2) / (t1 + t2);

    real3 t3 = cosTheta2 * a2plusb2 + sinTheta2 * sinTheta2;
    real3 t4 = t2 * sinTheta2;
    real3 Rp = Rs * (t3 - t4) / (t3 + t4);

    return 0.5 * (Rp + Rs);
}

// Conversion FO/IOR

TEMPLATE_2_REAL(IorToFresnel0, transmittedIor, incidentIor, return Sq((transmittedIor - incidentIor) / (transmittedIor + incidentIor)) )
// ior is a value between 1.0 and 3.0. 1.0 is air interface
real IorToFresnel0(real transmittedIor)
{
    return IorToFresnel0(transmittedIor, 1.0);
}

// Assume air interface for top
// Note: We don't handle the case fresnel0 == 1
//real Fresnel0ToIor(real fresnel0)
//{
//    real sqrtF0 = sqrt(fresnel0);
//    return (1.0 + sqrtF0) / (1.0 - sqrtF0);
//}
TEMPLATE_1_REAL(Fresnel0ToIor, fresnel0, return ((1.0 + sqrt(fresnel0)) / (1.0 - sqrt(fresnel0))) )

// 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 D_GGXNoPI(real NdotH, real roughness)
{
    real a2 = Sq(roughness);
    real s = (NdotH * a2 - NdotH) * NdotH + 1.0;
    return a2 / (s * s);
}

real D_GGX(real NdotH, real roughness)
{
    return INV_PI * D_GGXNoPI(NdotH, roughness);
}

// Ref: Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs, p. 19, 29.
real G_MaskingSmithGGX(real NdotV, real 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.
    // Assume that (VdotH > 0), e.i. (acos(LdotV) < Pi).

    return 1.0 / (0.5 + 0.5 * sqrt(1.0 + Sq(roughness) * (1.0 / Sq(NdotV) - 1.0)));
}

// Ref: Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs, p. 12.
real D_GGX_Visible(real NdotH, real NdotV, real VdotH, real roughness)
{
    return D_GGX(NdotH, roughness) * G_MaskingSmithGGX(NdotV, roughness) * VdotH / NdotV;
}

// Precompute part of lambdaV
real GetSmithJointGGXPartLambdaV(real NdotV, real roughness)
{
    real a2 = Sq(roughness);
    return sqrt((-NdotV * a2 + NdotV) * NdotV + a2);
}

// Note: V = G / (4 * NdotL * NdotV)
// Ref: http://jcgt.org/published/0003/02/03/paper.pdf
real V_SmithJointGGX(real NdotL, real NdotV, real roughness, real partLambdaV)
{
    real a2 = Sq(roughness);

    // Original formulation:
    // lambda_v = (-1 + sqrt(a2 * (1 - NdotL2) / NdotL2 + 1)) * 0.5
    // lambda_l = (-1 + sqrt(a2 * (1 - NdotV2) / NdotV2 + 1)) * 0.5
    // G        = 1 / (1 + lambda_v + lambda_l);

    // Reorder code to be more optimal:
    real lambdaV = NdotL * partLambdaV;
    real lambdaL = NdotV * sqrt((-NdotL * a2 + NdotL) * NdotL + a2);

    // Simplify visibility term: (2.0 * NdotL * NdotV) /  ((4.0 * NdotL * NdotV) * (lambda_v + lambda_l));
    return 0.5 / (lambdaV + lambdaL);
}

real V_SmithJointGGX(real NdotL, real NdotV, real roughness)
{
    real partLambdaV = GetSmithJointGGXPartLambdaV(NdotV, roughness);
    return V_SmithJointGGX(NdotL, NdotV, roughness, partLambdaV);
}

// Inline D_GGX() * V_SmithJointGGX() together for better code generation.
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 lambdaV = NdotL * partLambdaV;
    real lambdaL = NdotV * sqrt((-NdotL * a2 + NdotL) * NdotL + a2);

    real2 D = real2(a2, s * s);            // Fraction without the multiplier (1/Pi)
    real2 G = real2(1, lambdaV + lambdaL); // Fraction without the multiplier (1/2)

    return (INV_PI * 0.5) * (D.x * G.x) / (D.y * G.y);
}

real DV_SmithJointGGX(real NdotH, real NdotL, real NdotV, real roughness)
{
    real partLambdaV = GetSmithJointGGXPartLambdaV(NdotV, roughness);
    return DV_SmithJointGGX(NdotH, NdotL, NdotV, roughness, partLambdaV);
}

