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#ifndef O3D_POLYGON_HPP
#define O3D_POLYGON_HPP
#include <cstddef>
#include <array>
#include <type_traits>
#include <tuple>
#include "math/vector.hpp"
#include "math/utils.hpp"
#include "o3d/deriv_vertex.hpp"
#include "o3d/tri_deriv.hpp"
namespace engine::o3d::polygon {
template<typename T>
concept PolygonVectorTypeConcept = engine::math::VectorTypeConcept<T> && (std::is_same_v<T, engine::math::Vector3> || std::is_same_v<T, engine::math::Vector4>);
template<PolygonVectorTypeConcept VectorType, std::size_t max_points_count> struct Polygon;
template<engine::math::VectorTypeConcept VectorType>
constexpr Polygon<VectorType, 3> from_triangle_derived(const engine::o3d::TriangleDerived<VectorType>& triangle_derived);
template<PolygonVectorTypeConcept VectorType, std::size_t max_points_count, engine::math::vector_coords::VectorCoord coord_id, bool keep_geq>
constexpr Polygon<VectorType, max_points_count + 1> clip_aligned(float boundary, const Polygon<VectorType, max_points_count>& polygon);
template<PolygonVectorTypeConcept VectorType, std::size_t max_points_count>
struct Polygon {
std::size_t points_count;
std::array<engine::o3d::DerivedVertex<VectorType>, max_points_count> points;
constexpr Polygon() : points_count { 0 } {}
constexpr Polygon(std::size_t points_count, std::array<engine::o3d::DerivedVertex<VectorType>, max_points_count> points)
: points_count { points_count }, points { points } {}
constexpr Polygon<VectorType, max_points_count + 2> clip_z(float z1, float z2) const & {
return
clip_aligned<VectorType, max_points_count + 1, engine::math::vector_coords::VectorCoord::z, false>(z2,
clip_aligned<VectorType, max_points_count + 0, engine::math::vector_coords::VectorCoord::z, true >(z1,
*this));
}
constexpr Polygon<VectorType, max_points_count + 4> clip_xy(float x1, float y1, float x2, float y2) const & {
return
clip_aligned<VectorType, max_points_count + 3, engine::math::vector_coords::VectorCoord::y, false>(y2,
clip_aligned<VectorType, max_points_count + 2, engine::math::vector_coords::VectorCoord::x, false>(x2,
clip_aligned<VectorType, max_points_count + 1, engine::math::vector_coords::VectorCoord::y, true >(y1,
clip_aligned<VectorType, max_points_count + 0, engine::math::vector_coords::VectorCoord::x, true >(x1,
*this))));
}
constexpr Polygon<VectorType, max_points_count> map_xy(
const engine::math::Vector2& from1, const engine::math::Vector2& from2,
const engine::math::Vector2& to1, const engine::math::Vector2& to2) const & {
Polygon<VectorType, max_points_count> polygon;
polygon.points_count = points_count;
for (std::size_t i = 0; i < points_count; i++) {
auto& p = polygon.points[i];
if constexpr (std::is_same_v<VectorType, engine::math::Vector3>) {
p.vertex = {
points[i].vertex.xy().map(from1, from2, to1, to2),
points[i].vertex.z,
};
} else {
p.vertex = {
points[i].vertex.xy().map(from1, from2, to1, to2),
points[i].vertex.z,
points[i].vertex.w,
};
}
p.b0 = points[i].b0;
p.b1 = points[i].b1;
}
return polygon;
}
constexpr std::tuple<std::size_t, std::array<engine::o3d::TriangleDerived<engine::math::Vector3>, max_points_count - 2>> to_triangles() const &
requires (max_points_count >= 3)
{
std::array<engine::o3d::TriangleDerived<VectorType>, max_points_count - 2> triangles;
if (points_count < 3) return { 0, triangles };
for (std::size_t i = 0; i < points_count - 2; i++)
triangles[i] = { points[0], points[i + 1], points[i + 2] };
return { points_count - 2, triangles };
}
constexpr std::tuple<std::size_t, std::array<engine::o3d::TriangleDerived<engine::math::Vector3>, 0>> to_triangles() const & {
return { 0, {} };
}
};
template<engine::math::VectorTypeConcept VectorType>
constexpr Polygon<VectorType, 3> from_triangle_derived(const engine::o3d::TriangleDerived<VectorType>& triangle_derived) {
