// wo.z >= 0 is guaranteed
// Note the sampled wi ~ D(wh)*cos(thetah)/(4*dot(wo,wh))
// and pdf = 0 when dot(wo, wh) < 0 (make sure Pdf() does the same thing)
void
GGXForHeitz::Sample_f(const Vector &wo, Vector *wi, float u1, float u2,
float *pdf) const
{
// We allow cos(theta_o) == 0 because it doesn't break our computation
Assert(CosTheta(wo) >= 0.f);
// From [Walter et al., 2007]
float thetah = atanf(mAlpha * sqrt(u1) / sqrt(1.f-u1)),
costhetah = cosf(thetah),
sinthetah = sinf(thetah),
phih = u2 * 2.f * M_PI;
Vector wh = SphericalDirection(sinthetah, costhetah, phih);
// Compute incident direction by reflecting about $\wh$
float dotHO = Dot(wo, wh);
if (dotHO < sSmallValue) {
*pdf = 0.f;
} else {
*wi = -wo + 2.f * dotHO * wh;
// TODO: test
//if (wi->z < 0) {
// fprintf(stderr, "wi.z == %f\n", wi->z);
//}
// TODO: can be optimized
*pdf = D(wh) * costhetah / (4.f * dotHO);
}
}
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;
}
// 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);
}
// commented, dpl 10 august 2005
void Anisotropic::Sample_f(const Vector &wo, Vector *wi,
float u1, float u2, float *pdf) const {
// Sample from first quadrant and remap to hemisphere to sample \wh
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 = M_PI - phi;
} else if (u1 < .75f) {
u1 = 4.f * (u1 - .5f);
sampleFirstQuadrant(u1, u2, &phi, &costheta);
phi += M_PI;
} else {
u1 = 4.f * (1.f - u1);
sampleFirstQuadrant(u1, u2, &phi, &costheta);
phi = 2.f * M_PI - phi;
}
float sintheta = sqrtf(max(0.f, 1.f - costheta*costheta));
Vector H = SphericalDirection(sintheta, costheta, phi);
if (Dot(wo, H) < 0.f) H = -H;
// Compute incident direction by reflecting about $\wh$
*wi = -wo + 2.f * Dot(wo, H) * H;
// Compute PDF for \wi from Anisotropic distribution
float anisotropic_pdf = D(H) / (4.f * Dot(wo, H));
*pdf = anisotropic_pdf;
}
Vector SampleHG(const Vector &w, float g, float u1, float u2) {
float costheta;
if (fabsf(g) < 1e-3)
costheta = 1.f - 2.f * u1;
else {
float sqrTerm = (1.f - g * g) /
(1.f - g + 2.f * g * u1);
costheta = (1.f + g * g - sqrTerm * sqrTerm) / (2.f * g);
}
float sintheta = sqrtf(max(0.f, 1.f-costheta*costheta));
float phi = 2.f * M_PI * u2;
Vector v1, v2;
CoordinateSystem(w, &v1, &v2);
return SphericalDirection(sintheta, costheta, phi, v1, v2, w);
}
Vector SampleHG(const Vector &w, float g, const float u1, const float u2) {
float costheta;
if (fabsf(g) < 1e-3f)
costheta = 1.f - 2.f * u1;
else {
// NOTE - lordcrc - Bugfix, pbrt tracker id 0000082: bug in SampleHG
const float sqrTerm = (1.f - g * g) / (1.f - g + 2.f * g * u1);
costheta = (1.f + g * g - sqrTerm * sqrTerm) / (2.f * g);
}
const float sintheta = sqrtf(Max(0.f, 1.f - costheta * costheta));
const float phi = 2.f * M_PI * u2;
Vector v1, v2;
CoordinateSystem(w, &v1, &v2);
return SphericalDirection(sintheta, costheta, phi, v1, v2, w);
}
void Blinn::Sample_f(const Vector &wo, Vector *wi,
float u1, float u2, float *pdf) const {
