// commented, dpl 10 august 2005
Spectrum Lafortune::Sample_f(const Vector &wo, Vector *wi,
float u1, float u2, float *pdf) const {
u_int comp = RandomUInt() % (nLobes+1);
if (comp == nLobes) {
// Cosine-sample the hemisphere, flipping the direction if necessary
*wi = CosineSampleHemisphere(u1, u2);
if (wo.z < 0.) wi->z *= -1.f;
}
else {
// Sample lobe _comp_ for Lafortune BRDF
float xlum = x[comp].y();
float ylum = y[comp].y();
float zlum = z[comp].y();
float costheta = powf(u1, 1.f / (.8f * exponent[comp].y() + 1));
float sintheta = sqrtf(max(0.f, 1.f - costheta*costheta));
float phi = u2 * 2.f * M_PI;
Vector lobeCenter = Normalize(Vector(xlum * wo.x, ylum * wo.y, zlum * wo.z));
Vector lobeX, lobeY;
CoordinateSystem(lobeCenter, &lobeX, &lobeY);
*wi = SphericalDirection(sintheta, costheta, phi, lobeX, lobeY,
lobeCenter);
}
if (!SameHemisphere(wo, *wi)) return Spectrum(0.f);
*pdf = Pdf(wo, *wi);
return f(wo, *wi);
}
Vector3f TrowbridgeReitzDistribution::Sample_wh(const Vector3f &wo,
const Point2f &u) const {
Vector3f wh;
if (!sampleVisibleArea) {
Float cosTheta = 0, phi = (2 * Pi) * u[1];
if (alphax == alphay) {
Float tanTheta2 = alphax * alphax * u[0] / (1.0f - u[0]);
cosTheta = 1 / std::sqrt(1 + tanTheta2);
} else {
phi =
std::atan(alphay / alphax * std::tan(2 * Pi * u[1] + .5f * Pi));
if (u[1] > .5f) phi += Pi;
Float sinPhi = std::sin(phi), cosPhi = std::cos(phi);
const Float alphax2 = alphax * alphax, alphay2 = alphay * alphay;
const Float alpha2 =
1 / (cosPhi * cosPhi / alphax2 + sinPhi * sinPhi / alphay2);
Float tanTheta2 = alpha2 * u[0] / (1 - u[0]);
cosTheta = 1 / std::sqrt(1 + tanTheta2);
}
Float sinTheta =
std::sqrt(std::max((Float)0., (Float)1. - cosTheta * cosTheta));
wh = SphericalDirection(sinTheta, cosTheta, phi);
if (!SameHemisphere(wo, wh)) wh = -wh;
} else {
bool flip = wo.z < 0;
wh = TrowbridgeReitzSample(flip ? -wo : wo, alphax, alphay, u[0], u[1]);
if (flip) wh = -wh;
}
return wh;
}
float BxDF::PDF(const Vector3& p_wo, const Vector3& p_wi) const {
bool temp = SameHemisphere(p_wo, p_wi);
if (temp){
return AbsCosTheta(p_wi) * Maths::InvPi;
}
return 0.0f;
//return SameHemisphere(p_wo, p_wi) ? AbsCosTheta(p_wi) * Maths::InvPi : 0.f;
}
Spectrum MicrofacetReflection::Sample_f(const Vector3f &wo, Vector3f *wi,
const Point2f &u, Float *pdf,
BxDFType *sampledType) const {
// Sample microfacet orientation $\wh$ and reflected direction $\wi$
Vector3f wh = distribution->Sample_wh(wo, u);
*wi = Reflect(wo, wh);
if (!SameHemisphere(wo, *wi)) return Spectrum(0.f);
// Compute PDF of _wi_ for microfacet reflection
*pdf = distribution->Pdf(wo, wh) / (4 * Dot(wo, wh));
return f(wo, *wi);
}
float
Heitz::Pdf(const Vector &wo, const Vector &wi) const
{
// TODO: for test
if (mUseUniformSampling) {
return SameHemisphere(wo, wi) ? AbsCosTheta(wi) * INV_PI : 0.f;
} else {
float pdfSpec = 0.f;
if (wo.z < 0.f) {
// Reverse side
pdfSpec = mDistribution.Pdf(-wo, -wi);
