💿🐜 Antkeeper source code
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244 lines
6.6 KiB
244 lines
6.6 KiB
/*
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* Copyright (C) 2023 Christopher J. Howard
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*
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* This file is part of Antkeeper source code.
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*
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* Antkeeper source code is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* Antkeeper source code is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with Antkeeper source code. If not, see <http://www.gnu.org/licenses/>.
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*/
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#ifndef ANTKEEPER_GEOM_COORDINATES_HPP
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#define ANTKEEPER_GEOM_COORDINATES_HPP
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#include <engine/geom/primitives/point.hpp>
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#include <bit>
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#include <cstdint>
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#include <cmath>
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namespace geom {
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/**
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* Voronoi regions of a triangle.
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*/
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enum class triangle_region: std::uint8_t
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{
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/// Face ABC region.
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abc = 0b000,
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/// Edge AB region.
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ab = 0b100,
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/// Edge BC region.
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bc = 0b001,
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/// Edge CA region.
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ca = 0b010,
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/// Vertex A region.
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a = 0b110,
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/// Vertex B region.
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b = 0b101,
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/// Vertex C region.
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c = 0b011
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};
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/**
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* Checks whether a triangle voronoi region is a face region.
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*
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* @param region Triangle region.
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*
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* @return `true` if @p region is a face region, `false` otherwise.
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*/
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[[nodiscard]] inline constexpr bool is_face_region(triangle_region region) noexcept
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{
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return !static_cast<bool>(region);
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}
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/**
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* Checks whether a triangle voronoi region is an edge region.
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*
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* @param region Triangle region.
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*
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* @return `true` if @p region is an edge region, `false` otherwise.
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*/
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[[nodiscard]] inline constexpr bool is_edge_region(triangle_region region) noexcept
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{
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return std::has_single_bit(static_cast<std::uint8_t>(region));
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}
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/**
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* Checks whether a triangle voronoi region is a vertex region.
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*
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* @param region Triangle region.
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*
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* @return `true` if @p region is an vertex region, `false` otherwise.
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*/
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[[nodiscard]] inline constexpr bool is_vertex_region(triangle_region region) noexcept
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{
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return static_cast<bool>(region) && !std::has_single_bit(static_cast<std::uint8_t>(region));
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}
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/**
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* Returns the edge index of an edge region.
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*
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* @param region Triangle edge region.
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*
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* @return Edge index.
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*/
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[[nodiscard]] inline constexpr std::uint8_t edge_index(triangle_region region) noexcept
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{
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return static_cast<std::uint8_t>(region) & std::uint8_t{0b11};
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}
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/**
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* Returns the vertex index of a vertex region.
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*
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* @param region Triangle vertex region.
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*
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* @return Vertex index.
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*/
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[[nodiscard]] inline constexpr std::uint8_t vertex_index(triangle_region region) noexcept
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{
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return std::uint8_t{3} - (static_cast<std::uint8_t>(region) >> 1);
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}
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/**
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* Classifies barycentric coordinates according to their Voronoi region.
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*
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* @tparam T Real type.
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*
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* @param p Barycentric coordinates of point to classify.
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*
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* @return Voronoi region of point @p p.
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*/
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template <class T>
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[[nodiscard]] constexpr triangle_region barycentric_to_region(const point<T, 3>& p) noexcept
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{
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std::uint8_t region = static_cast<std::uint8_t>(p.x() <= T{0});
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region |= static_cast<std::uint8_t>(p.y() <= T{0}) << std::uint8_t{1};
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region |= static_cast<std::uint8_t>(p.z() <= T{0}) << std::uint8_t{2};
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return static_cast<triangle_region>(region);
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}
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/**
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* Converts Cartesian coordinates to barycentric coordinates.
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*
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* @tparam T Real type.
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*
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* @param p Barycentric coordinates of point to convert.
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* @param a Cartesian coordinates of first point of triangle.
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* @param b Cartesian coordinates of second point of triangle.
