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Small improvements in spherical importance sampler
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@dictoon
dictoon committed Apr 6, 2020
1 parent 996be12 commit 35f8c26
Showing 1 changed file with 82 additions and 85 deletions.
167 changes: 82 additions & 85 deletions src/appleseed/foundation/math/sampling/sphericalimportancesampler.h
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Original file line number Diff line number Diff line change
Expand Up @@ -45,18 +45,30 @@
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <map>
#include <unordered_map>
#include <vector>

namespace foundation
{

//
// References:
//
// http://en.wikipedia.org/wiki/Regular_icosahedron#Cartesian_coordinates
//
// Creating an icosphere mesh in code
// http://blog.andreaskahler.com/2009/06/creating-icosphere-mesh-in-code.html
//
// Stratified Sampling of Spherical Triangles
// http://www.graphics.cornell.edu/pubs/1995/Arv95c.pdf
//

template <typename T>
class SphericalImportanceSampler
: public foundation::NonCopyable
{
public:
explicit SphericalImportanceSampler(const size_t subdivisions);
explicit SphericalImportanceSampler(const std::size_t subdivisions);

Vector<T, 3> sample(const Vector<T, 3>& s) const;

Expand All @@ -66,53 +78,51 @@ class SphericalImportanceSampler
private:
struct Tri
{
size_t m_v0, m_v1, m_v2;
std::size_t m_v0, m_v1, m_v2;

Tri() {}
Tri() = default;

Tri(const size_t v0, const size_t v1, const size_t v2)
Tri(const std::size_t v0, const std::size_t v1, const std::size_t v2)
: m_v0(v0)
, m_v1(v1)
, m_v2(v2)
{
}
};

typedef std::map<std::uint64_t, size_t> PointCache;
using PointCache = std::unordered_map<std::uint64_t, std::size_t>;

std::vector<Vector<T, 3>> m_verts;
std::vector<Tri> m_tris;
CDF<size_t, T> m_cdf;
CDF<std::size_t, T> m_cdf;

void create_regular_icosahedron();
void subdivide(const size_t subdivisions);
size_t get_or_create_middle_point(PointCache& point_cache, size_t v0, size_t v1);
void push_regular_icosahedron();
void subdivide(const std::size_t subdivisions);
std::size_t get_or_create_middle_point(PointCache& point_cache, std::size_t v0, std::size_t v1);
void build_cdf();
};


//
// SphericalImportanceSampler class implementation.
//
// References:
//
// http://en.wikipedia.org/wiki/Regular_icosahedron#Cartesian_coordinates
// http://blog.andreaskahler.com/2009/06/creating-icosphere-mesh-in-code.html
// http://www.graphics.cornell.edu/pubs/1995/Arv95c.pdf
//

template <typename T>
SphericalImportanceSampler<T>::SphericalImportanceSampler(const size_t subdivisions)
SphericalImportanceSampler<T>::SphericalImportanceSampler(const std::size_t subdivisions)
{
create_regular_icosahedron();
const std::size_t four_power = pow_int<std::size_t>(4, subdivisions);
m_verts.reserve(10 * four_power + 2); // see https://oeis.org/A122973
m_tris.reserve(20 * four_power);

push_regular_icosahedron();
subdivide(subdivisions);
build_cdf();
}

template <typename T>
Vector<T, 3> SphericalImportanceSampler<T>::sample(const Vector<T, 3>& s) const
{
const size_t tri_index = m_cdf.sample(s[0]).first;
const std::size_t tri_index = m_cdf.sample(s[0]).first;
const Tri& tri = m_tris[tri_index];

return
Expand All @@ -131,15 +141,11 @@ bool SphericalImportanceSampler<T>::dump_as_obj(const char* filepath) const
if (file == nullptr)
return false;

for (size_t i = 0; i < m_verts.size(); ++i)
{
const Vector<T, 3>& vert = m_verts[i];
for (const Vector<T, 3>& vert : m_verts)
std::fprintf(file, "v %.15f %.15f %.15f\n", vert.x, vert.y, vert.z);
}

