💿🐜 Antkeeper source code
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372 lines
12 KiB
372 lines
12 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 <engine/math/matrix.hpp>
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#include <cmath>
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#include <tuple>
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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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* Constructs 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 near Signed distance to the near clipping plane.
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* @param 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 mat4<T> ortho(T left, T right, T bottom, T top, T near, T 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} / (far - near), T{0}},
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{-((right + left) / (right - left)), -((top + bottom) / (top - bottom)), -((far + near) / (far - near)), T{1}}
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}};
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}
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/**
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* Constructs an orthographic projection matrix which will transform the near and far clipping planes to `[-1, 1]`, respectively, along with its inverse.
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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 near Signed distance to the near clipping plane.
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* @param far Signed distance to the far clipping plane.
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*
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* @return Tuple containing the orthographic projection matrix, followed by its inverse.
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*
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* @note Constructing the inverse orthographic projection matrix from projection parameters is faster and more precise than inverting matrix.
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*/
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template <class T>
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[[nodiscard]] constexpr std::tuple<mat4<T>, mat4<T>> ortho_inv(T left, T right, T bottom, T top, T near, T far) noexcept
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{
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return
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{
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mat4<T>
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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} / (far - near), T{0}},
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{-((right + left) / (right - left)), -((top + bottom) / (top - bottom)), -((far + near) / (far - near)), T{1}}
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}},
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mat4<T>
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{{
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{(right - left) / T{2}, T{0}, T{0}, T{0}},
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{T{0}, (top - bottom) / T{2}, T{0}, T{0}},
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{T{0}, T{0}, (-far + near) / T{2}, T{0}},
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{(right + left) / T{2}, (bottom + top) / T{2}, (-far - near) / T{2}, T{1}}
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}}
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};
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}
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/**
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* Constructs 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 near Signed distance to the near clipping plane.
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* @param 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 mat4<T> ortho_half_z(T left, T right, T bottom, T top, T near, T 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} / (far - near), T{0}},
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{-((right + left) / (right - left)), -((top + bottom) / (top - bottom)), -near / (far - near), T{1}}
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}};
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}
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/**
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* Constructs an orthographic projection matrix which will transform the near and far clipping planes to `[0, 1]`, respectively, along with its inverse.
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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 near Signed distance to the near clipping plane.
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* @param far Signed distance to the far clipping plane.
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*
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* @return Tuple containing the orthographic projection matrix, followed by its inverse.
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*
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* @note Constructing the inverse orthographic projection matrix from projection parameters is faster and more precise than inverting matrix.
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*/
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template <class T>
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[[nodiscard]] constexpr std::tuple<mat4<T>, mat4<T>> ortho_half_z_inv(T left, T right, T bottom, T top, T near, T far) noexcept
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{
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return
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{
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mat4<T>
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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} / (far - near), T{0}},
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{-((right + left) / (right - left)), -((top + bottom) / (top - bottom)), -near / (far - near), T{1}}
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}},
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mat4<T>
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{{
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{(right - left) / T{2}, T{0}, T{0}, T{0}},
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{T{0}, (top - bottom) / T{2}, T{0}, T{0}},
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{T{0}, T{0}, -far + near, T{0}},
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{(right + left) / T{2}, (bottom + top) / T{2}, -near, T{1}}
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}}
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};
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}
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/**
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* Constructs 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 near Distance to the near clipping plane.
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* @param 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]] mat4<T> perspective(T vertical_fov, T aspect_ratio, T near, T far)
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{
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const T half_fov = vertical_fov * T{0.5};
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const 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}, (far + near) / (near - far), T{-1}},
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{T{0}, T{0}, (T{2} * far * near) / (near - far), T{0}}
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}};
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}
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/**
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* Constructs a perspective projection matrix which will transform the near and far clipping planes to `[-1, 1]`, respectively, along with its inverse.
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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 near Distance to the near clipping plane.
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* @param far Distance to the far clipping plane.
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*
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* @return Arraay containing the perspective projection matrix, followed by its inverse.
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*
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* @note Constructing the inverse perspective projection matrix from projection parameters is faster and more precise than inverting matrix.
