Spectrum FourierBSDF::f(const Vector3f &wo, const Vector3f &wi) const {
// Find the zenith angle cosines and azimuth difference angle
Float muI = CosTheta(-wi), muO = CosTheta(wo);
Float cosPhi = CosDPhi(-wi, wo);
// Compute Fourier coefficients $a_k$ for $(\mui, \muo)$
// Determine offsets and weights for $\mui$ and $\muo$
int offsetI, offsetO;
Float weightsI[4], weightsO[4];
if (!bsdfTable.GetWeightsAndOffset(muI, &offsetI, weightsI) ||
!bsdfTable.GetWeightsAndOffset(muO, &offsetO, weightsO))
return Spectrum(0.f);
// Allocate storage to accumulate _ak_ coefficients
Float *ak = ALLOCA(Float, bsdfTable.mMax * bsdfTable.nChannels);
memset(ak, 0, bsdfTable.mMax * bsdfTable.nChannels * sizeof(Float));
// Accumulate weighted sums of nearby $a_k$ coefficients
int mMax = 0;
for (int b = 0; b < 4; ++b) {
for (int a = 0; a < 4; ++a) {
// Add contribution of _(a, b)_ to $a_k$ values
Float weight = weightsI[a] * weightsO[b];
if (weight != 0) {
int m;
const Float *ap = bsdfTable.GetAk(offsetI + a, offsetO + b, &m);
mMax = std::max(mMax, m);
for (int c = 0; c < bsdfTable.nChannels; ++c)
for (int k = 0; k < m; ++k)
ak[c * bsdfTable.mMax + k] += weight * ap[c * m + k];
}
}
}
// Evaluate Fourier expansion for angle $\phi$
Float Y = std::max((Float)0, Fourier(ak, mMax, cosPhi));
Float scale = muI != 0 ? (1 / std::abs(muI)) : (Float)0;
// Update _scale_ to account for adjoint light transport
if (mode == TransportMode::Radiance && muI * muO > 0) {
float eta = muI > 0 ? 1 / bsdfTable.eta : bsdfTable.eta;
scale *= eta * eta;
}
if (bsdfTable.nChannels == 1)
return Spectrum(Y * scale);
else {
// Compute and return RGB colors for tabulated BSDF
Float R = Fourier(ak + 1 * bsdfTable.mMax, mMax, cosPhi);
Float B = Fourier(ak + 2 * bsdfTable.mMax, mMax, cosPhi);
Float G = 1.39829f * Y - 0.100913f * B - 0.297375f * R;
Float rgb[3] = {R * scale, G * scale, B * scale};
return Spectrum::FromRGB(rgb).Clamp();
}
}
vtkRectilinearGrid* avtFFTFilter::ComputeFFT(std::vector<double>* data, long nData, double dt) {
debug5 <<"avtFFTFilter::ComputeFFT() - Entering" <<std::endl;
// 1. Find the power of 2 greater than length of history data
//We make a variable containing the value 2.0
//So that the windows compiler knows which "log" method we're trying to call
double doubleTwo = 2.0;
long nPwr2 = ceil(log((double)nData)/log(doubleTwo));
// 2) Get length of work array: nFFT = 2^nPwr2, nFFTdouble = 2*nFFT, nFFThalf = nFFT/2
long longTwo = 2;
long nFFT = pow((long double)longTwo, (int)nPwr2);
long nFFTdouble = 2 * nFFT;
long nFFThalf = nFFT / 2;
// 3) new double fftData[nFFTdouble], and zero-fill.
double* fftData = new double[nFFTdouble];
for(long i = 0; i < nFFTdouble; i++) {
fftData[i] = 0;
}
// 4) copy data over to fftData, with stride 2
for(long i = 0; i < nData; i++) {
fftData[i * 2] = data->operator[](i);
}
// 5) perform the FFT, Fourier(fftData,nFFT,1)
Fourier(fftData, nFFT, 1);
// 6) compute complex amplitude, dB, and compress in array
double oneENeg25 = pow((double)10, -25);
for(int i = 0; i < nFFThalf; i++) {
int jIndex = i * 2;
fftData[i] = 10 * log10(std::max(oneENeg25, (pow(fftData[jIndex], 2) + pow(fftData[jIndex + 1], 2))));
}
// 7) df = 1.0/(nFFT*dt)
double df = 1.0/(nFFT * dt);
// 8) get frequency axis: new freqs[nFFThalf], freq[i]=i*df
std::vector<double> freqs;
freqs.reserve(nFFThalf);
for(long i = 0; i < nFFThalf; i++) {
freqs.push_back(i * df);
}
// 9) Plot fftData[0:nFFThalf-1] vs. freqs.
