Add convex body utilities to cg

This commit is contained in:
Nikita Lisitsa 2020-11-05 18:11:08 +03:00
parent 26440b0faf
commit 1a6444d010
8 changed files with 747 additions and 615 deletions

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@ -14,576 +14,18 @@
#include <psemek/geom/intersection.hpp>
#include <psemek/geom/distance.hpp>
#include <psemek/cg/body/icosahedron.hpp>
#include <psemek/cg/body/box.hpp>
#include <psemek/cg/body/frustum.hpp>
#include <psemek/cg/body/prism.hpp>
#include <psemek/cg/convex/inside.hpp>
#include <psemek/cg/convex/separation.hpp>
#include <psemek/util/clock.hpp>
#include <psemek/util/to_string.hpp>
#include <psemek/util/moving_average.hpp>
#include <psemek/util/recursive.hpp>
namespace psemek::cg
{
template <typename T, std::size_t N>
struct box;
template <typename T, std::size_t N>
box(geom::box<T, N>) -> box<T, N>;
template <typename T>
struct box<T, 3>
{
box() = default;
box(geom::box<T, 3> const & b);
std::array<geom::point<T, 3>, 8> vertices;
};
template <typename T>
box<T, 3>::box(geom::box<T, 3> const & b)
{
for (std::size_t z = 0; z < 2; ++z)
{
for (std::size_t y = 0; y < 2; ++y)
{
for (std::size_t x = 0; x < 2; ++x)
{
std::size_t i = z * 4 + y * 2 + x;
vertices[i][0] = (x == 0) ? b[0].min : b[0].max;
vertices[i][1] = (y == 0) ? b[1].min : b[1].max;
vertices[i][2] = (z == 0) ? b[2].min : b[2].max;
}
}
}
}
template <typename T>
auto const & vertices(box<T, 3> const & b)
{
return b.vertices;
}
namespace detail
{
inline auto const & cubiod_edges()
{
static const std::array<geom::segment<std::uint8_t>, 12> result =
{{
{ 0b000, 0b001 },
{ 0b010, 0b011 },
{ 0b100, 0b101 },
{ 0b110, 0b111 },
{ 0b000, 0b010 },
{ 0b001, 0b011 },
{ 0b100, 0b110 },
{ 0b101, 0b111 },
{ 0b000, 0b100 },
{ 0b001, 0b101 },
{ 0b010, 0b110 },
{ 0b011, 0b111 },
}};
return result;
}
inline auto const & cubiod_faces()
{
static const std::array<std::array<std::uint8_t, 4>, 6> result =
{{
{{ 0b000, 0b100, 0b110, 0b010 }},
{{ 0b001, 0b011, 0b111, 0b101 }},
{{ 0b000, 0b001, 0b101, 0b100 }},
{{ 0b010, 0b110, 0b111, 0b011 }},
{{ 0b000, 0b010, 0b011, 0b001 }},
{{ 0b100, 0b101, 0b111, 0b110 }},
}};
return result;
}
}
template <typename T>
auto const & edges(box<T, 3> const &)
{
return detail::cubiod_edges();
}
template <typename T>
auto const & faces(box<T, 3> const &)
{
return detail::cubiod_faces();
}
template <typename T>
auto const & face_normals(box<T, 3> const &)
{
static const std::array<geom::vector<T, 3>, 6> result =
{{
{-1, 0, 0},
{ 1, 0, 0},
{ 0, -1, 0},
{ 0, 1, 0},
{ 0, 0, -1},
{ 0, 0, 1},
}};
return result;
}
template <typename T>
auto const & edge_directions(box<T, 3> const &)
{
static const std::array<geom::vector<T, 3>, 3> result =
{{
{ 1, 0, 0},
{ 0, 1, 0},
{ 0, 0, 1},
}};
return result;
}
template <typename T, std::size_t N>
struct frustum;
template <typename T, std::size_t N>
frustum(geom::matrix<T, N, N>) -> frustum<T, N-1>;
template <typename T>
struct frustum<T, 3>
{
frustum(geom::matrix<T, 4, 4> const & m);
std::array<geom::point<T, 3>, 8> vertices;
std::array<geom::vector<T, 3>, 6> face_normals;
};
template <typename T>
frustum<T, 3>::frustum(geom::matrix<T, 4, 4> const & m)
{
bool flip = (geom::det(m) < 0);
for (std::size_t z = 0; z < 2; ++z)
{
for (std::size_t y = 0; y < 2; ++y)
{
for (std::size_t x = 0; x < 2; ++x)
{
std::size_t i = z * 4 + y * 2 + (flip ? 1 - x : x);
geom::vector<T, 4> p;
p[0] = (x == 0) ? -1 : 1;
p[1] = (y == 0) ? -1 : 1;
p[2] = (z == 0) ? -1 : 1;
p[3] = 1;
geom::gauss(m, p);
vertices[i] = geom::as_point(p);
}
}
}
}