// 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 H = SphericalDirection(sintheta, costheta, phi);
if (Dot(wo, H) < 0.f) H = -H;
// Compute incident direction by reflecting about $\wh$
*wi = -wo + 2.f * Dot(wo, H) * H;
// Compute PDF for \wi from Blinn distribution
float blinn_pdf = ((exponent + 2.f) *
powf(costheta, exponent)) /
(2.f * M_PI * 4.f * Dot(wo, H));
*pdf = blinn_pdf;
}
Interaction Sphere::Sample(const Interaction &ref, const Point2f &u) const {
// Compute coordinate system for sphere sampling
Point3f pCenter = (*ObjectToWorld)(Point3f(0, 0, 0));
Vector3f wc = Normalize(pCenter - ref.p);
Vector3f wcX, wcY;
CoordinateSystem(wc, &wcX, &wcY);
// Sample uniformly on sphere if $\pt{}$ is inside it
Point3f pOrigin =
OffsetRayOrigin(ref.p, ref.pError, ref.n, pCenter - ref.p);
if (DistanceSquared(pOrigin, pCenter) <= radius * radius) return Sample(u);
// Sample sphere uniformly inside subtended cone
// Compute $\theta$ and $\phi$ values for sample in cone
Float sinThetaMax2 = radius * radius / DistanceSquared(ref.p, pCenter);
Float cosThetaMax = std::sqrt(std::max((Float)0, 1 - sinThetaMax2));
Float cosTheta = (1 - u[0]) + u[0] * cosThetaMax;
Float sinTheta = std::sqrt(1 - cosTheta * cosTheta);
Float phi = u[1] * 2 * Pi;
// Compute angle $\alpha$ from center of sphere to sampled point on surface
Float dc = Distance(ref.p, pCenter);
Float ds = dc * cosTheta -
std::sqrt(std::max(
(Float)0, radius * radius - dc * dc * sinTheta * sinTheta));
Float cosAlpha = (dc * dc + radius * radius - ds * ds) / (2 * dc * radius);
Float sinAlpha = std::sqrt(std::max((Float)0, 1 - cosAlpha * cosAlpha));
// Compute surface normal and sampled point on sphere
Vector3f nObj =
SphericalDirection(sinAlpha, cosAlpha, phi, -wcX, -wcY, -wc);
Point3f pObj = radius * Point3f(nObj.x, nObj.y, nObj.z);
// Return _Interaction_ for sampled point on sphere
Interaction it;
// Reproject _pObj_ to sphere surface and compute _pObjError_
pObj *= radius / Distance(pObj, Point3f(0, 0, 0));
Vector3f pObjError = gamma(5) * Abs((Vector3f)pObj);
it.p = (*ObjectToWorld)(pObj, pObjError, &it.pError);
it.n = (*ObjectToWorld)(Normal3f(nObj));
if (reverseOrientation) it.n *= -1.f;
return it;
}
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;
}
// HenyeyGreenstein Method Definitions
Float HenyeyGreenstein::Sample_p(const Vector3f &wo, Vector3f *wi,
const Point2f &u) const {
// Compute $\cos \theta$ for Henyey--Greenstein sample
Float cosTheta;
if (std::abs(g) < 1e-3)
cosTheta = 1 - 2 * u[0];
else {
Float sqrTerm = (1 - g * g) / (1 - g + 2 * g * u[0]);
cosTheta = (1 + g * g - sqrTerm * sqrTerm) / (2 * g);
}
// Compute direction _wi_ for Henyey--Greenstein sample
Float sinTheta = std::sqrt(std::max((Float)0, 1 - cosTheta * cosTheta));
Float phi = 2 * Pi * u[1];
Vector3f v1, v2;
CoordinateSystem(wo, &v1, &v2);
*wi = SphericalDirection(sinTheta, cosTheta, phi, v1, v2, -wo);
return PhaseHG(-cosTheta, g);
}
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;
}
MeasuredMaterial::MeasuredMaterial(string matName, const string &filename,