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*/
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template <class T>
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[[nodiscard]] std::tuple<mat4<T>, mat4<T>> perspective_inv(T vertical_fov, T aspect_ratio, T near, T far)
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{
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const T half_fov = vertical_fov * T{0.5};
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const T f = std::cos(half_fov) / std::sin(half_fov);
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return
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{
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mat4<T>
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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}, (far + near) / (near - far), T{-1}},
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{T{0}, T{0}, (T{2} * far * near) / (near - far), T{0}}
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}},
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mat4<T>
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{{
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{aspect_ratio / f, T{0}, T{0}, T{0}},
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{T{0}, T{1} / f, T{0}, T{0}},
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{T{0}, T{0}, T{0}, (near - far) / (T{2} * near * far)},
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{T{0}, T{0}, T{-1}, (near + far) / (T{2} * near * far)}
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}}
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};
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}
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/**
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* Constructs 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 near Distance to the near clipping plane.
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* @param 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]] mat4<T> perspective_half_z(T vertical_fov, T aspect_ratio, T near, T far)
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{
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const T half_fov = vertical_fov * T{0.5};
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const 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}, far / (near - far), T{-1}},
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{T{0}, T{0}, -(far * near) / (far - near), T{0}}
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}};
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}
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/**
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* Constructs a perspective projection matrix which will transform the near and far clipping planes to `[0, 1]`, respectively, along with its inverse.
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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 near Distance to the near clipping plane.
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* @param far Distance to the far clipping plane.
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*
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* @return Tuple containing the perspective projection matrix, followed by its inverse.
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*
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* @note Constructing the inverse perspective projection matrix from projection parameters is faster and more precise than inverting matrix.
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*/
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template <class T>
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[[nodiscard]] std::tuple<mat4<T>, mat4<T>> perspective_half_z_inv(T vertical_fov, T aspect_ratio, T near, T far)
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{
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const T half_fov = vertical_fov * T{0.5};
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const T f = std::cos(half_fov) / std::sin(half_fov);
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return
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{
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mat4<T>
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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}, far / (near - far), T{-1}},
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{T{0}, T{0}, -(far * near) / (far - near), T{0}}
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}},
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mat4<T>
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{{
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{aspect_ratio / f, T{0}, T{0}, T{0}},
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{T{0}, T{1} / f, T{0}, T{0}},
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{T{0}, T{0}, T{0}, T{1} / far - T{1} / near},
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{T{0}, T{0}, T{-1}, T{1} / near}
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}}
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};
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}
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/**
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* Constructs a perspective projection matrix, with an infinite far plane, which will transform the near and far clipping planes to `[1, 0]`, 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 near Distance to the near 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]] mat4<T> inf_perspective_half_z_reverse(T vertical_fov, T aspect_ratio, T near)
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{
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const T half_fov = vertical_fov * T{0.5};
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const 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}, T{0}, T{-1}},
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{T{0}, T{0}, near, T{0}}
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}};
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}
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/**
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* Constructs a perspective projection matrix, with an infinite far plane, which will transform the near and far clipping planes to `[1, 0]`, respectively, along with its inverse.
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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 near Distance to the near clipping plane.
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*
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* @return Tuple containing the perspective projection matrix, followed by its inverse.
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*
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* @note Constructing the inverse perspective projection matrix from projection parameters is faster and more precise than inverting matrix.
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*/
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template <class T>
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[[nodiscard]] std::tuple<mat4<T>, mat4<T>> inf_perspective_half_z_reverse_inv(T vertical_fov, T aspect_ratio, T near)
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{
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const T half_fov = vertical_fov * T{0.5};
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const T f = std::cos(half_fov) / std::sin(half_fov);
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return
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{
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mat4<T>
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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}, T{0}, T{-1}},
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{T{0}, T{0}, near, T{0}}
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}},
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mat4<T>
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{{
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{aspect_ratio / f, T{0}, T{0}, T{0}},
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{T{0}, T{1} / f, T{0}, T{0}},
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{T{0}, T{0}, T{0}, T{1} / near},
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{T{0}, T{0}, T{-1}, T{0}}
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}}
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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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