template <typename T>
auto const & vertices(frustum<T, 3> const & f)
{
return f.vertices;
}
template <typename T>
auto const & edges(frustum<T, 3> const &)
{
return detail::cubiod_edges();
}
template <typename T>
auto const & faces(frustum<T, 3> const &)
{
return detail::cubiod_faces();
}
template <typename T>
struct triangular_prism
{
triangular_prism() = default;
triangular_prism(geom::triangle<geom::point<T, 3>> const & t, geom::vector<T, 3> const & d);
std::array<geom::point<T, 3>, 6> vertices;
std::array<geom::vector<T, 3>, 4> edge_directions;
};
template <typename T>
triangular_prism<T>::triangular_prism(geom::triangle<geom::point<T, 3>> const & t, geom::vector<T, 3> const & d)
{
for (std::size_t i = 0; i < 3; ++i)
{
vertices[i] = t[i];
vertices[i + 3] = t[i] + d;
}
if (geom::dot(geom::normal(vertices[0], vertices[1], vertices[2]), d) < 0)
{
std::swap(vertices[1], vertices[2]);
std::swap(vertices[4], vertices[5]);
}
for (std::size_t i = 0; i < 3; ++i)
{
edge_directions[i] = geom::normalized(vertices[(i + 1) % 3] - vertices[i]);
}
edge_directions[3] = geom::normalized(d);
}
template <typename T>
auto const & vertices(triangular_prism<T> const & p)
{
return p.vertices;
}
template <typename T>
auto const & edges(triangular_prism<T> const &)
{
static const std::array<geom::segment<std::uint8_t>, 9> result =
{{
{ 0, 1 },
{ 1, 2 },
{ 2, 0 },
{ 3, 4 },
{ 4, 5 },
{ 5, 3 },
{ 0, 3 },
{ 1, 4 },
{ 2, 5 },
}};
return result;
}
template <typename T>
auto const & faces(triangular_prism<T> const &)
{
static std::array<std::vector<std::uint8_t>, 5> result =
{{
{ 0, 2, 1 },
{ 3, 4, 5 },
{ 0, 1, 4, 3 },
{ 1, 2, 5, 4 },
{ 2, 0, 3, 5 },
}};
return result;
}
template <typename T>
auto const & edge_directions(triangular_prism<T> const & p)
{
return p.edge_directions;
}
namespace detail
{
template <typename Container>
struct has_static_size
: std::false_type
{};
template <typename T, std::size_t N>
struct has_static_size<std::array<T, N>>
: std::true_type
{};
template <typename Container>
constexpr bool has_static_size_v = has_static_size<Container>::value;
template <typename Container>
struct static_size;
template <typename T, std::size_t N>
struct static_size<std::array<T, N>>
{
static constexpr std::size_t value = N;
};
template <typename Container>
constexpr std::size_t static_size_v = static_size<Container>::value;
}
template <typename Body>
auto triangles(Body const & b)
{
auto const & fs = faces(b);
using faces_type = std::remove_cvref_t<decltype(fs)>;
using face_type = std::remove_cvref_t<decltype(*std::begin(fs))>;
using index_type = std::remove_cvref_t<decltype((*std::begin(fs))[0])>;
auto impl = [&fs](auto out)
{
for (auto const & f : fs)
{
auto it0 = std::begin(f);
for (auto it = std::next(it0), jt = std::next(it); jt < std::end(f); it = jt++)
{
*out++ = {*it0, *it, *jt};
}
}
};
if constexpr (detail::has_static_size_v<faces_type> && detail::has_static_size_v<face_type>)
{
constexpr std::size_t faces_count = detail::static_size_v<faces_type>;
constexpr std::size_t face_size = detail::static_size_v<face_type>;
std::array<geom::triangle<index_type>, faces_count * (face_size - 2)> result;
impl(result.begin());
return result;
}
else
{
std::vector<geom::triangle<index_type>> result;
if constexpr (detail::has_static_size_v<face_type>)
{
constexpr std::size_t face_size = detail::static_size_v<face_type>;
result.reserve(fs.size() * (face_size - 2));
}
else
{
result.reserve(fs.size());
}
impl(std::back_inserter(result));
return result;
}
}
template <typename Body>
