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Correct importance sampling as per d'Eon paper #256

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Dec 13, 2019
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Correct importance sampling as per d'Eon paper #256

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112 changes: 57 additions & 55 deletions src/materials/hair.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -290,28 +290,28 @@ Spectrum HairBSDF::f(const Vector3f &wo, const Vector3f &wi) const {
std::array<Spectrum, pMax + 1> ap = Ap(cosThetaO, eta, h, T);
Spectrum fsum(0.);
for (int p = 0; p < pMax; ++p) {
// Compute $\sin \thetai$ and $\cos \thetai$ terms accounting for scales
Float sinThetaIp, cosThetaIp;
// Compute $\sin \thetao$ and $\cos \thetao$ terms accounting for scales
Float sinThetaOp, cosThetaOp;
if (p == 0) {
sinThetaIp = sinThetaI * cos2kAlpha[1] + cosThetaI * sin2kAlpha[1];
cosThetaIp = cosThetaI * cos2kAlpha[1] - sinThetaI * sin2kAlpha[1];
sinThetaOp = sinThetaO * cos2kAlpha[1] - cosThetaO * sin2kAlpha[1];
cosThetaOp = cosThetaO * cos2kAlpha[1] + sinThetaO * sin2kAlpha[1];
}

// Handle remainder of $p$ values for hair scale tilt
else if (p == 1) {
sinThetaIp = sinThetaI * cos2kAlpha[0] - cosThetaI * sin2kAlpha[0];
cosThetaIp = cosThetaI * cos2kAlpha[0] + sinThetaI * sin2kAlpha[0];
sinThetaOp = sinThetaO * cos2kAlpha[0] + cosThetaO * sin2kAlpha[0];
cosThetaOp = cosThetaO * cos2kAlpha[0] - sinThetaO * sin2kAlpha[0];
} else if (p == 2) {
sinThetaIp = sinThetaI * cos2kAlpha[2] - cosThetaI * sin2kAlpha[2];
cosThetaIp = cosThetaI * cos2kAlpha[2] + sinThetaI * sin2kAlpha[2];
sinThetaOp = sinThetaO * cos2kAlpha[2] + cosThetaO * sin2kAlpha[2];
cosThetaOp = cosThetaO * cos2kAlpha[2] - sinThetaO * sin2kAlpha[2];
} else {
sinThetaIp = sinThetaI;
cosThetaIp = cosThetaI;
sinThetaOp = sinThetaO;
cosThetaOp = cosThetaO;
}

// Handle out-of-range $\cos \thetai$ from scale adjustment
cosThetaIp = std::abs(cosThetaIp);
fsum += Mp(cosThetaIp, cosThetaO, sinThetaIp, sinThetaO, v[p]) * ap[p] *
// Handle out-of-range $\cos \thetao$ from scale adjustment
cosThetaOp = std::abs(cosThetaOp);
fsum += Mp(cosThetaI, cosThetaOp, sinThetaI, sinThetaOp, v[p]) * ap[p] *
Np(phi, p, s, gammaO, gammaT);
}

Expand Down Expand Up @@ -367,30 +367,32 @@ Spectrum HairBSDF::Sample_f(const Vector3f &wo, Vector3f *wi, const Point2f &u2,
u[0][0] -= apPdf[p];
}

// Rotate $\sin \thetao$ and $\cos \thetao$ to account for hair scale tilt
Float sinThetaOp, cosThetaOp;
if (p == 0) {
sinThetaOp = sinThetaO * cos2kAlpha[1] - cosThetaO * sin2kAlpha[1];
cosThetaOp = cosThetaO * cos2kAlpha[1] + sinThetaO * sin2kAlpha[1];
}
else if (p == 1) {
sinThetaOp = sinThetaO * cos2kAlpha[0] + cosThetaO * sin2kAlpha[0];
cosThetaOp = cosThetaO * cos2kAlpha[0] - sinThetaO * sin2kAlpha[0];
} else if (p == 2) {
sinThetaOp = sinThetaO * cos2kAlpha[2] + cosThetaO * sin2kAlpha[2];
cosThetaOp = cosThetaO * cos2kAlpha[2] - sinThetaO * sin2kAlpha[2];
} else {
sinThetaOp = sinThetaO;
cosThetaOp = cosThetaO;
}

