void weak_white_furnace_test(
size_t num_runs,
const float alpha_x,
const float alpha_y,
const float gamma,
const float angle_step,
WeakWhiteFurnaceTestResult& result)
{
result.m_min_G1 = numeric_limits<float>::max();
result.m_max_G1 = -numeric_limits<float>::max();
result.m_min_result = numeric_limits<float>::max();
result.m_max_result = -numeric_limits<float>::max();
MDF mdf;
for (size_t i = 0; i < num_runs; ++i)
{
static const size_t Bases[] = { 2 };
const Vector2f s = hammersley_sequence<float, 2>(Bases, num_runs, i);
const Vector3f v = sample_hemisphere_uniform(s);
const float G1 = mdf.G1(v, Vector3f(0.0f, 1.0, 0.0f), alpha_x, alpha_y, gamma);
result.m_min_G1 = std::min(result.m_min_G1, G1);
result.m_max_G1 = std::max(result.m_max_G1, G1);
const float cos_thetha_o_4 = std::abs(4.0f * v.y);
float integral = 0.0f;
for (float theta = 0.0f; theta < Pi<float>(); theta += angle_step)
{
const float cos_theta = std::cos(theta);
const float sin_theta = std::sin(theta);
for (float phi = 0.0f; phi < TwoPi<float>(); phi += angle_step)
{
const float cos_phi = std::cos(phi);
const float sin_phi = std::sin(phi);
const Vector3f l =
Vector3f::make_unit_vector(
cos_theta,
sin_theta,
cos_phi,
sin_phi);
const Vector3f h = normalize(v + l);
if (h.y > 0.0f)
integral += sin_theta * mdf.D(h, alpha_x, alpha_y, gamma) * G1 / cos_thetha_o_4;
}
}
// Result should be 1.
integral *= square(angle_step);
result.m_min_result = std::min(result.m_min_result, integral);
result.m_max_result = std::max(result.m_max_result, integral);
}
}
void weak_white_furnace_test(
size_t num_runs,
const double alpha_x,
const double alpha_y,
const double angle_step,
WeakWhiteFurnaceTestResult& result)
{
result.m_min_G1 = numeric_limits<double>::max();
result.m_max_G1 = -numeric_limits<double>::max();
result.m_min_result = numeric_limits<double>::max();
result.m_max_result = -numeric_limits<double>::max();
MDF mdf;
for (size_t i = 0; i < num_runs; ++i)
{
static const size_t Bases[] = { 2 };
const Vector2d s = hammersley_sequence<double, 2>(Bases, num_runs, i);
const Vector3d v = sample_hemisphere_uniform(s);
const double G1 = mdf.G1(v, Vector3d(0.0, 1.0, 0.0), alpha_x, alpha_y);
result.m_min_G1 = std::min(result.m_min_G1, G1);
result.m_max_G1 = std::max(result.m_max_G1, G1);
const double cos_thetha_o_4 = std::abs(4.0 * v.y);
double integral = 0.0;
for (double theta = 0.0; theta < Pi<double>(); theta += angle_step)
{
const double cos_theta = std::cos(theta);
const double sin_theta = std::sin(theta);
for (double phi = 0.0; phi < TwoPi<double>(); phi += angle_step)
{
const double cos_phi = std::cos(phi);
const double sin_phi = std::sin(phi);
const Vector3d l =
Vector3d::make_unit_vector(
cos_theta,
sin_theta,
cos_phi,
sin_phi);
const Vector3d h = normalize(v + l);
if (h.y > 0.0)
integral += sin_theta * mdf.D(h, alpha_x, alpha_y) * G1 / cos_thetha_o_4;
}
}
// Result should be 1.
integral *= square(angle_step);
result.m_min_result = std::min(result.m_min_result, integral);
result.m_max_result = std::max(result.m_max_result, integral);
}
}
bool is_positive(
const MDF& mdf,
const typename MDF::ValueType alpha_x,
const typename MDF::ValueType alpha_y,
const size_t 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, sample_count, i);
const Vector<typename MDF::ValueType, 3> h = sample_hemisphere_uniform(s);
const double value = mdf.D(h, alpha_x, alpha_y);
if (value < 0.0)
return false;
}
return true;
}
bool is_positive(
const MDF& mdf,
const float alpha_x,
const float alpha_y,
const size_t sample_count,
const float gamma = 0.0f)
{
for (size_t i = 0; i < sample_count; ++i)
{
static const size_t Bases[] = { 2 };
const Vector2f s = hammersley_sequence<float, 2>(Bases, sample_count, i);
const Vector3f h = sample_hemisphere_uniform(s);
const float value = mdf.D(h, alpha_x, alpha_y, gamma);
if (value < 0.0f)
return false;
}
return true;
}
float integrate(
const MDF& mdf,
const float alpha,
const size_t sample_count,
const float gamma = 0.0f)
{
float integral = 0.0f;
for (size_t i = 0; i < sample_count; ++i)
{
const float theta = radical_inverse_base2<float>(i) * HalfPi<float>();
const Vector3f h(0.0f, cos(theta), 0.0f);
const float value = mdf.D(h, alpha, alpha, gamma);
integral += value * h.y * sin(theta);
}
integral *= HalfPi<float>() / sample_count; // integration over theta
integral *= TwoPi<float>(); // integration over phi
return integral;
}
typename MDF::ValueType integrate(
const MDF& mdf,
const typename MDF::ValueType alpha,
const size_t sample_count)
{
typedef typename MDF::ValueType ValueType;
ValueType integral = ValueType(0.0);
for (size_t i = 0; i < sample_count; ++i)
{
const ValueType theta = radical_inverse_base2<ValueType>(i) * HalfPi<ValueType>();
const Vector<ValueType, 3> h(ValueType(0.0), cos(theta), ValueType(0.0));
const ValueType value = mdf.D(h, alpha, alpha);
integral += value * h.y * sin(theta);
}
integral *= HalfPi<ValueType>() / sample_count; // integration over theta
integral *= TwoPi<ValueType>(); // integration over phi
return integral;
}