auto edge_directions(Body const & b)
{
auto const & vs = vertices(b);
auto const & es = edges(b);
using edges_type = std::remove_cvref_t<decltype(es)>;
using vector_type = std::remove_cvref_t<decltype(vs[0] - vs[0])>;
auto impl = [&es, &vs](auto out)
{
for (auto const & e : es)
{
*out++ = geom::normalized(vs[e[1]] - vs[e[0]]);
}
};
if constexpr (detail::has_static_size_v<edges_type>)
{
constexpr std::size_t edges_count = detail::static_size_v<edges_type>;
std::array<vector_type, edges_count> result;
impl(result.begin());
return result;
}
else
{
std::vector<vector_type> result;
result.reserve(es.size());
impl(std::back_inserter(result));
return result;
}
}
template <typename Body>
auto faces(Body const & b)
{
return triangles(b);
}
template <typename Body>
auto face_normals(Body const & b)
{
auto const & vs = vertices(b);
auto const & fs = faces(b);
using faces_type = std::remove_cvref_t<decltype(fs)>;
using vector_type = std::remove_cvref_t<decltype(vs[0] - vs[0])>;
auto impl = [&fs, &vs](auto out)
{
for (auto const & f : fs)
{
*out++ = geom::normal(vs[f[0]], vs[f[1]], vs[f[2]]);
}
};
if constexpr (detail::has_static_size_v<faces_type>)
{
constexpr std::size_t faces_count = detail::static_size_v<faces_type>;
std::array<vector_type, faces_count> result;
impl(result.begin());
return result;
}
else
{
std::vector<vector_type> result;
result.reserve(fs.size());
impl(std::back_inserter(result));
return result;
}
}
template <typename P, typename Body>
bool inside(P const & p, Body const & body)
{
auto const & vs = vertices(body);
auto const & fs = faces(body);
for (auto const & f : fs)
{
if (geom::orientation(vs[f[0]], vs[f[1]], vs[f[2]], p) == geom::sign_t::negative)
return false;
}
return true;
}
// returns pair(normalized vector from 1 to 2, signed distance)
// distance <= 0 means intersection
template <typename Body1, typename Body2>
auto separation(Body1 const & b1, Body2 const & b2)
{
auto const & vs1 = vertices(b1);
auto const & vs2 = vertices(b2);
auto const & fs1 = faces(b1);
auto const & fs2 = faces(b2);
auto const & eds1 = edge_directions(b1);
auto const & eds2 = edge_directions(b2);
using vector_type = std::remove_cvref_t<decltype(vs1[0] - vs1[0])>;
using scalar_type = std::remove_cvref_t<decltype(vs1[0][0])>;
vector_type res_n = vector_type::zero();
auto res_d = -std::numeric_limits<scalar_type>::infinity();
auto process_faces = [](auto const & vs1, auto const & fs1, auto const & vs2)
{
vector_type res_n = vector_type::zero();
scalar_type res_d = -std::numeric_limits<scalar_type>::infinity();
for (auto const & f : fs1)
{
auto const face_n = geom::normal(vs1[f[0]], vs1[f[1]], vs1[f[2]]);
scalar_type face_d = std::numeric_limits<scalar_type>::infinity();
auto const face_p = vs1[f[0]];
for (auto const & v : vs2)
{
auto const d = geom::dot(face_n, v - face_p);
face_d = std::min(d, face_d);
}
if (face_d == std::numeric_limits<scalar_type>::infinity())
{
throw 42;
}
if (face_d > res_d)
{
res_d = face_d;
res_n = face_n;
}
}
return std::make_pair(res_n, res_d);
};
auto process_edges = [](auto const & vs1, auto const & eds1, auto const & vs2, auto const & eds2)
{
vector_type res_n = vector_type::zero();
scalar_type res_d = -std::numeric_limits<scalar_type>::infinity();
for (auto const & ed1 : eds1)
{
for (auto const & ed2 : eds2)
{
auto edge_n = geom::cross(ed1, ed2);
auto l = geom::length(edge_n);
if (l == 0) continue;
edge_n /= l;
geom::interval<scalar_type> i1, i2;
for (auto const & v : vs1)
{
i1 |= geom::dot(geom::homogeneous(v), geom::homogeneous(edge_n));
}
for (auto const & v : vs2)