Reference<Texture<float> > bump): Material(matName) {
bumpMap = bump;
const char *suffix = strrchr(filename.c_str(), '.');
regularHalfangleData = NULL;
thetaPhiData = NULL;
if (!suffix)
Error("No suffix in measured BRDF filename \"%s\". "
"Can't determine file type (.brdf / .merl)", filename.c_str());
else if (!strcmp(suffix, ".brdf") || !strcmp(suffix, ".BRDF")) {
// Load $(\theta, \phi)$ measured BRDF data
if (loadedThetaPhi.find(filename) != loadedThetaPhi.end()) {
thetaPhiData = loadedThetaPhi[filename];
return;
}
vector<float> values;
if (!ReadFloatFile(filename.c_str(), &values)) {
Error("Unable to read BRDF data from file \"%s\"", filename.c_str());
return;
}
uint32_t pos = 0;
int numWls = int(values[pos++]);
if ((values.size() - 1 - numWls) % (4 + numWls) != 0) {
Error("Excess or insufficient data in theta, phi BRDF file \"%s\"",
filename.c_str());
return;
}
vector<float> wls;
for (int i = 0; i < numWls; ++i)
wls.push_back(values[pos++]);
BBox bbox;
vector<IrregIsotropicBRDFSample> samples;
while (pos < values.size()) {
float thetai = values[pos++];
float phii = values[pos++];
float thetao = values[pos++];
float phio = values[pos++];
Vector wo = SphericalDirection(sinf(thetao), cosf(thetao), phio);
Vector wi = SphericalDirection(sinf(thetai), cosf(thetai), phii);
Spectrum s = Spectrum::FromSampled(&wls[0], &values[pos], numWls);
pos += numWls;
pbrt::Point p = BRDFRemap(wo, wi);
samples.push_back(IrregIsotropicBRDFSample(p, s));
bbox = Union(bbox, p);
}
loadedThetaPhi[filename] = thetaPhiData = new KdTree<IrregIsotropicBRDFSample>(samples);
}
else {
// Load RegularHalfangle BRDF Data
nThetaH = 90;
nThetaD = 90;
nPhiD = 180;
if (loadedRegularHalfangle.find(filename) != loadedRegularHalfangle.end()) {
regularHalfangleData = loadedRegularHalfangle[filename];
return;
}
FILE *f = fopen(filename.c_str(), "rb");
if (!f) {
Error("Unable to open BRDF data file \"%s\"", filename.c_str());
return;
}
int dims[3];
if (fread(dims, sizeof(int), 3, f) != 3) {
Error("Premature end-of-file in measured BRDF data file \"%s\"",
filename.c_str());
fclose(f);
return;
}
uint32_t n = dims[0] * dims[1] * dims[2];
if (n != nThetaH * nThetaD * nPhiD) {
Error("Dimensions don't match\n");
fclose(f);
return;
}
regularHalfangleData = new float[3*n];
const uint32_t chunkSize = 2*nPhiD;
double *tmp = ALLOCA(double, chunkSize);
uint32_t nChunks = n / chunkSize;
Assert((n % chunkSize) == 0);
float scales[3] = { 1.f/1500.f, 1.15f/1500.f, 1.66f/1500.f };
for (int c = 0; c < 3; ++c) {
int offset = 0;
for (uint32_t i = 0; i < nChunks; ++i) {
if (fread(tmp, sizeof(double), chunkSize, f) != chunkSize) {
Error("Premature end-of-file in measured BRDF data file \"%s\"",
filename.c_str());
delete[] regularHalfangleData;
regularHalfangleData = NULL;
fclose(f);
return;
}
for (uint32_t j = 0; j < chunkSize; ++j)
regularHalfangleData[3 * offset++ + c] = max(0., tmp[j] * scales[c]);
}
}
loadedRegularHalfangle[filename] = regularHalfangleData;
fclose(f);
}
}