} else {
pdfSpec = mDistribution.Pdf(wo, wi);
}
float pdfDiff = SameHemisphere(wo, wi) ? AbsCosTheta(wi) * INV_PI : 0.f;
// TODO: what percentage between diffuse and specular? Currently use 50%
return (pdfDiff + pdfSpec) * 0.5f;
}
}
Float MicrofacetTransmission::Pdf(const Vector3f &wo,
const Vector3f &wi) const {
if (SameHemisphere(wo, wi)) return 0;
// Compute $\wh$ from $\wo$ and $\wi$ for microfacet transmission
Float eta = CosTheta(wo) > 0 ? (etaB / etaA) : (etaA / etaB);
Vector3f wh = Normalize(wo + wi * eta);
// Compute change of variables _dwh\_dwi_ for microfacet transmission
Float sqrtDenom = Dot(wo, wh) + eta * Dot(wi, wh);
Float dwh_dwi =
std::abs((eta * eta * Dot(wi, wh)) / (sqrtDenom * sqrtDenom));
return distribution->Pdf(wo, wh) * dwh_dwi;
}
float Lafortune::Pdf(const Vector &wo, const Vector &wi) const {
if (!SameHemisphere(wo, wi)) return 0.f;
float pdfSum = fabsf(wi.z) * INV_PI;
for (u_int i = 0; i < nLobes; ++i) {
float xlum = x[i].y();
float ylum = y[i].y();
float zlum = z[i].y();
Vector lobeCenter =
Normalize(Vector(wo.x * xlum, wo.y * ylum, wo.z * zlum));
float e = .8f * exponent[i].y();
pdfSum += (e + 1.f) * powf(max(0.f, Dot(wi, lobeCenter)), e);
}
return pdfSum / (1.f + nLobes);
}
// commented, dpl 10 august 2005
Spectrum FresnelBlend::Sample_f(const Vector &wo,
Vector *wi, float u1, float u2, float *pdf) const {
if (u1 < .5) {
u1 = 2.f * u1;
// Cosine-sample the hemisphere, flipping the direction if necessary
*wi = CosineSampleHemisphere(u1, u2);
if (wo.z < 0.) wi->z *= -1.f;
}
else {
u1 = 2.f * (u1 - .5f);
distribution->Sample_f(wo, wi, u1, u2, pdf);
if (!SameHemisphere(wo, *wi)) return Spectrum(0.f);
}
*pdf = Pdf(wo, *wi);
return f(wo, *wi);
}
void SampleBlinn(const Vector &wo, Vector *wi, float u1, float u2, float *pdf,
float exponent) {
// Compute sampled half-angle vector $\wh$ for Blinn distribution
float costheta = powf(u1, 1.f / (exponent+1));
float sintheta = sqrtf(max(0.f, 1.f - costheta*costheta));
float phi = u2 * 2.f * M_PI;
Vector wh = SphericalDirection(sintheta, costheta, phi);
if (!SameHemisphere(wo, wh)) wh = -wh;
// Compute incident direction by reflecting about $\wh$
*wi = -wo + 2.f * Dot(wo, wh) * wh;
// Compute PDF for $\wi$ from Blinn distribution
float blinn_pdf = ((exponent + 1.f) * powf(costheta, exponent)) /
(2.f * M_PI * 4.f * Dot(wo, wh));
if (Dot(wo, wh) < 0.f) blinn_pdf = 0.f;
*pdf = blinn_pdf;
}
Spectrum FresnelBlend::Sample_f(const Vector3f &wo, Vector3f *wi,
const Point2f &uOrig, Float *pdf,
BxDFType *sampledType) const {
Point2f u = uOrig;
if (u[0] < .5) {
u[0] = 2 * u[0];
// Cosine-sample the hemisphere, flipping the direction if necessary
*wi = CosineSampleHemisphere(u);
if (wo.z < 0) wi->z *= -1;
} else {
u[0] = 2 * (u[0] - .5f);
// Sample microfacet orientation $\wh$ and reflected direction $\wi$
Vector3f wh = distribution->Sample_wh(wo, u);
*wi = Reflect(wo, wh);
if (!SameHemisphere(wo, *wi)) return Spectrum(0.f);