{
i2 |= geom::dot(geom::homogeneous(v), geom::homogeneous(edge_n));
}
auto edge_d12 = i2.min - i1.max;
auto edge_d21 = i1.min - i2.max;
scalar_type edge_d;
if (edge_d12 > edge_d21)
{
edge_d = edge_d12;
}
else
{
edge_d = edge_d21;
edge_n = -edge_n;
}
if (edge_d > res_d)
{
res_d = edge_d;
res_n = edge_n;
}
}
}
return std::make_pair(res_n, res_d);
};
{
auto res12 = process_faces(vs1, fs1, vs2);
if (res12.second > res_d)
{
res_d = res12.second;
res_n = res12.first;
}
}
{
auto res21 = process_faces(vs2, fs2, vs1);
if (res21.second > res_d)
{
res_d = res21.second;
res_n = -res21.first;
}
}
{
auto rese = process_edges(vs1, eds1, vs2, eds2);
if (rese.second > res_d)
{
res_d = rese.second;
res_n = rese.first;
}
}
return std::make_pair(res_n, res_d);
}
}
using namespace psemek;
template <typename Value, typename T>
@ -617,53 +59,6 @@ private:
T speed_;
};
static const float icosa_a = 0.850650808; // phi / sqrt(1 + phi^2)
static const float icosa_b = 0.525731112; // 1 / sqrt(1 + phi^2)
static const float icosa_side = 1.05146222; // 2 / sqrt(phi * sqrt(5))
static const geom::vector<float, 3> icosa_vertices[12] =
{
{-icosa_a, -icosa_b, 0.0}, // 0
{-icosa_a, icosa_b, 0.0}, // 1
{ icosa_a, -icosa_b, 0.0}, // 2
{ icosa_a, icosa_b, 0.0}, // 3
{0.0, -icosa_a, -icosa_b}, // 4
{0.0, -icosa_a, icosa_b}, // 5
{0.0, icosa_a, -icosa_b}, // 6
{0.0, icosa_a, icosa_b}, // 7
{-icosa_b, 0.0, -icosa_a}, // 8
{ icosa_b, 0.0, -icosa_a}, // 9
{-icosa_b, 0.0, icosa_a}, // 10
{ icosa_b, 0.0, icosa_a}, // 11
};
static const std::size_t icosa_faces[20][3] =
{
{0, 1, 8,},
{0, 10, 1,},
{2, 9, 3,},
{2, 3, 11,},
{4, 5, 0,},
{4, 2, 5,},
{6, 1, 7,},
{6, 7, 3,},
{8, 9, 4,},
{8, 6, 9,},
{10, 5, 11,},
{10, 11, 7,},
{0, 8, 4,},
{0, 5, 10,},
{1, 6, 8,},
{1, 10, 7,},
{2, 4, 9,},
{2, 11, 5,},
{3, 9, 6,},
{3, 7, 11},
};
static char const tile_vs[] =
R"(#version 330
@ -935,6 +330,12 @@ std::ostream & operator << (std::ostream & os, std::vector<T> const & v)
void srtm_app::present()
{
cg::icosahedron<float> icosahedron{geom::point<float, 3>::zero(), 1.f};
auto const & icosa_vertices = cg::vertices(icosahedron);
auto const & icosa_faces = cg::faces(icosahedron);
auto const icosa_side = geom::distance(icosa_vertices[icosa_faces[0][0]], icosa_vertices[icosa_faces[0][1]]);
std::vector<std::string> info;
gl::ClearColor(0.9f, 0.9f, 0.9f, 0.f);
@ -1113,9 +514,9 @@ void srtm_app::present()
for (int f = 0; f < 20; ++f)
{
geom::vector<float, 3> v[3];
v[0] = icosa_vertices[icosa_faces[f][0]];
v[1] = icosa_vertices[icosa_faces[f][1]];
v[2] = icosa_vertices[icosa_faces[f][2]];
v[0] = icosa_vertices[icosa_faces[f][0]] - geom::point<float, 3>::zero();
v[1] = icosa_vertices[icosa_faces[f][1]] - geom::point<float, 3>::zero();
v[2] = icosa_vertices[icosa_faces[f][2]] - geom::point<float, 3>::zero();
id.push_back(f);
visit(v);
id.pop_back();

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@ -0,0 +1,210 @@
#pragma once
#include <psemek/geom/simplex.hpp>
#include <psemek/geom/vector.hpp>
#include <psemek/geom/point.hpp>
#include <vector>
#include <array>
#include <tuple>
#include <algorithm>
namespace psemek::cg
{
/* The basic interface of a 3D body is
* vertices(body) -> [point]
* edges(body) -> [(index, index)]
* faces(body) -> [[index]]
* triangles(body) -> [(index, index, index)]
* face_normals(body) -> [vector]
* edge_directions(body) -> [vector]
*
* Note that faces(body).size() == face_normals(body).size
* However, it is possible that edges(body).size() != edge_directions(body).size,
* if there are many collinear edges.
