void plot(
MapleFile& file,
const string& name,
const MDF& mdf,
const size_t point_count,
const size_t sample_count)
{
vector<double> angles(point_count);
vector<double> densities(point_count);
for (size_t i = 0; i < point_count; ++i)
{
const double angle =
fit(
static_cast<double>(i), 0.0, static_cast<double>(point_count - 1),
-HalfPi, +HalfPi);
const double cos_angle = cos(angle);
angles[i] = rad_to_deg(angle);
densities[i] = mdf.evaluate(cos_angle) * cos_angle;
}
vector<double> angle_samples(sample_count);
vector<double> density_samples(sample_count);
for (size_t i = 0; i < sample_count; ++i)
{
static const size_t Bases[] = { 2 };
const Vector2d s = hammersley_sequence<double, 2>(Bases, i, sample_count);
const Vector3d w = mdf.sample(s);
const double cos_angle = w.y;
const double angle = acos(cos_angle) * (w.x < 0.0 ? -1.0 : 1.0);
angle_samples[i] = rad_to_deg(angle);
density_samples[i] = mdf.evaluate(cos_angle) * cos_angle;
}
file.define(name, angles, densities);
file.define(name + "_samples", angle_samples, density_samples);
file.plot(
make_vector(
MaplePlotDef(name)
.set_legend("Microfacet Distribution Function (" + name + ")"),
MaplePlotDef(name + "_samples")
.set_legend("Integration Samples")
.set_style("point")
.set_color("red")));
}
double integrate_sampling(
const MDF& mdf,
const Sampler& sampler,
const size_t sample_count)
{
double integral = 0.0;
for (size_t i = 0; i < sample_count; ++i)
{
static const size_t Bases[] = { 2 };
const Vector2d s = hammersley_sequence<double, 2>(Bases, i, sample_count);
const Vector3d w = sampler.sample(s);
const double pdf = sampler.pdf(w);
const double cos_theta = w.y;
const double value = mdf.evaluate(cos_theta);
const double sample = value / pdf;
integral += sample * cos_theta;
}
integral /= static_cast<double>(sample_count);
return integral;
}
static void compute_specular_albedo(
const MDF& mdf,
const Spectrum& rs,
const Vector3d& V,
Spectrum& albedo)
{
// V must lie above or in the surface.
assert(V.y >= 0.0);
albedo.set(0.0f);
for (size_t i = 0; i < AlbedoSampleCount; ++i)
{
// Generate a uniform sample in [0,1)^2.
static const size_t Bases[] = { 2 };
const Vector2d s = hammersley_sequence<double, 2>(Bases, i, AlbedoSampleCount);
// Sample the microfacet distribution to get an halfway vector H.
const Vector3d H = mdf.sample(s);
const double dot_HV = dot(H, V);
if (dot_HV <= 0.0)
continue;
// L is the reflection of V around H.
const Vector3d L = (dot_HV + dot_HV) * H - V;
// Reject L if it lies in or below the surface.
if (L.y <= 0.0)
continue;
// Evaluate the PDF of L.
const double dot_HN = H.y;
const double pdf_H = mdf.evaluate_pdf(dot_HN);
const double pdf_L = pdf_H / (4.0 * dot_HV);
assert(pdf_L >= 0.0);
if (pdf_L == 0.0)
continue;
// Sanity checks.
assert(is_normalized(V));
assert(is_normalized(H));
assert(is_normalized(L));
// Evaluate the specular component for this (L, V) pair.
Spectrum fr_spec;
fr_spec = fresnel_dielectric_schlick(rs, dot_HV);
fr_spec *= static_cast<float>((L.y * mdf.evaluate(dot_HN)) / (4.0 * pdf_L * dot_HV * dot_HV));
albedo += fr_spec;
}
albedo /= static_cast<float>(AlbedoSampleCount);
}
static void evaluate_fr_spec(
const MDF& mdf,
const Spectrum& rs,
const double dot_HL, // cos_beta in the paper
const double dot_HN,
Spectrum& fr_spec)
{
assert(dot_HL >= 0.0);
assert(dot_HN >= 0.0);
fr_spec = fresnel_dielectric_schlick(rs, dot_HL);
fr_spec *= static_cast<float>(mdf.evaluate(dot_HN) / (4.0 * dot_HL * dot_HL));
}
bool is_positive(
const MDF& mdf,
const size_t sample_count)
{
for (size_t i = 0; i < sample_count; ++i)
{
const double theta = radical_inverse_base2<double>(i) * HalfPi;
const double cos_theta = cos(theta);
const double value = mdf.evaluate(cos_theta);
if (value < 0.0)
return false;
}
return true;
}
double integrate_quadrature(
const MDF& mdf,
const size_t sample_count)
{
double integral = 0.0;
for (size_t i = 0; i < sample_count; ++i)
{
const double theta = radical_inverse_base2<double>(i) * HalfPi;
const double cos_theta = cos(theta);
const double sin_theta = sin(theta);
const double value = mdf.evaluate(cos_theta);
integral += value * cos_theta * sin_theta;
}
integral *= HalfPi / sample_count; // integration over theta
integral *= TwoPi; // integration over phi
return integral;
}