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* @param c Cartesian coordinates of third point of triangle.
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*
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* @return Cartesian coordinates of point @p p.
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*/
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template <class T>
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[[nodiscard]] inline constexpr point<T, 3> barycentric_to_cartesian(const point<T, 3>& p, const point<T, 3>& a, const point<T, 3>& b, const point<T, 3>& c) noexcept
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{
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return a * p.x() + b * p.y() + c * p.z();
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}
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/**
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* Converts Cartesian coordinates to barycentric coordinates.
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*
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* @tparam T Real type.
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*
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* @param p Cartesian coordinates of point to convert.
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* @param a Cartesian coordinates of first point of triangle.
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* @param b Cartesian coordinates of second point of triangle.
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* @param c Cartesian coordinates of third point of triangle.
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*
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* @return Barycentric coordinates of point @p p.
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*/
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template <class T>
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[[nodiscard]] constexpr point<T, 3> cartesian_to_barycentric(const point<T, 3>& p, const point<T, 3>& a, const point<T, 3>& b, const point<T, 3>& c) noexcept
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{
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point<T, 3> uvw;
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// Cross product version:
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const auto ab = b - a;
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const auto ca = a - c;
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const auto ap = p - a;
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const auto n = math::cross(ab, ca);
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const auto d = math::sqr_length(n);
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const auto q = math::cross(n, ap);
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uvw.z() = math::dot(q, ab) / d;
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uvw.y() = math::dot(q, ca) / d;
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uvw.x() = T{1} - uvw.y() - uvw.z();
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// Dot product version:
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// const auto ab = b - a;
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// const auto ac = c - a;
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// const auto ap = p - a;
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// const auto ab_dot_ab = math::dot(ab, ab);
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// const auto ab_dot_ac = math::dot(ab, ac);
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// const auto ac_dot_ac = math::dot(ac, ac);
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// const auto ap_dot_ab = math::dot(ap, ab);
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// const auto ap_dot_ac = math::dot(ap, ac);
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// const auto d = ab_dot_ab * ac_dot_ac - ab_dot_ac * ab_dot_ac;
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// uvw.z() = (ab_dot_ab * ap_dot_ac - ab_dot_ac * ap_dot_ab) / d;
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// uvw.y() = (ac_dot_ac * ap_dot_ab - ab_dot_ac * ap_dot_ac) / d;
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// uvw.x() = T{1} - uvw.y() - uvw.z();
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return uvw;
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}
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/**
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* Converts Cartesian (rectangular) coordinates to spherical coordinates.
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*
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* @tparam T Real type.
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*
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* @param p Cartesian coordinates of point to convert.
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*
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* @return Spherical coordinates of point @p p, in the ISO order of radial distance, polar angle (radians), and azimuthal angle (radians).
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*/
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template <class T>
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[[nodiscard]] point<T, 3> cartesian_to_spherical(const point<T, 3>& p)
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{
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const T xx_yy = p.x() * p.x() + p.y() * p.y();
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return
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{
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std::sqrt(xx_yy + p.z() * p.z()),
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std::atan2(p.z(), std::sqrt(xx_yy)),
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std::atan2(p.y(), p.x())
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};
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}
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/**
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* Converts spherical coordinates to Cartesian (rectangular) coordinates.
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*
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* @tparam T Real type.
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*
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* @param p Spherical coordinates to convert, in the ISO order of radial distance, polar angle (radians), and azimuthal angle (radians).
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*
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* @return Cartesian coordinates of point @p p.
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*/
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template <class T>
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[[nodiscard]] point<T, 3> spherical_to_cartesian(const point<T, 3>& p)
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{
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const T x = p.x() * std::cos(p.y());
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return
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{
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x * std::cos(p.z()),
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x * std::sin(p.z()),
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p.x() * std::sin(p.y())
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};
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}
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} // namespace geom
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#endif // ANTKEEPER_GEOM_COORDINATES_HPP
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