*
* Minimal set of required functions:
* vertices
* edges
* faces/triangles
*/
namespace detail
{
template <typename Container>
struct has_static_size
: std::false_type
{};
template <typename T, std::size_t N>
struct has_static_size<std::array<T, N>>
: std::true_type
{};
template <typename Container>
constexpr bool has_static_size_v = has_static_size<Container>::value;
template <typename Container>
struct static_size;
template <typename T, std::size_t N>
struct static_size<std::array<T, N>>
{
static constexpr std::size_t value = N;
};
template <typename Container>
constexpr std::size_t static_size_v = static_size<Container>::value;
}
template <typename Body>
auto faces(Body const & b)
{
return triangles(b);
}
template <typename Body>
auto edges(Body const & b)
{
auto const & fs = faces(b);
using index_type = std::remove_cvref_t<decltype((*std::begin(fs))[0])>;
std::vector<geom::segment<index_type>> result;
for (auto const & f : fs)
{
for (auto it = std::begin(f), jt = std::prev(std::end(f)); ++it, ++jt; it != std::end(f))
{
geom::segment<index_type> s{*jt, *it};
if (s[0] > s[1]) std::swap(s[0], s[1]);
result.push_back(s);
}
}
auto compare = [](auto const & s1, auto const & s2)
{
return std::tie(s1[0], s1[1]) < std::tie(s2[0], s2[1]);
};
std::sort(result.begin(), result.end(), compare);
result.erase(std::unique(result.begin(), result.end()), result.end());
return result;
}
template <typename Body>
auto triangles(Body const & b)
{
auto const & fs = faces(b);
using faces_type = std::remove_cvref_t<decltype(fs)>;
using face_type = std::remove_cvref_t<decltype(*std::begin(fs))>;
using index_type = std::remove_cvref_t<decltype((*std::begin(fs))[0])>;
auto impl = [&fs](auto out)
{
for (auto const & f : fs)
{
auto it0 = std::begin(f);
for (auto it = std::next(it0), jt = std::next(it); jt < std::end(f); it = jt++)
{
*out++ = {*it0, *it, *jt};
}
}
};
if constexpr (detail::has_static_size_v<faces_type> && detail::has_static_size_v<face_type>)
{
constexpr std::size_t faces_count = detail::static_size_v<faces_type>;
constexpr std::size_t face_size = detail::static_size_v<face_type>;
std::array<geom::triangle<index_type>, faces_count * (face_size - 2)> result;
impl(result.begin());
return result;
}
else
{
std::vector<geom::triangle<index_type>> result;
if constexpr (detail::has_static_size_v<face_type>)
{
constexpr std::size_t face_size = detail::static_size_v<face_type>;
result.reserve(fs.size() * (face_size - 2));
}
else
{
result.reserve(fs.size());
}
impl(std::back_inserter(result));
return result;
}
}
template <typename Body>
auto edge_directions(Body const & b)
{
auto const & vs = vertices(b);
auto const & es = edges(b);
using edges_type = std::remove_cvref_t<decltype(es)>;
using vector_type = std::remove_cvref_t<decltype(vs[0] - vs[0])>;
auto impl = [&es, &vs](auto out)
{
for (auto const & e : es)
{
*out++ = geom::normalized(vs[e[1]] - vs[e[0]]);
}
};
if constexpr (detail::has_static_size_v<edges_type>)
{
constexpr std::size_t edges_count = detail::static_size_v<edges_type>;
std::array<vector_type, edges_count> result;
impl(result.begin());
return result;
}
else
{
std::vector<vector_type> result;
result.reserve(es.size());
impl(std::back_inserter(result));
return result;
}
}
template <typename Body>
auto face_normals(Body const & b)
{
auto const & vs = vertices(b);
auto const & fs = faces(b);
using faces_type = std::remove_cvref_t<decltype(fs)>;
using vector_type = std::remove_cvref_t<decltype(vs[0] - vs[0])>;