// Precompute a part of LambdaV.
// Note on this linear approximation.
// Exact for roughness values of 0 and 1. Also, exact when the cosine is 0 or 1.
// Otherwise, the worst case relative error is around 10%.
// https://www.desmos.com/calculator/wtp8lnjutx
real GetSmithJointGGXPartLambdaVApprox(real NdotV, real roughness)
{
    real a = roughness;
    return NdotV * (1 - a) + a;
}

real V_SmithJointGGXApprox(real NdotL, real NdotV, real roughness, real partLambdaV)
{
    real a = roughness;

    real lambdaV = NdotL * partLambdaV;
    real lambdaL = NdotV * (NdotL * (1 - a) + a);

    return 0.5 / (lambdaV + lambdaL);
}

real V_SmithJointGGXApprox(real NdotL, real NdotV, real roughness)
{
    real partLambdaV = GetSmithJointGGXPartLambdaVApprox(NdotV, roughness);
    return V_SmithJointGGXApprox(NdotL, NdotV, roughness, partLambdaV);
}

// roughnessT -> roughness in tangent direction
// roughnessB -> roughness in bitangent direction
real D_GGXAnisoNoPI(real TdotH, real BdotH, real NdotH, real roughnessT, real roughnessB)
{
    real a2 = roughnessT * roughnessB;
    real3 v = real3(roughnessB * TdotH, roughnessT * BdotH, a2 * NdotH);
    real  s = dot(v, v);

    return a2 * Sq(a2 / s);
}

real D_GGXAniso(real TdotH, real BdotH, real NdotH, real roughnessT, real roughnessB)
{
    return INV_PI * D_GGXAnisoNoPI(TdotH, BdotH, NdotH, roughnessT, roughnessB);
}

real GetSmithJointGGXAnisoPartLambdaV(real TdotV, real BdotV, real NdotV, real roughnessT, real roughnessB)
{
    return length(real3(roughnessT * TdotV, roughnessB * BdotV, NdotV));
}

// Note: V = G / (4 * NdotL * NdotV)
// Ref: https://cedec.cesa.or.jp/2015/session/ENG/14698.html The Rendering Materials of Far Cry 4
real V_SmithJointGGXAniso(real TdotV, real BdotV, real NdotV, real TdotL, real BdotL, real NdotL, real roughnessT, real roughnessB, real partLambdaV)
{
    real lambdaV = NdotL * partLambdaV;
    real lambdaL = NdotV * length(real3(roughnessT * TdotL, roughnessB * BdotL, NdotL));

    return 0.5 / (lambdaV + lambdaL);
}

real V_SmithJointGGXAniso(real TdotV, real BdotV, real NdotV, real TdotL, real BdotL, real NdotL, real roughnessT, real roughnessB)
{
    real partLambdaV = GetSmithJointGGXAnisoPartLambdaV(TdotV, BdotV, NdotV, roughnessT, roughnessB);
    return V_SmithJointGGXAniso(TdotV, BdotV, NdotV, TdotL, BdotL, NdotL, roughnessT, roughnessB, partLambdaV);
}

// 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 a2 = roughnessT * roughnessB;
    real3 v = real3(roughnessB * TdotH, roughnessT * BdotH, a2 * NdotH);
    real  s = dot(v, v);

    real lambdaV = NdotL * partLambdaV;
    real lambdaL = NdotV * length(real3(roughnessT * TdotL, roughnessB * BdotL, NdotL));

    real2 D = real2(a2 * a2 * a2, s * s);  // Fraction without the multiplier (1/Pi)
    real2 G = real2(1, lambdaV + lambdaL); // Fraction without the multiplier (1/2)

    return (INV_PI * 0.5) * (D.x * G.x) / (D.y * G.y);
}

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 partLambdaV = GetSmithJointGGXAnisoPartLambdaV(TdotV, BdotV, NdotV, roughnessT, roughnessB);
    return DV_SmithJointGGXAniso(TdotH, BdotH, NdotH, NdotV, TdotL, BdotL, NdotL,
        roughnessT, roughnessB, partLambdaV);
}

//-----------------------------------------------------------------------------
// Diffuse BRDF - diffuseColor is expected to be multiply by the caller
//-----------------------------------------------------------------------------

real LambertNoPI()
{
    return 1.0;
}

real Lambert()
{
    return INV_PI;
}

real DisneyDiffuseNoPI(real NdotV, real NdotL, real LdotV, real perceptualRoughness)
{
    // (2 * LdotH * LdotH) = 1 + LdotV
    // real fd90 = 0.5 + 2 * LdotH * LdotH * perceptualRoughness;
    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);

    // 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,
    // integrate (brdf * cos(theta_light)) over all light directions.
    // The resulting value is for (theta_view = 0), which is actually a little bit larger
    // than the value of the integral for (theta_view = Pi/4).
    // Hopefully, the compiler folds the constant together with (1/Pi).
    return rcp(1.03571) * (lightScatter * viewScatter);
}

real DisneyDiffuse(real NdotV, real NdotL, real LdotV, real perceptualRoughness)
{
    return INV_PI * DisneyDiffuseNoPI(NdotV, NdotL, LdotV, perceptualRoughness);
}