return { 3, { triangle_derived.derived_vertex1, triangle_derived.derived_vertex2, triangle_derived.derived_vertex3 } };
}
template<PolygonVectorTypeConcept VectorType, std::size_t max_points_count, engine::math::vector_coords::VectorCoord coord_id, bool keep_geq>
constexpr Polygon<VectorType, max_points_count + 1> clip_aligned(float boundary, const Polygon<VectorType, max_points_count>& polygon)
{
using transposition = engine::math::vector_coords::transpose<engine::math::vector_coords::VectorCoord::x, coord_id>;
constexpr auto y_coord_id = transposition::template id<engine::math::vector_coords::VectorCoord::y>();
constexpr auto z_coord_id = transposition::template id<engine::math::vector_coords::VectorCoord::z>();
constexpr auto is_in = [](const engine::o3d::DerivedVertex<VectorType>& p, float boundary) constexpr {
if constexpr (keep_geq) return p.vertex.template v<coord_id>() >= boundary;
else return p.vertex.template v<coord_id>() <= boundary;
};
Polygon<VectorType, max_points_count + 1> new_polygon;
for (size_t i = 0; i < polygon.points_count; i++) {
const auto& prev = polygon.points[(i + polygon.points_count - 1) % polygon.points_count];
const auto& cur = polygon.points[i];
if (is_in(prev, boundary) != is_in(cur, boundary)) {
float fac = (boundary - prev.vertex.template v<coord_id>()) / (cur.vertex.template v<coord_id>() - prev.vertex.template v<coord_id>());
auto& new_point = new_polygon.points[new_polygon.points_count++];
new_point.vertex.template v<coord_id>() = boundary;
new_point.vertex.template v<y_coord_id>() = engine::math::utils::lerp(prev.vertex.template v<y_coord_id>(), cur.vertex.template v<y_coord_id>(), fac);
if constexpr (std::is_same_v<VectorType, engine::math::Vector3>) {
// called new_w because it represents w, but because we only need x, y and w, we use
// Vector3, and therefore the vector coordinate's name is z
float new_w = 1.f / ((1.f - fac) / prev.vertex.z + fac / cur.vertex.z);
new_point.vertex.template v<z_coord_id>() = new_w;
new_point.b0 = new_w * engine::math::utils::lerp(prev.b0 / prev.vertex.z, cur.b0 / cur.vertex.z, fac);
new_point.b1 = new_w * engine::math::utils::lerp(prev.b1 / prev.vertex.z, cur.b1 / cur.vertex.z, fac);
} else { // Vector4
constexpr auto w_coord_id = transposition::template id<engine::math::vector_coords::VectorCoord::w>();
new_point.vertex.template v<z_coord_id>() = engine::math::utils::lerp(prev.vertex.template v<z_coord_id>(), cur.vertex.template v<z_coord_id>(), fac);
new_point.vertex.template v<w_coord_id>() = engine::math::utils::lerp(prev.vertex.template v<w_coord_id>(), cur.vertex.template v<w_coord_id>(), fac);
new_point.b0 = engine::math::utils::lerp(prev.b0, cur.b0, fac);
new_point.b1 = engine::math::utils::lerp(prev.b1, cur.b1, fac);
}
}
if (is_in(cur, boundary))
new_polygon.points[new_polygon.points_count++] = cur;
}
return new_polygon;
}
template<std::size_t max_points_count>
constexpr Polygon<engine::math::Vector3, max_points_count> div_by_w(const Polygon<engine::math::Vector4, max_points_count>& polygon) {
Polygon<engine::math::Vector3, max_points_count> new_polygon;
new_polygon.points_count = polygon.points_count;
for (std::size_t i = 0; i < polygon.points_count; i++)
new_polygon.points[i] = polygon.points[i].div_by_w();
return new_polygon;
}
template<std::size_t max_points_count>
constexpr float signed_area_xy(const Polygon<engine::math::Vector3, max_points_count>& polygon) {
float res = 0.f;
if (polygon.points_count > 0) {
for (std::size_t i = 0; i < polygon.points_count - 1; i++)
res += polygon.points[i].vertex.xy().det(polygon.points[i + 1].vertex.xy());
res += polygon.points[polygon.points_count - 1].vertex.xy().det(polygon.points[0].vertex.xy());
}
return .5f * res;
}
}
#endif // O3D_POLYGON_HPP
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