auto impl = [&fs, &vs](auto out)
{
for (auto const & f : fs)
{
*out++ = geom::normal(vs[f[0]], vs[f[1]], vs[f[2]]);
}
};
if constexpr (detail::has_static_size_v<faces_type>)
{
constexpr std::size_t faces_count = detail::static_size_v<faces_type>;
std::array<vector_type, faces_count> result;
impl(result.begin());
return result;
}
else
{
std::vector<vector_type> result;
result.reserve(fs.size());
impl(std::back_inserter(result));
return result;
}
}
}

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#pragma once
#include <psemek/cg/body/body.hpp>
#include <psemek/geom/box.hpp>
namespace psemek::cg
{
template <typename T, std::size_t N>
struct box;
template <typename T, std::size_t N>
box(geom::box<T, N>) -> box<T, N>;
template <typename T>
struct box<T, 3>
{
box() = default;
box(geom::box<T, 3> const & b);
std::array<geom::point<T, 3>, 8> vertices;
};
template <typename T>
box<T, 3>::box(geom::box<T, 3> const & b)
{
for (std::size_t z = 0; z < 2; ++z)
{
for (std::size_t y = 0; y < 2; ++y)
{
for (std::size_t x = 0; x < 2; ++x)
{
std::size_t i = z * 4 + y * 2 + x;
vertices[i][0] = (x == 0) ? b[0].min : b[0].max;
vertices[i][1] = (y == 0) ? b[1].min : b[1].max;
vertices[i][2] = (z == 0) ? b[2].min : b[2].max;
}
}
}
}
template <typename T>
auto const & vertices(box<T, 3> const & b)
{
return b.vertices;
}
template <typename T>
auto const & edges(box<T, 3> const &)
{
static const std::array<geom::segment<std::uint8_t>, 12> result =
{{
{ 0b000, 0b001 },
{ 0b010, 0b011 },
{ 0b100, 0b101 },
{ 0b110, 0b111 },
{ 0b000, 0b010 },
{ 0b001, 0b011 },
{ 0b100, 0b110 },
{ 0b101, 0b111 },
{ 0b000, 0b100 },
{ 0b001, 0b101 },
{ 0b010, 0b110 },
{ 0b011, 0b111 },
}};
return result;
}
template <typename T>
auto const & faces(box<T, 3> const &)
{
static const std::array<std::array<std::uint8_t, 4>, 6> result =
{{
{{ 0b000, 0b100, 0b110, 0b010 }},
{{ 0b001, 0b011, 0b111, 0b101 }},
{{ 0b000, 0b001, 0b101, 0b100 }},
{{ 0b010, 0b110, 0b111, 0b011 }},
{{ 0b000, 0b010, 0b011, 0b001 }},
{{ 0b100, 0b101, 0b111, 0b110 }},
}};
return result;
}
template <typename T>
auto const & face_normals(box<T, 3> const &)
{
static const std::array<geom::vector<T, 3>, 6> result =
{{
{-1, 0, 0},
{ 1, 0, 0},
{ 0, -1, 0},
{ 0, 1, 0},
{ 0, 0, -1},
{ 0, 0, 1},
}};
return result;
}
template <typename T>
auto const & edge_directions(box<T, 3> const &)
{
static const std::array<geom::vector<T, 3>, 3> result =
{{
{ 1, 0, 0},
{ 0, 1, 0},
{ 0, 0, 1},
}};
return result;
}
}

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#pragma once
#include <psemek/cg/body/body.hpp>
#include <psemek/cg/body/box.hpp>
#include <psemek/geom/matrix.hpp>
#include <psemek/geom/gauss.hpp>
#include <psemek/geom/homogeneous.hpp>
namespace psemek::cg
{
template <typename T, std::size_t N>
struct frustum;
template <typename T, std::size_t N>
frustum(geom::matrix<T, N, N>) -> frustum<T, N-1>;
template <typename T>
struct frustum<T, 3>
{
frustum(geom::matrix<T, 4, 4> const & m);
std::array<geom::point<T, 3>, 8> vertices;
};
template <typename T>
frustum<T, 3>::frustum(geom::matrix<T, 4, 4> const & m)
{
bool flip = (geom::det(m) < 0);
for (std::size_t z = 0; z < 2; ++z)
{
for (std::size_t y = 0; y < 2; ++y)
{
for (std::size_t x = 0; x < 2; ++x)
{
std::size_t i = z * 4 + y * 2 + (flip ? 1 - x : x);
geom::vector<T, 4> p;
p[0] = (x == 0) ? -1 : 1;
p[1] = (y == 0) ? -1 : 1;
p[2] = (z == 0) ? -1 : 1;
p[3] = 1;
geom::gauss(m, p);