// 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 transmitL = F_Transm_Schlick(0, NdotL);
    real transmitV = F_Transm_Schlick(0, NdotV);
    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;
}

real3 DiffuseGGX(real3 albedo, real NdotV, real NdotL, real NdotH, real LdotV, real roughness)
{
    // Note that we could save 2 cycles by inlining the multiplication by INV_PI.
    return INV_PI * DiffuseGGXNoPI(albedo, NdotV, NdotL, NdotH, LdotV, roughness);
}

//-----------------------------------------------------------------------------
// Iridescence
//-----------------------------------------------------------------------------

// Ref: https://belcour.github.io/blog/research/2017/05/01/brdf-thin-film.html
// Evaluation XYZ sensitivity curves in Fourier space
real3 EvalSensitivity(real opd, real shift)
{
    // Use Gaussian fits, given by 3 parameters: val, pos and var
    real phase = 2.0 * PI * opd * 1e-6;
    real3 val = real3(5.4856e-13, 4.4201e-13, 5.2481e-13);
    real3 pos = real3(1.6810e+06, 1.7953e+06, 2.2084e+06);
    real3 var = real3(4.3278e+09, 9.3046e+09, 6.6121e+09);
    real3 xyz = val * sqrt(2.0 * PI * var) * cos(pos * phase + shift) * exp(-var * phase * phase);
    xyz.x += 9.7470e-14 * sqrt(2.0 * PI * 4.5282e+09) * cos(2.2399e+06 * phase + shift) * exp(-4.5282e+09 * phase * phase);
    return xyz / 1.0685e-7;
}

// Evaluate the reflectance for a thin-film layer on top of a dielectric medum.
real3 EvalIridescence(real eta_1, real cosTheta1, real iridescenceThickness, real3 baseLayerFresnel0)
{
    // iridescenceThickness unit is micrometer for this equation here. Mean 0.5 is 500nm.
    real Dinc = 3.0 * iridescenceThickness;

    // Note: Unlike the code provide with the paper, here we use schlick approximation
    // Schlick is a very poor approximation when dealing with iridescence to the Fresnel
    // term and there is no "neutral" value in this unlike in the original paper.
    // We use Iridescence mask here to allow to have neutral value

    // Hack: In order to use only one parameter (DInc), we deduced the ior of iridescence from current Dinc iridescenceThickness
    // and we use mask instead to fade out the effect
    real eta_2 = lerp(2.0, 1.0, iridescenceThickness);
    // Following line from original code is not needed for us, it create a discontinuity
    // Force eta_2 -> eta_1 when Dinc -> 0.0
    // real eta_2 = lerp(eta_1, eta_2, smoothstep(0.0, 0.03, Dinc));
    // Evaluate the cosTheta on the base layer (Snell law)
    real cosTheta2 = sqrt(1.0 - Sq(eta_1 / eta_2) * (1.0 - Sq(cosTheta1)));

    // First interface
    real R0 = IorToFresnel0(eta_2, eta_1);
    real R12 = F_Schlick(R0, cosTheta1);
    real R21 = R12;
    real T121 = 1.0 - R12;
    real phi12 = 0.0;
    real phi21 = PI - phi12;

    // Second interface
    real3 R23 = F_Schlick(baseLayerFresnel0, cosTheta2);
    real  phi23 = 0.0;

    // Phase shift
    real OPD = Dinc * cosTheta2;
    real phi = phi21 + phi23;

    // Compound terms
    real3 R123 = R12 * R23;
    real3 r123 = sqrt(R123);
    real3 Rs = Sq(T121) * R23 / (real3(1.0, 1.0, 1.0) - R123);

    // Reflectance term for m = 0 (DC term amplitude)
    real3 C0 = R12 + Rs;
    real3 I = C0;

    // Reflectance term for m > 0 (pairs of diracs)
    real3 Cm = Rs - T121;
    for (int m = 1; m <= 2; ++m)
    {
        Cm *= r123;
        real3 Sm = 2.0 * EvalSensitivity(m * OPD, m * phi);
        //vec3 SmP = 2.0 * evalSensitivity(m*OPD, m*phi2.y);
        I += Cm * Sm;
    }

    // Convert back to RGB reflectance
    //I = clamp(mul(I, XYZ_TO_RGB), real3(0.0, 0.0, 0.0), real3(1.0, 1.0, 1.0));
    //I = mul(XYZ_TO_RGB, I);

    return I;
}

#endif // UNITY_BSDF_INCLUDED