💿🐜 Antkeeper source code
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160 lines
5.2 KiB
160 lines
5.2 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_MATH_PROJECTION_HPP
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#define ANTKEEPER_MATH_PROJECTION_HPP
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#include "math/matrix.hpp"
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#include <cmath>
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namespace math {
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/**
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* Calculates a horizontal FoV given a vertical FoV and aspect ratio.
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*
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* @param v Vertical FoV, in radians.
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* @param r Ratio of width to height.
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*
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* @return Horizontal FoV, in radians.
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*
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* @see https://en.wikipedia.org/wiki/Field_of_view_in_video_games
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*/
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template <class T>
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[[nodiscard]] T horizontal_fov(T v, T r)
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{
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return T{2} * std::atan(std::tan(v * T{0.5}) * r);
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}
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/**
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* Calculates a vertical FoV given a horizontal FoV and aspect ratio.
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*
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* @param h Horizontal FoV, in radians.
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* @param r Ratio of width to height.
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*
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* @return Vertical FoV, in radians.
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*
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* @see https://en.wikipedia.org/wiki/Field_of_view_in_video_games
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*/
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template <class T>
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[[nodiscard]] T vertical_fov(T h, T r)
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{
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return T{2} * std::atan(std::tan(h * T{0.5}) / r);
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}
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/**
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* Creates an orthographic projection matrix which will transform the near and far clipping planes to `[-1, 1]`, respectively.
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*
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* @param left Signed distance to the left clipping plane.
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* @param right Signed distance to the right clipping plane.
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* @param bottom Signed distance to the bottom clipping plane.
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* @param top Signed distance to the top clipping plane.
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* @param z_near Signed distance to the near clipping plane.
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* @param z_far Signed distance to the far clipping plane.
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*
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* @return Orthographic projection matrix.
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*/
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template <class T>
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[[nodiscard]] constexpr matrix<T, 4, 4> ortho(T left, T right, T bottom, T top, T z_near, T z_far) noexcept
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{
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return
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{{
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{T(2) / (right - left), T(0), T(0), T(0)},
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{T(0), T(2) / (top - bottom), T(0), T(0)},
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{T(0), T(0), T(-2) / (z_far - z_near), T(0)},
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{-((right + left) / (right - left)), -((top + bottom) / (top - bottom)), -((z_far + z_near) / (z_far - z_near)), T(1)}
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}};
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}
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/**
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* Creates an orthographic projection matrix which will transform the near and far clipping planes to `[0, 1]`, respectively.
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*
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* @param left Signed distance to the left clipping plane.
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* @param right Signed distance to the right clipping plane.
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* @param bottom Signed distance to the bottom clipping plane.
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* @param top Signed distance to the top clipping plane.
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* @param z_near Signed distance to the near clipping plane.
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* @param z_far Signed distance to the far clipping plane.
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*
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* @return Orthographic projection matrix.
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*/
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template <class T>
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[[nodiscard]] constexpr matrix<T, 4, 4> ortho_half_z(T left, T right, T bottom, T top, T z_near, T z_far) noexcept
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{
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return
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{{
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{T(2) / (right - left), T(0), T(0), T(0)},
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{T(0), T(2) / (top - bottom), T(0), T(0)},
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{T(0), T(0), T(-1) / (z_far - z_near), T(0)},
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{-((right + left) / (right - left)), -((top + bottom) / (top - bottom)), -z_near / (z_far - z_near), T(1)}
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}};
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}
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/**
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* Creates a perspective projection matrix which will transform the near and far clipping planes to `[-1, 1]`, respectively.
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*
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* @param vertical_fov Vertical field of view angle, in radians.
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* @param aspect_ratio Aspect ratio which determines the horizontal field of view.
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* @param z_near Distance to the near clipping plane.
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* @param z_far Distance to the far clipping plane.
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*
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* @return Perspective projection matrix.
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*/
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template <class T>
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[[nodiscard]] matrix<T, 4, 4> perspective(T vertical_fov, T aspect_ratio, T z_near, T z_far)
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{
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T half_fov = vertical_fov * T(0.5);
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T f = std::cos(half_fov) / std::sin(half_fov);
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return
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{{
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{f / aspect_ratio, T(0), T(0), T(0)},
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{T(0), f, T(0), T(0)},
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{T(0), T(0), (z_far + z_near) / (z_near - z_far), T(-1)},
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{T(0), T(0), (T(2) * z_far * z_near) / (z_near - z_far), T(0)}
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}};
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}
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/**
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* Creates a perspective projection matrix which will transform the near and far clipping planes to `[0, 1]`, respectively.
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*
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* @param vertical_fov Vertical field of view angle, in radians.
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* @param aspect_ratio Aspect ratio which determines the horizontal field of view.
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* @param z_near Distance to the near clipping plane.
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* @param z_far Distance to the far clipping plane.
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*
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* @return Perspective projection matrix.
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*/
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template <class T>
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[[nodiscard]] matrix<T, 4, 4> perspective_half_z(T vertical_fov, T aspect_ratio, T z_near, T z_far)
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{
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T half_fov = vertical_fov * T(0.5);
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T f = std::cos(half_fov) / std::sin(half_fov);
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return
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{{
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{f / aspect_ratio, T(0), T(0), T(0)},
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{T(0), f, T(0), T(0)},
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{T(0), T(0), z_far / (z_near - z_far), T(-1)},
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{T(0), T(0), -(z_far * z_near) / (z_far - z_near), T(0)}
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}};
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}
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} // namespace math
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#endif // ANTKEEPER_MATH_PROJECTION_HPP
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