}
*pdf = Pdf(wo, *wi);
return f(wo, *wi);
}
Vector3f BeckmannDistribution::Sample_wh(const Vector3f &wo,
const Point2f &u) const {
if (!sampleVisibleArea) {
// Sample full distribution of normals for Beckmann distribution
// Compute $\tan^2 \theta$ and $\phi$ for Beckmann distribution sample
Float tan2Theta, phi;
if (alphax == alphay) {
Float logSample = std::log(u[0]);
if (std::isinf(logSample)) logSample = 0;
tan2Theta = -alphax * alphax * logSample;
phi = u[1] * 2 * Pi;
} else {
// Compute _tan2Theta_ and _phi_ for anisotropic Beckmann
// distribution
Float logSample = std::log(u[0]);
if (std::isinf(logSample)) logSample = 0;
phi = std::atan(alphay / alphax *
std::tan(2 * Pi * u[1] + 0.5f * Pi));
if (u[1] > 0.5f) phi += Pi;
Float sinPhi = std::sin(phi), cosPhi = std::cos(phi);
Float alphax2 = alphax * alphax, alphay2 = alphay * alphay;
tan2Theta = -logSample /
(cosPhi * cosPhi / alphax2 + sinPhi * sinPhi / alphay2);
}
// Map sampled Beckmann angles to normal direction _wh_
Float cosTheta = 1 / std::sqrt(1 + tan2Theta);
Float sinTheta = std::sqrt(std::max((Float)0, 1 - cosTheta * cosTheta));
Vector3f wh = SphericalDirection(sinTheta, cosTheta, phi);
if (!SameHemisphere(wo, wh)) wh = -wh;
return wh;
} else {
// Sample visible area of normals with Beckmann distribution
Vector3f wh;
bool flip = wo.z < 0;
wh = BeckmannSample(flip ? -wo : wo, alphax, alphay, u[0], u[1]);
if (flip) wh = -wh;
return wh;
}
}
//复制自PBRT
void Anisotropic::Sample_f(const Vector3f &wo, Vector3f *wi, Float u1, Float u2,
Float *pdf) const {
Float phi, costheta;
if (u1 < .25f) {
sampleFirstQuadrant(4.f * u1, u2, &phi, &costheta);
} else if (u1 < .5f) {
u1 = 4.f * (.5f - u1);
sampleFirstQuadrant(u1, u2, &phi, &costheta);
phi = Pi - phi;
} else if (u1 < .75f) {
u1 = 4.f * (u1 - .5f);
sampleFirstQuadrant(u1, u2, &phi, &costheta);
phi += Pi;
} else {
u1 = 4.f * (1.f - u1);
sampleFirstQuadrant(u1, u2, &phi, &costheta);
phi = 2.f * Pi - phi;
}
Float sintheta = sqrtf(std::max(0.f, 1.f - costheta * costheta));
Vector3f wh = SphericalDirection(sintheta, costheta, phi);
if (!SameHemisphere(wo, wh))
wh = -wh;
// Compute incident direction by reflecting about $\wh$
*wi = -wo + 2.f * Dot(wo, wh) * wh;
// Compute PDF for $\wi$ from anisotropic distribution
Float costhetah = AbsCosTheta(wh);
Float ds = 1.f - costhetah * costhetah;
Float anisotropic_pdf = 0.f;
if (ds > 0.f && Dot(wo, wh) > 0.f) {
Float e = (ex * wh.x * wh.x + ey * wh.y * wh.y) / ds;
Float d = sqrtf((ex + 1.f) * (ey + 1.f)) * InvTwoPi
* powf(costhetah, e);
anisotropic_pdf = d / (4.f * Dot(wo, wh));
}
*pdf = anisotropic_pdf;
}
// BxDF Method Definitions
bool BxDF::SampleF(const SpectrumWavelengths &sw, const Vector &wo, Vector *wi,
float u1, float u2, SWCSpectrum *const f, float *pdf, float *pdfBack,
bool reverse) const
{
// Cosine-sample the hemisphere, flipping the direction if necessary
*wi = CosineSampleHemisphere(u1, u2);