vertices[i] = geom::as_point(p);
}
}
}
}
template <typename T>
auto const & vertices(frustum<T, 3> const & f)
{
return f.vertices;
}
template <typename T>
auto const & edges(frustum<T, 3> const &)
{
return edges(box<T, 3>{});
}
template <typename T>
auto const & faces(frustum<T, 3> const &)
{
return faces(box<T, 3>{});
}
}

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#pragma once
#include <psemek/cg/body/body.hpp>
namespace psemek::cg
{
template <typename T>
struct icosahedron
{
icosahedron() = default;
icosahedron(geom::point<T, 3> const & origin, T radius);
std::array<geom::point<T, 3>, 12> vertices;
};
template <typename T>
icosahedron<T>::icosahedron(geom::point<T, 3> const & origin, T radius)
{
static const T icosa_a = radius * 0.850650808; // radius * phi / sqrt(1 + phi^2)
static const T icosa_b = radius * 0.525731112; // radius / sqrt(1 + phi^2)
vertices =
{{
origin + geom::vector<T, 3>{-icosa_a, -icosa_b, 0}, // 0
origin + geom::vector<T, 3>{-icosa_a, icosa_b, 0}, // 1
origin + geom::vector<T, 3>{ icosa_a, -icosa_b, 0}, // 2
origin + geom::vector<T, 3>{ icosa_a, icosa_b, 0}, // 3
origin + geom::vector<T, 3>{0, -icosa_a, -icosa_b}, // 4
origin + geom::vector<T, 3>{0, -icosa_a, icosa_b}, // 5
origin + geom::vector<T, 3>{0, icosa_a, -icosa_b}, // 6
origin + geom::vector<T, 3>{0, icosa_a, icosa_b}, // 7
origin + geom::vector<T, 3>{-icosa_b, 0, -icosa_a}, // 8
origin + geom::vector<T, 3>{ icosa_b, 0, -icosa_a}, // 9
origin + geom::vector<T, 3>{-icosa_b, 0, icosa_a}, // 10
origin + geom::vector<T, 3>{ icosa_b, 0, icosa_a}, // 11
}};
}
template <typename T>
auto const & vertices(icosahedron<T> const & i)
{
return i.vertices;
}
template <typename T>
auto const & faces(icosahedron<T> const &)
{
static const std::array<geom::triangle<std::uint8_t>, 20> result =
{{
{0, 1, 8,},
{0, 10, 1,},
{2, 9, 3,},
{2, 3, 11,},
{4, 5, 0,},
{4, 2, 5,},
{6, 1, 7,},
{6, 7, 3,},
{8, 9, 4,},
{8, 6, 9,},
{10, 5, 11,},
{10, 11, 7,},
{0, 8, 4,},
{0, 5, 10,},
{1, 6, 8,},
{1, 10, 7,},
{2, 4, 9,},
{2, 11, 5,},
{3, 9, 6,},
{3, 7, 11},
}};
return result;
}
}

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#pragma once
#include <psemek/cg/body/body.hpp>
namespace psemek::cg
{
template <typename T>
struct triangular_prism
{
triangular_prism() = default;
triangular_prism(geom::triangle<geom::point<T, 3>> const & t, geom::vector<T, 3> const & d);
std::array<geom::point<T, 3>, 6> vertices;
std::array<geom::vector<T, 3>, 4> edge_directions;
};
template <typename T>
triangular_prism<T>::triangular_prism(geom::triangle<geom::point<T, 3>> const & t, geom::vector<T, 3> const & d)
{
for (std::size_t i = 0; i < 3; ++i)
{
vertices[i] = t[i];
vertices[i + 3] = t[i] + d;
}
if (geom::dot(geom::normal(vertices[0], vertices[1], vertices[2]), d) < 0)
{
std::swap(vertices[1], vertices[2]);
std::swap(vertices[4], vertices[5]);
}
for (std::size_t i = 0; i < 3; ++i)
{
edge_directions[i] = geom::normalized(vertices[(i + 1) % 3] - vertices[i]);
}
edge_directions[3] = geom::normalized(d);
}
template <typename T>
auto const & vertices(triangular_prism<T> const & p)
{
return p.vertices;
}
template <typename T>
auto const & edges(triangular_prism<T> const &)
{
static const std::array<geom::segment<std::uint8_t>, 9> result =
{{
{ 0, 1 },
{ 1, 2 },
{ 2, 0 },
{ 3, 4 },
{ 4, 5 },
{ 5, 3 },
{ 0, 3 },
{ 1, 4 },
{ 2, 5 },
}};
return result;
}
template <typename T>
auto const & faces(triangular_prism<T> const &)
{
