💿🐜 Antkeeper source code
https://antkeeper.com
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121 lines
3.5 KiB
121 lines
3.5 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 <cmath>
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namespace geom {
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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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const auto ab = b - a;
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const auto ca = a - c;
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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, p - a);
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point<T, 3> uvw;
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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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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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