for (size_t i = 0; i < m_tris.size(); ++i)
for (const Tri& tri : m_tris)
{
const Tri& tri = m_tris[i];
std::fprintf(
file,
"f " FMT_SIZE_T " " FMT_SIZE_T " " FMT_SIZE_T "\n",
Expand All @@ -154,9 +160,8 @@ bool SphericalImportanceSampler<T>::dump_as_obj(const char* filepath) const
template <typename T>
void SphericalImportanceSampler<T>::dump_to_vpython_file(VPythonFile& file) const
{
for (size_t i = 0; i < m_tris.size(); ++i)
for (const Tri& tri : m_tris)
{
const Tri& tri = m_tris[i];
const Vector3d points[] =
{
Vector3d(m_verts[tri.m_v0]),
Expand All @@ -170,87 +175,79 @@ void SphericalImportanceSampler<T>::dump_to_vpython_file(VPythonFile& file) cons
}

template <typename T>
void SphericalImportanceSampler<T>::create_regular_icosahedron()
void SphericalImportanceSampler<T>::push_regular_icosahedron()
{
m_verts.reserve(12);
m_tris.reserve(20);
const T phi = GoldenRatio<T>();

m_verts.push_back(normalize(Vector<T, 3>(T(-1.0), GoldenRatio<T>(), T(0.0))));
m_verts.push_back(normalize(Vector<T, 3>(T( 1.0), GoldenRatio<T>(), T(0.0))));
m_verts.push_back(normalize(Vector<T, 3>(T(-1.0), -GoldenRatio<T>(), T(0.0))));
m_verts.push_back(normalize(Vector<T, 3>(T( 1.0), -GoldenRatio<T>(), T(0.0))));
m_verts.emplace_back(normalize(Vector<T, 3>(T(-1.0), phi, T(0.0))));
m_verts.emplace_back(normalize(Vector<T, 3>(T( 1.0), phi, T(0.0))));
m_verts.emplace_back(normalize(Vector<T, 3>(T(-1.0), -phi, T(0.0))));
m_verts.emplace_back(normalize(Vector<T, 3>(T( 1.0), -phi, T(0.0))));

m_verts.push_back(normalize(Vector<T, 3>(T(0.0), T(-1.0), GoldenRatio<T>())));
m_verts.push_back(normalize(Vector<T, 3>(T(0.0), T( 1.0), GoldenRatio<T>())));
m_verts.push_back(normalize(Vector<T, 3>(T(0.0), T(-1.0), -GoldenRatio<T>())));
m_verts.push_back(normalize(Vector<T, 3>(T(0.0), T( 1.0), -GoldenRatio<T>())));
m_verts.emplace_back(normalize(Vector<T, 3>(T(0.0), T(-1.0), phi)));
m_verts.emplace_back(normalize(Vector<T, 3>(T(0.0), T( 1.0), phi)));
m_verts.emplace_back(normalize(Vector<T, 3>(T(0.0), T(-1.0), -phi)));
m_verts.emplace_back(normalize(Vector<T, 3>(T(0.0), T( 1.0), -phi)));

m_verts.push_back(normalize(Vector<T, 3>( GoldenRatio<T>(), T(0.0), T(-1.0))));
m_verts.push_back(normalize(Vector<T, 3>( GoldenRatio<T>(), T(0.0), T( 1.0))));
m_verts.push_back(normalize(Vector<T, 3>(-GoldenRatio<T>(), T(0.0), T(-1.0))));
m_verts.push_back(normalize(Vector<T, 3>(-GoldenRatio<T>(), T(0.0), T( 1.0))));
m_verts.emplace_back(normalize(Vector<T, 3>( phi, T(0.0), T(-1.0))));
m_verts.emplace_back(normalize(Vector<T, 3>( phi, T(0.0), T( 1.0))));
m_verts.emplace_back(normalize(Vector<T, 3>(-phi, T(0.0), T(-1.0))));
m_verts.emplace_back(normalize(Vector<T, 3>(-phi, T(0.0), T( 1.0))));

// 5 faces around point 0.
m_tris.push_back(Tri(0, 11, 5));
m_tris.push_back(Tri(0, 5, 1));
m_tris.push_back(Tri(0, 1, 7));
m_tris.push_back(Tri(0, 7, 10));
m_tris.push_back(Tri(0, 10, 11));
m_tris.emplace_back(0, 11, 5);
m_tris.emplace_back(0, 5, 1);
m_tris.emplace_back(0, 1, 7);
m_tris.emplace_back(0, 7, 10);
m_tris.emplace_back(0, 10, 11);

// 5 adjacent faces.
m_tris.push_back(Tri(1, 5, 9));
m_tris.push_back(Tri(5, 11, 4));
m_tris.push_back(Tri(11, 10, 2));
m_tris.push_back(Tri(10, 7, 6));
m_tris.push_back(Tri(7, 1, 8));
m_tris.emplace_back(1, 5, 9);
m_tris.emplace_back(5, 11, 4);
m_tris.emplace_back(11, 10, 2);
m_tris.emplace_back(10, 7, 6);
m_tris.emplace_back(7, 1, 8);

