Float fresnel(Float cosThetaI, Float etaExt, Float etaInt) {
Float etaI = etaExt, etaT = etaInt;
/* Swap the indices of refraction if the interaction starts
at the inside of the object */
if (cosThetaI < 0.0f)
std::swap(etaI, etaT);
/* Using Snell's law, calculate the sine of the angle
between the transmitted ray and the surface normal */
Float sinThetaT = etaI / etaT *
std::sqrt(std::max((Float) 0.0f, 1.0f - cosThetaI*cosThetaI));
if (sinThetaT > 1.0f)
return 1.0f; /* Total internal reflection! */
Float cosThetaT = std::sqrt(1.0f - sinThetaT*sinThetaT);
/* Finally compute the reflection coefficient */
return fresnelDielectric(std::abs(cosThetaI),
cosThetaT, etaI, etaT);
}
Float microfacet(Float mu_o, Float mu_i, std::complex<Float> eta_,
Float alpha, Float phi_d) {
Float sinThetaI = math::safe_sqrt(1-mu_i*mu_i),
sinThetaO = math::safe_sqrt(1-mu_o*mu_o),
cosPhi = std::cos(phi_d),
sinPhi = std::sin(phi_d);
Vector wi(-sinThetaI, 0, -mu_i);
Vector wo(sinThetaO*cosPhi, sinThetaO*sinPhi, mu_o);
bool reflect = -mu_i*mu_o > 0;
if (mu_o == 0 || mu_i == 0)
return 0.f;
bool conductor = eta_.imag() != 0.0f;
if (conductor && !reflect)
return 0.0f;
std::complex<Float> eta =
(-mu_i > 0 || conductor) ? eta_ : std::complex<Float>(1) / eta_;
Vector H = (wi + wo * (reflect ? 1.0f : eta.real())).normalized();
H *= math::signum(Frame::cosTheta(H));
Float cosThetaH2 = Frame::cosTheta2(H),
exponent = -Frame::tanTheta2(H) / (alpha*alpha),
D = std::exp(exponent) / (math::Pi * alpha*alpha * cosThetaH2*cosThetaH2),
F = !conductor ? fresnelDielectric(wi.dot(H), eta_.real())
: fresnelConductor(std::abs(wi.dot(H)), eta),
G = smithG1(wi, H, alpha) * smithG1(wo, H, alpha);
if (reflect) {
return F * D * G / (4.0f * std::abs(mu_i*mu_o));
} else {
Float sqrtDenom = wi.dot(H) + eta.real() * wo.dot(H);
return std::abs(((1 - F) * D * G * eta.real() * eta.real() * wi.dot(H)
* wo.dot(H)) / (mu_i*mu_o * sqrtDenom * sqrtDenom));
}
}
Spectrum sample(BSDFQueryRecord &bRec, Float &pdf, const Point2 &sample) const {
bool sampleReflection = (bRec.typeMask & EDeltaReflection)
&& (bRec.component == -1 || bRec.component == 0);
bool sampleTransmission = (bRec.typeMask & EDeltaTransmission)
&& (bRec.component == -1 || bRec.component == 1);
if (!sampleTransmission && !sampleReflection)
return Spectrum(0.0f);
Float cosThetaI = Frame::cosTheta(bRec.wi),
etaI = m_extIOR,
etaT = m_intIOR;
bool entering = cosThetaI > 0.0f;
/* Determine the respective indices of refraction */
if (!entering)
std::swap(etaI, etaT);
/* Using Snell's law, calculate the squared sine of the
angle between the normal and the transmitted ray */
Float eta = etaI / etaT,
sinThetaTSqr = eta*eta * Frame::sinTheta2(bRec.wi);
Float Fr, cosThetaT = 0;
if (sinThetaTSqr >= 1.0f) {
/* Total internal reflection */
Fr = 1.0f;
} else {
cosThetaT = std::sqrt(1.0f - sinThetaTSqr);
/* Compute the Fresnel refletance */
Fr = fresnelDielectric(std::abs(cosThetaI),
cosThetaT, etaI, etaT);
if (entering)
cosThetaT = -cosThetaT;
}
/* Calculate the refracted/reflected vectors+coefficients */
if (sampleTransmission && sampleReflection) {
/* Importance sample according to the reflectance/transmittance */
if (sample.x <= Fr) {
bRec.sampledComponent = 0;
bRec.sampledType = EDeltaReflection;
bRec.wo = reflect(bRec.wi);
pdf = Fr * std::abs(Frame::cosTheta(bRec.wo));
return m_specularReflectance->getValue(bRec.its) * Fr;
} else {
bRec.sampledComponent = 1;
bRec.sampledType = EDeltaTransmission;
/* Given cos(N, transmittedRay), compute the
transmitted direction */
bRec.wo = refract(bRec.wi, eta, cosThetaT);
pdf = (1-Fr) * std::abs(Frame::cosTheta(bRec.wo));
/* When transporting radiance, account for the solid angle
change at boundaries with different indices of refraction. */
return m_specularTransmittance->getValue(bRec.its)
* (1-Fr) * (bRec.quantity == ERadiance ? (eta*eta) : (Float) 1);
}
} else if (sampleReflection) {
bRec.sampledComponent = 0;
bRec.sampledType = EDeltaReflection;
bRec.wo = reflect(bRec.wi);
pdf = std::abs(Frame::cosTheta(bRec.wo));
return m_specularReflectance->getValue(bRec.its) * Fr;
} else {
bRec.sampledComponent = 1;
bRec.sampledType = EDeltaTransmission;
if (Fr == 1.0f) /* Total internal reflection */
return Spectrum(0.0f);
bRec.wo = refract(bRec.wi, eta, cosThetaT);
pdf = std::abs(Frame::cosTheta(bRec.wo));
/* When transporting radiance, account for the solid angle
change at boundaries with different indices of refraction. */
return m_specularTransmittance->getValue(bRec.its)
* ((1-Fr) * (bRec.quantity == ERadiance ? (eta*eta) : (Float) 1));
}
}