if (wo.z < 0.f)
wi->z = -(wi->z);
// wi may be in the tangent plane, which will
// fail the SameHemisphere test in Pdf()
if (!SameHemisphere(wo, *wi))
return false;
*pdf = Pdf(sw, wo, *wi);
if (pdfBack)
*pdfBack = Pdf(sw, *wi, wo);
*f = SWCSpectrum(0.f);
if (reverse)
F(sw, *wi, wo, f);
else
F(sw, wo, *wi, f);
*f /= *pdf;
return true;
}
Spectrum MicrofacetTransmission::f(const Vector3f &wo,
const Vector3f &wi) const {
if (SameHemisphere(wo, wi)) return 0; // transmission only
Float cosThetaO = CosTheta(wo);
Float cosThetaI = CosTheta(wi);
if (cosThetaI == 0 || cosThetaO == 0) return Spectrum(0);
// Compute $\wh$ from $\wo$ and $\wi$ for microfacet transmission
Float eta = CosTheta(wo) > 0 ? (etaB / etaA) : (etaA / etaB);
Vector3f wh = Normalize(wo + wi * eta);
if (wh.z < 0) wh = -wh;
Spectrum F = fresnel.Evaluate(Dot(wo, wh));
Float sqrtDenom = Dot(wo, wh) + eta * Dot(wi, wh);
Float factor = (mode == TransportMode::Radiance) ? (1 / eta) : 1;
return (Spectrum(1.f) - F) * T *
std::abs(distribution->D(wh) * distribution->G(wo, wi) * eta * eta *
AbsDot(wi, wh) * AbsDot(wo, wh) * factor * factor /
(cosThetaI * cosThetaO * sqrtDenom * sqrtDenom));
}
Float BxDF::Pdf(const Vector3f &wo, const Vector3f &wi) const {
return SameHemisphere(wo, wi) ? AbsCosTheta(wi) * InvPi : 0;
}
float BxDF::Pdf(const Vector &wo, const Vector &wi) const {
return
SameHemisphere(wo, wi) ? fabsf(wi.z) * INV_PI : 0.f;
}
float BxDF::Pdf(const SpectrumWavelengths &sw, const Vector &wo, const Vector &wi) const {
return SameHemisphere(wo, wi) ? fabsf(wi.z) * INV_PI : 0.f;
}
Float FresnelBlend::Pdf(const Vector3f &wo, const Vector3f &wi) const {
if (!SameHemisphere(wo, wi)) return 0;
Vector3f wh = Normalize(wo + wi);
Float pdf_wh = distribution->Pdf(wo, wh);
return .5f * (AbsCosTheta(wi) * InvPi + pdf_wh / (4 * Dot(wo, wh)));
}
Spectrum Microfacet::Sample_f(const Vector &wo, Vector *wi,
float u1, float u2, float *pdf) const {
distribution->Sample_f(wo, wi, u1, u2, pdf);
if (!SameHemisphere(wo, *wi)) return Spectrum(0.f);
return f(wo, *wi);
}
float Microfacet::Pdf(const Vector &wo,
const Vector &wi) const {
if (!SameHemisphere(wo, wi)) return 0.f;
return distribution->Pdf(wo, wi);
}
Float MicrofacetReflection::Pdf(const Vector3f &wo, const Vector3f &wi) const {
if (!SameHemisphere(wo, wi)) return 0;
Vector3f wh = Normalize(wo + wi);
return distribution->Pdf(wo, wh) / (4 * Dot(wo, wh));
}
float FresnelBlend::Pdf(const Vector &wo,
const Vector &wi) const {
if (!SameHemisphere(wo, wi)) return 0.f;
return .5f * (fabsf(wi.z) * INV_PI +
distribution->Pdf(wo, wi));
}
// the pdf for the sampled direction
float Bxdf::Pdf( const Vector& wo , const Vector& wi ) const
{
if( !SameHemisphere( wo , wi ) )
return 0.0f;
return fabs(CosHemispherePdf( wi ));
}
Float LambertianTransmission::Pdf(const Vector3f &wo,
const Vector3f &wi) const {
return !SameHemisphere(wo, wi) ? AbsCosTheta(wi) * InvPi : 0;
}