vtkRectilinearGrid* outGrid = PopulateRGrid(&freqs, fftData, nFFThalf);
delete []fftData;
debug5 <<"avtFFTFilter::ComputeFFT() - Returning" <<std::endl;
return outGrid;
}
void CLjz153View::OnFft()
{
// TODO: Add your command handler code here
if (lpDIB_FFT)
free(lpDIB_FFT);
lpDIB_IFFT = NULL;
Fourier();
Invalidate();
}
static void split (COMPLEX *in, int r, int m, COMPLEX *out)
{
register unsigned k, s, i, j;
for (k = 0, j = 0; k < r; k++)
for (s = 0, i = k; s < m; s++, i += r, j++)
out [j] = in [i];
for (k = 0; k < r; k++, out += m, in += m)
Fourier (out, m, in);
}
rft (
COMPLEX *in,
unsigned n,
COMPLEX *out
)
{
if (W_init (n) == -1)
return -1;
Fourier (in, n, out);
return 0;
}
Float FourierBSDF::Pdf(const Vector3f &wo, const Vector3f &wi) const {
// Find the zenith angle cosines and azimuth difference angle
Float muI = CosTheta(-wi), muO = CosTheta(wo);
Float cosPhi = CosDPhi(-wi, wo);
// Compute luminance Fourier coefficients $a_k$ for $(\mui, \muo)$
int offsetI, offsetO;
Float weightsI[4], weightsO[4];
if (!bsdfTable.GetWeightsAndOffset(muI, &offsetI, weightsI) ||
!bsdfTable.GetWeightsAndOffset(muO, &offsetO, weightsO))
return 0;
Float *ak = ALLOCA(Float, bsdfTable.mMax * bsdfTable.nChannels);
memset(ak, 0, bsdfTable.mMax * bsdfTable.nChannels * sizeof(Float));
int mMax = 0;
for (int o = 0; o < 4; ++o) {
for (int i = 0; i < 4; ++i) {
Float weight = weightsI[i] * weightsO[o];
if (weight == 0) continue;
int order;
const Float *coeffs =
bsdfTable.GetAk(offsetI + i, offsetO + o, &order);
mMax = std::max(mMax, order);
for (int k = 0; k < order; ++k) ak[k] += *coeffs++ * weight;
}
}
// Evaluate probability of sampling _wi_
Float rho = 0;
for (int o = 0; o < 4; ++o) {
if (weightsO[o] == 0) continue;
rho +=
weightsO[o] *
bsdfTable.cdf[(offsetO + o) * bsdfTable.nMu + bsdfTable.nMu - 1] *
(2 * Pi);
}
Float Y = Fourier(ak, mMax, cosPhi);
return (rho > 0 && Y > 0) ? (Y / rho) : 0;
}
int fft (
COMPLEX *in,
unsigned n,
COMPLEX *out
)
{
unsigned i;
for (i = 0; i < n; i++)
c_conj (in [i]);
if (W_init (n) == -1)
return -1;
Fourier (in, n, out);
for (i = 0; i < n; i++) {
c_conj (out [i]);
c_realdiv (out [i], n);
}
return 0;
}
Spectrum FourierBSDF::Sample_f(const Vector3f &wo, Vector3f *wi,
const Point2f &u, Float *pdf,
BxDFType *sampledType) const {
// Sample zenith angle component for _FourierBSDF_
Float muO = CosTheta(wo);
Float pdfMu;
Float muI = SampleCatmullRom2D(bsdfTable.nMu, bsdfTable.nMu, bsdfTable.mu,
bsdfTable.mu, bsdfTable.avg, bsdfTable.cdf,
muO, u[1], nullptr, &pdfMu);
// Compute Fourier coefficients $a_k$ for $(\mui, \muo)$
// Determine offsets and weights for $\mui$ and $\muo$
int offsetI, offsetO;
Float weightsI[4], weightsO[4];
if (!bsdfTable.GetWeightsAndOffset(muI, &offsetI, weightsI) ||
!bsdfTable.GetWeightsAndOffset(muO, &offsetO, weightsO))
return Spectrum(0.f);
// Allocate storage to accumulate _ak_ coefficients
Float *ak = ALLOCA(Float, bsdfTable.mMax * bsdfTable.nChannels);
memset(ak, 0, bsdfTable.mMax * bsdfTable.nChannels * sizeof(Float));
// Accumulate weighted sums of nearby $a_k$ coefficients
int mMax = 0;
for (int b = 0; b < 4; ++b) {
for (int a = 0; a < 4; ++a) {
// Add contribution of _(a, b)_ to $a_k$ values
Float weight = weightsI[a] * weightsO[b];
if (weight != 0) {
int m;
const Float *ap = bsdfTable.GetAk(offsetI + a, offsetO + b, &m);
mMax = std::max(mMax, m);
for (int c = 0; c < bsdfTable.nChannels; ++c)
for (int k = 0; k < m; ++k)
ak[c * bsdfTable.mMax + k] += weight * ap[c * m + k];
}
}
}
// Importance sample the luminance Fourier expansion
Float phi, pdfPhi;
Float Y = SampleFourier(ak, bsdfTable.recip, mMax, u[0], &pdfPhi, &phi);
*pdf = std::max((Float)0, pdfPhi * pdfMu);
// Compute the scattered direction for _FourierBSDF_
Float sin2ThetaI = 1 - muI * muI;
Float norm = std::sqrt(sin2ThetaI / Sin2Theta(wo));
Float sinPhi = std::sin(phi), cosPhi = std::cos(phi);
*wi = -Vector3f(norm * (cosPhi * wo.x - sinPhi * wo.y),
norm * (sinPhi * wo.x + cosPhi * wo.y), muI);
// Evaluate remaining Fourier expansions for angle $\phi$
Float scale = muI != 0 ? (1 / std::abs(muI)) : (Float)0;
if (mode == TransportMode::Radiance && muI * muO > 0) {
float eta = muI > 0 ? 1 / bsdfTable.eta : bsdfTable.eta;
scale *= eta * eta;
}
if (bsdfTable.nChannels == 1) return Spectrum(Y * scale);
Float R = Fourier(ak + 1 * bsdfTable.mMax, mMax, cosPhi);
Float B = Fourier(ak + 2 * bsdfTable.mMax, mMax, cosPhi);
Float G = 1.39829f * Y - 0.100913f * B - 0.297375f * R;
Float rgb[3] = {R * scale, G * scale, B * scale};
return Spectrum::FromRGB(rgb).Clamp();
}
