bool DipoleBSSRDF::sample(
SamplingContext& sampling_context,
const void* data,
BSSRDFSample& sample) const
{
const DipoleBSSRDFInputValues* values =
reinterpret_cast<const DipoleBSSRDFInputValues*>(data);
if (values->m_weight == 0.0)
return false;
sampling_context.split_in_place(3, 1);
const Vector3d s = sampling_context.next_vector2<3>();
// Sample a channel.
const size_t channel =
sample_cdf(
&values->m_channel_cdf[0],
&values->m_channel_cdf[0] + values->m_channel_cdf.size(),
s[0]);
// Sample a radius.
const double sigma_tr = values->m_sigma_tr[channel];
const double radius = sample_exponential_distribution(s[1], sigma_tr);
// Sample an angle.
const double phi = TwoPi * s[2];
sample.m_eta = values->m_eta;
sample.m_channel = channel;
sample.m_point = Vector2d(radius * cos(phi), radius * sin(phi));
sample.m_rmax2 = values->m_rmax2;
return true;
}
double normalized_diffusion_sample(
const double u,
const double l,
const double s,
const double eps,
const size_t max_iterations)
{
assert(u >= 0.0);
assert(u < 1.0);
const double d = l / s;
// Handle the case where u is greater than the value we consider 1 in our CDF.
if (u >= nd_cdf_rmax)
return NdCdfTableRmax * d;
// Use the CDF to find an initial interval for the root of cdf(r, 1) - u = 0.
const size_t i = sample_cdf(nd_cdf_table, nd_cdf_table + NdCdfTableSize, u);
assert(i > 0);
assert(nd_cdf_table[i - 1] <= u);
assert(nd_cdf_table[i] > u);
// Transform the cdf(r, 1) interval to cdf(r, d) using the fact that cdf(r, d) == cdf(r/d, 1).
double rmin = fit<size_t, double>(i - 1, 0, NdCdfTableSize - 1, 0.0, NdCdfTableRmax) * d;
double rmax = fit<size_t, double>(i, 0, NdCdfTableSize - 1, 0.0, NdCdfTableRmax) * d;
assert(normalized_diffusion_cdf(rmin, d) <= u);
assert(normalized_diffusion_cdf(rmax, d) > u);
double r = (rmax + rmin) * 0.5;
// Refine the root.
for (size_t i = 0; i < max_iterations; ++i)
{
// Use bisection if we go out of bounds.
if (r < rmin || r > rmax)
r = (rmax + rmin) * 0.5;
const double f = normalized_diffusion_cdf(r, d) - u;
// Convergence test.
if (abs(f) <= eps)
break;
// Update bounds.
f < 0.0 ? rmin = r : rmax = r;
// Newton step.
const double df = normalized_diffusion_pdf(r, d);
r -= f / df;
}
return r;
}
double normalized_diffusion_sample(
const double u,
const double l,
const double s,
const double eps,
const size_t max_iterations)
{
assert(u >= 0.0);
assert(u < 1.0);
const double d = l / s;
// Handle the case where u is greater than the value we consider 1 in our CDF.
if (u >= nd_cdf_rmax)
return NDCDFTableRmax * d;
// Use the CDF to find an initial interval for the root of cdf(r, 1) - u = 0.
const size_t i = sample_cdf(nd_cdf_table, nd_cdf_table + NDCDFTableSize, u);
assert(i > 0);
assert(nd_cdf_table[i - 1] <= u);
assert(nd_cdf_table[i] > u);
// Transform the cdf(r, 1) interval to cdf(r, d) using the fact that cdf(r, d) == cdf(r/d, 1).
const double rmin = fit<size_t, double>(i - 1, 0, NDCDFTableSize - 1, 0.0, NDCDFTableRmax) * d;
const double rmax = fit<size_t, double>(i, 0, NDCDFTableSize - 1, 0.0, NDCDFTableRmax) * d;
return invert_cdf_function(
NDCDFFun(d),
NDPDFFun(d),
u,
rmin,
rmax,
(rmax + rmin) * 0.5,
eps,
max_iterations);
}
size_t CompositeClosure::choose_closure(const double w) const
{
return sample_cdf(m_cdf, m_cdf + get_num_closures(), w);
}