// Sample $M_p$ to compute $\thetai$
u[1][0] = std::max(u[1][0], Float(1e-5));
Float cosTheta =
1 + v[p] * std::log(u[1][0] + (1 - u[1][0]) * std::exp(-2 / v[p]));
Float sinTheta = SafeSqrt(1 - Sqr(cosTheta));
Float cosPhi = std::cos(2 * Pi * u[1][1]);
Float sinThetaI = -cosTheta * sinThetaO + sinTheta * cosPhi * cosThetaO;
Float sinThetaI = -cosTheta * sinThetaOp + sinTheta * cosPhi * cosThetaOp;
Float cosThetaI = SafeSqrt(1 - Sqr(sinThetaI));

// Update sampled $\sin \thetai$ and $\cos \thetai$ to account for scales
Float sinThetaIp = sinThetaI, cosThetaIp = cosThetaI;
if (p == 0) {
sinThetaIp = sinThetaI * cos2kAlpha[1] - cosThetaI * sin2kAlpha[1];
cosThetaIp = cosThetaI * cos2kAlpha[1] + sinThetaI * sin2kAlpha[1];
} else if (p == 1) {
sinThetaIp = sinThetaI * cos2kAlpha[0] + cosThetaI * sin2kAlpha[0];
cosThetaIp = cosThetaI * cos2kAlpha[0] - sinThetaI * sin2kAlpha[0];
} else if (p == 2) {
sinThetaIp = sinThetaI * cos2kAlpha[2] + cosThetaI * sin2kAlpha[2];
cosThetaIp = cosThetaI * cos2kAlpha[2] - sinThetaI * sin2kAlpha[2];
}
sinThetaI = sinThetaIp;
cosThetaI = cosThetaIp;

// Sample $N_p$ to compute $\Delta\phi$

// Compute $\gammat$ for refracted ray
Expand All @@ -412,28 +414,28 @@ Spectrum HairBSDF::Sample_f(const Vector3f &wo, Vector3f *wi, const Point2f &u2,
// Compute PDF for sampled hair scattering direction _wi_
*pdf = 0;
for (int p = 0; p < pMax; ++p) {
// Compute $\sin \thetai$ and $\cos \thetai$ terms accounting for scales
Float sinThetaIp, cosThetaIp;
// Compute $\sin \thetao$ and $\cos \thetao$ terms accounting for scales
Float sinThetaOp, cosThetaOp;
if (p == 0) {
sinThetaIp = sinThetaI * cos2kAlpha[1] + cosThetaI * sin2kAlpha[1];
cosThetaIp = cosThetaI * cos2kAlpha[1] - sinThetaI * sin2kAlpha[1];
sinThetaOp = sinThetaO * cos2kAlpha[1] - cosThetaO * sin2kAlpha[1];
cosThetaOp = cosThetaO * cos2kAlpha[1] + sinThetaO * sin2kAlpha[1];
}

// Handle remainder of $p$ values for hair scale tilt
else if (p == 1) {
sinThetaIp = sinThetaI * cos2kAlpha[0] - cosThetaI * sin2kAlpha[0];
cosThetaIp = cosThetaI * cos2kAlpha[0] + sinThetaI * sin2kAlpha[0];
sinThetaOp = sinThetaO * cos2kAlpha[0] + cosThetaO * sin2kAlpha[0];
cosThetaOp = cosThetaO * cos2kAlpha[0] - sinThetaO * sin2kAlpha[0];
} else if (p == 2) {
sinThetaIp = sinThetaI * cos2kAlpha[2] - cosThetaI * sin2kAlpha[2];
cosThetaIp = cosThetaI * cos2kAlpha[2] + sinThetaI * sin2kAlpha[2];
sinThetaOp = sinThetaO * cos2kAlpha[2] + cosThetaO * sin2kAlpha[2];
cosThetaOp = cosThetaO * cos2kAlpha[2] - sinThetaO * sin2kAlpha[2];
} else {
sinThetaIp = sinThetaI;
cosThetaIp = cosThetaI;
sinThetaOp = sinThetaO;
cosThetaOp = cosThetaO;
}