// 5 faces around point 3.
m_tris.push_back(Tri(3, 9, 4));
m_tris.push_back(Tri(3, 4, 2));
m_tris.push_back(Tri(3, 2, 6));
m_tris.push_back(Tri(3, 6, 8));
m_tris.push_back(Tri(3, 8, 9));
m_tris.emplace_back(3, 9, 4);
m_tris.emplace_back(3, 4, 2);
m_tris.emplace_back(3, 2, 6);
m_tris.emplace_back(3, 6, 8);
m_tris.emplace_back(3, 8, 9);

// 5 adjacent faces.
m_tris.push_back(Tri(4, 9, 5));
m_tris.push_back(Tri(2, 4, 11));
m_tris.push_back(Tri(6, 2, 10));
m_tris.push_back(Tri(8, 6, 7));
m_tris.push_back(Tri(9, 8, 1));
m_tris.emplace_back(4, 9, 5);
m_tris.emplace_back(2, 4, 11);
m_tris.emplace_back(6, 2, 10);
m_tris.emplace_back(8, 6, 7);
m_tris.emplace_back(9, 8, 1);
}

template <typename T>
void SphericalImportanceSampler<T>::subdivide(const size_t subdivisions)
void SphericalImportanceSampler<T>::subdivide(const std::size_t subdivisions)
{
PointCache point_cache;

for (size_t s = 0; s < subdivisions; ++s)
for (std::size_t s = 0; s < subdivisions; ++s)
{
const size_t tri_count = m_tris.size();

std::vector<Tri> new_tris;
new_tris.reserve(4 * tri_count);
PointCache point_cache;

for (size_t t = 0; t < tri_count; ++t)
for (std::size_t i = 0, e = m_tris.size(); i < e; ++i)
{
const Tri& tri = m_tris[t];
const Tri input_tri = m_tris[i];

const size_t a = get_or_create_middle_point(point_cache, tri.m_v0, tri.m_v1);
const size_t b = get_or_create_middle_point(point_cache, tri.m_v1, tri.m_v2);
const size_t c = get_or_create_middle_point(point_cache, tri.m_v2, tri.m_v0);
const std::size_t a = get_or_create_middle_point(point_cache, input_tri.m_v0, input_tri.m_v1);
const std::size_t b = get_or_create_middle_point(point_cache, input_tri.m_v1, input_tri.m_v2);
const std::size_t c = get_or_create_middle_point(point_cache, input_tri.m_v2, input_tri.m_v0);

new_tris.push_back(Tri(tri.m_v0, a, c));
new_tris.push_back(Tri(tri.m_v1, b, a));
new_tris.push_back(Tri(tri.m_v2, c, b));
new_tris.push_back(Tri(a, b, c));
m_tris[i] = Tri(input_tri.m_v0, a, c);
m_tris.emplace_back(input_tri.m_v1, b, a);
m_tris.emplace_back(input_tri.m_v2, c, b);
m_tris.emplace_back(a, b, c);
}

m_tris.swap(new_tris);
}
}

template <typename T>
size_t SphericalImportanceSampler<T>::get_or_create_middle_point(PointCache& point_cache, size_t v0, size_t v1)
std::size_t SphericalImportanceSampler<T>::get_or_create_middle_point(PointCache& point_cache, std::size_t v0, std::size_t v1)
{
if (v0 > v1)
std::swap(v0, v1);
Expand All @@ -266,7 +263,7 @@ size_t SphericalImportanceSampler<T>::get_or_create_middle_point(PointCache& poi
const Vector<T, 3>& p1 = m_verts[v1];
const Vector<T, 3> pm = normalize(p0 + p1);

const size_t vm = m_verts.size();
const std::size_t vm = m_verts.size();
point_cache[key] = vm;
m_verts.push_back(pm);

Expand All @@ -276,10 +273,10 @@ size_t SphericalImportanceSampler<T>::get_or_create_middle_point(PointCache& poi
template <typename T>
void SphericalImportanceSampler<T>::build_cdf()
{
const size_t tri_count = m_tris.size();
const std::size_t tri_count = m_tris.size();
m_cdf.reserve(tri_count);

for (size_t i = 0; i < tri_count; ++i)
for (std::size_t i = 0; i < tri_count; ++i)
{
const Tri& tri = m_tris[i];

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