static std::array<std::vector<std::uint8_t>, 5> result =
{{
{ 0, 2, 1 },
{ 3, 4, 5 },
{ 0, 1, 4, 3 },
{ 1, 2, 5, 4 },
{ 2, 0, 3, 5 },
}};
return result;
}
template <typename T>
auto const & edge_directions(triangular_prism<T> const & p)
{
return p.edge_directions;
}
}

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#pragma once
#include <psemek/cg/body/body.hpp>
#include <psemek/geom/orientation.hpp>
namespace psemek::cg
{
template <typename T, std::size_t N, typename Body>
bool inside(geom::point<T, N> const & p, Body const & body)
{
auto const & vs = vertices(body);
auto const & fs = faces(body);
for (auto const & f : fs)
{
if (geom::orientation(vs[f[0]], vs[f[1]], vs[f[2]], p) == geom::sign_t::negative)
return false;
}
return true;
}
}

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#pragma once
#include <psemek/cg/body/body.hpp>
#include <psemek/geom/interval.hpp>
#include <psemek/geom/homogeneous.hpp>
namespace psemek::cg
{
// returns pair(normalized vector from 1 to 2, signed distance)
// distance <= 0 means intersection
template <typename Body1, typename Body2>
auto separation(Body1 const & b1, Body2 const & b2)
{
auto const & vs1 = vertices(b1);
auto const & vs2 = vertices(b2);
auto const & fs1 = faces(b1);
auto const & fs2 = faces(b2);
auto const & eds1 = edge_directions(b1);
auto const & eds2 = edge_directions(b2);
using vector_type = std::remove_cvref_t<decltype(vs1[0] - vs1[0])>;
using scalar_type = std::remove_cvref_t<decltype(vs1[0][0])>;
vector_type res_n = vector_type::zero();
auto res_d = -std::numeric_limits<scalar_type>::infinity();
auto process_faces = [](auto const & vs1, auto const & fs1, auto const & vs2)
{
vector_type res_n = vector_type::zero();
scalar_type res_d = -std::numeric_limits<scalar_type>::infinity();
for (auto const & f : fs1)
{
auto const face_n = geom::normal(vs1[f[0]], vs1[f[1]], vs1[f[2]]);
scalar_type face_d = std::numeric_limits<scalar_type>::infinity();
auto const face_p = vs1[f[0]];
for (auto const & v : vs2)
{
auto const d = geom::dot(face_n, v - face_p);
face_d = std::min(d, face_d);
}
if (face_d > res_d)
{
res_d = face_d;
res_n = face_n;
}
}
return std::make_pair(res_n, res_d);
};
auto process_edges = [](auto const & vs1, auto const & eds1, auto const & vs2, auto const & eds2)
{
vector_type res_n = vector_type::zero();
scalar_type res_d = -std::numeric_limits<scalar_type>::infinity();
for (auto const & ed1 : eds1)
{
for (auto const & ed2 : eds2)
{
auto edge_n = geom::cross(ed1, ed2);
auto l = geom::length(edge_n);
if (l == 0) continue;
edge_n /= l;
geom::interval<scalar_type> i1, i2;
for (auto const & v : vs1)
{
i1 |= geom::dot(geom::homogeneous(v), geom::homogeneous(edge_n));
}
for (auto const & v : vs2)
{
i2 |= geom::dot(geom::homogeneous(v), geom::homogeneous(edge_n));
}
auto edge_d12 = i2.min - i1.max;
auto edge_d21 = i1.min - i2.max;
scalar_type edge_d;
if (edge_d12 > edge_d21)
{
edge_d = edge_d12;
}
else
{
edge_d = edge_d21;
edge_n = -edge_n;
}
if (edge_d > res_d)
{
res_d = edge_d;
res_n = edge_n;
}
}
}
return std::make_pair(res_n, res_d);
};
{
auto res12 = process_faces(vs1, fs1, vs2);
if (res12.second > res_d)
{
res_d = res12.second;
res_n = res12.first;
}
}
{
auto res21 = process_faces(vs2, fs2, vs1);
if (res21.second > res_d)
{
res_d = res21.second;
res_n = -res21.first;
}
}
{
auto rese = process_edges(vs1, eds1, vs2, eds2);
if (rese.second > res_d)
{
res_d = rese.second;
res_n = rese.first;
}
}
return std::make_pair(res_n, res_d);
}
}