// Handle out-of-range $\cos \thetai$ from scale adjustment
cosThetaIp = std::abs(cosThetaIp);
*pdf += Mp(cosThetaIp, cosThetaO, sinThetaIp, sinThetaO, v[p]) *
// Handle out-of-range $\cos \thetao$ from scale adjustment
cosThetaOp = std::abs(cosThetaOp);
*pdf += Mp(cosThetaI, cosThetaOp, sinThetaI, sinThetaOp, v[p]) *
apPdf[p] * Np(dphi, p, s, gammaO, gammaT);
}
*pdf += Mp(cosThetaI, cosThetaO, sinThetaI, sinThetaO, v[pMax]) *
Expand Down Expand Up @@ -465,28 +467,28 @@ Float HairBSDF::Pdf(const Vector3f &wo, const Vector3f &wi) const {
Float phi = phiI - phiO;
Float pdf = 0;
for (int p = 0; p < pMax; ++p) {
// Compute $\sin \thetai$ and $\cos \thetai$ terms accounting for scales
Float sinThetaIp, cosThetaIp;
// Compute $\sin \thetao$ and $\cos \thetao$ terms accounting for scales
Float sinThetaOp, cosThetaOp;
if (p == 0) {
sinThetaIp = sinThetaI * cos2kAlpha[1] + cosThetaI * sin2kAlpha[1];
cosThetaIp = cosThetaI * cos2kAlpha[1] - sinThetaI * sin2kAlpha[1];
sinThetaOp = sinThetaO * cos2kAlpha[1] - cosThetaO * sin2kAlpha[1];
cosThetaOp = cosThetaO * cos2kAlpha[1] + sinThetaO * sin2kAlpha[1];
}

// Handle remainder of $p$ values for hair scale tilt
else if (p == 1) {
sinThetaIp = sinThetaI * cos2kAlpha[0] - cosThetaI * sin2kAlpha[0];
cosThetaIp = cosThetaI * cos2kAlpha[0] + sinThetaI * sin2kAlpha[0];
sinThetaOp = sinThetaO * cos2kAlpha[0] + cosThetaO * sin2kAlpha[0];
cosThetaOp = cosThetaO * cos2kAlpha[0] - sinThetaO * sin2kAlpha[0];
} else if (p == 2) {
sinThetaIp = sinThetaI * cos2kAlpha[2] - cosThetaI * sin2kAlpha[2];
cosThetaIp = cosThetaI * cos2kAlpha[2] + sinThetaI * sin2kAlpha[2];
sinThetaOp = sinThetaO * cos2kAlpha[2] + cosThetaO * sin2kAlpha[2];
cosThetaOp = cosThetaO * cos2kAlpha[2] - sinThetaO * sin2kAlpha[2];
} else {
sinThetaIp = sinThetaI;
cosThetaIp = cosThetaI;
sinThetaOp = sinThetaO;
cosThetaOp = cosThetaO;
}

// Handle out-of-range $\cos \thetai$ from scale adjustment
cosThetaIp = std::abs(cosThetaIp);
pdf += Mp(cosThetaIp, cosThetaO, sinThetaIp, sinThetaO, v[p]) *
// Handle out-of-range $\cos \thetao$ from scale adjustment
cosThetaOp = std::abs(cosThetaOp);
pdf += Mp(cosThetaI, cosThetaOp, sinThetaI, sinThetaOp, v[p]) *
apPdf[p] * Np(phi, p, s, gammaO, gammaT);
}
pdf += Mp(cosThetaI, cosThetaO, sinThetaI, sinThetaO, v[pMax]) *
Expand Down