💿🐜 Antkeeper source code
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1241 lines
36 KiB
1241 lines
36 KiB
/*
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* Copyright (C) 2021 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_MATRIX_HPP
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#define ANTKEEPER_MATH_MATRIX_HPP
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#include "math/vector.hpp"
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#include <cstddef>
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#include <istream>
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#include <iterator>
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#include <ostream>
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#include <type_traits>
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#include <utility>
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namespace math {
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/**
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* *n* by *m* column-major matrix.
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*
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* @tparam T Matrix element data type.
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* @tparam N Number of columns.
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* @tparam M Number of rows.
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*
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* @see https://en.wikipedia.org/wiki/Row-_and_column-major_order
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*/
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template <typename T, std::size_t N, std::size_t M>
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struct matrix
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{
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/// Matrix element data type.
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typedef T element_type;
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/// Number of matrix columns.
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static constexpr std::size_t column_count = N;
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/// Number of matrix rows.
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static constexpr std::size_t row_count = M;
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/// Number of matrix elements.
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static constexpr std::size_t element_count = column_count * row_count;
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/// Matrix column vector data type.
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typedef vector<element_type, row_count> column_vector_type;
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/// Matrix row vector data type.
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typedef vector<element_type, column_count> row_vector_type;
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/// Array of matrix column vectors.
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column_vector_type columns[column_count];
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/**
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* Returns a reference to the column vector at a given index.
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*
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* @param i Index of a column vector.
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*
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* @return Reference to the column vector at index @p i.
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*/
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/// @{
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constexpr inline column_vector_type& operator[](std::size_t i) noexcept
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{
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return columns[i];
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}
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constexpr inline const column_vector_type& operator[](std::size_t i) const noexcept
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{
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return columns[i];
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}
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constexpr inline column_vector_type& column(std::size_t i) noexcept
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{
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return columns[i];
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}
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constexpr inline const column_vector_type& column(std::size_t i) const noexcept
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{
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return columns[i];
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}
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/// @}
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/**
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* Returns a reference to the element at a given column-major index.
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*
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* @param i Column-major index of a matrix element.
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*
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* @return Reference to the element at column-major index @p i.
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*/
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/// @{
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constexpr inline T& element(std::size_t i) noexcept
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{
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return columns[i / row_count][i % row_count];
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}
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constexpr inline const T& element(std::size_t i) const noexcept
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{
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return columns[i / row_count][i % row_count];
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}
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/// @}
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/// Returns a reference to the first column vector.
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/// @{
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constexpr inline column_vector_type& front() noexcept
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{
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return columns[0];
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}
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constexpr inline const column_vector_type& front() const noexcept
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{
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return columns[0];
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}
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/// @}
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/// Returns a reference to the last column vector.
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/// @{
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constexpr inline column_vector_type& back() noexcept
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{
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return columns[column_count - 1];
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}
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constexpr inline const column_vector_type& back() const noexcept
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{
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return columns[column_count - 1];
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}
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/// @}
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/**
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* Returns a pointer to the first element.
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*
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* @warning If matrix::element_type is not a POD type, elements may not be stored contiguously.
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*/
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/// @{
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constexpr inline element_type* data() noexcept
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{
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return &columns[0][0];
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};
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constexpr inline const element_type* data() const noexcept
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{
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return &columns[0][0];
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};
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/// @}
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/// Returns an iterator to the first column vector.
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/// @{
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constexpr inline column_vector_type* begin() noexcept
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{
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return columns;
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}
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constexpr inline const column_vector_type* begin() const noexcept
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{
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return columns;
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}
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constexpr inline const column_vector_type* cbegin() const noexcept
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{
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return columns;
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}
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/// @}
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/// Returns an iterator to the column vector following the last column vector.
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/// @{
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constexpr inline column_vector_type* end() noexcept
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{
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return columns + column_count;
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}
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constexpr inline const column_vector_type* end() const noexcept
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{
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return columns + column_count;
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}
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constexpr inline const column_vector_type* cend() const noexcept
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{
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return columns + column_count;
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}
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/// @}
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/// Returns a reverse iterator to the first column vector of the reversed matrix.
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/// @{
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constexpr inline std::reverse_iterator<column_vector_type*> rbegin() noexcept
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{
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return std::reverse_iterator<column_vector_type*>(columns + column_count);
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}
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constexpr inline std::reverse_iterator<const column_vector_type*> rbegin() const noexcept
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{
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return std::reverse_iterator<const column_vector_type*>(columns + column_count);
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}
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constexpr inline std::reverse_iterator<const column_vector_type*> crbegin() const noexcept
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{
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return std::reverse_iterator<const column_vector_type*>(columns + column_count);
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}
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/// @}
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/// Returns a reverse iterator to the column vector following the last column vector of the reversed matrix.
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/// @{
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constexpr inline std::reverse_iterator<column_vector_type*> rend() noexcept
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{
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return std::reverse_iterator<column_vector_type*>(columns);
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}
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constexpr inline std::reverse_iterator<const column_vector_type*> rend() const noexcept
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{
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return std::reverse_iterator<const column_vector_type*>(columns);
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}
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constexpr inline std::reverse_iterator<const column_vector_type*> crend() const noexcept
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{
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return std::reverse_iterator<const column_vector_type*>(columns);
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}
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/// @}
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/// Returns the number of elements in the matrix.
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constexpr inline std::size_t size() const noexcept
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{
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return element_count;
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};
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/// @private
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template <class U, std::size_t... I>
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constexpr inline matrix<U, N, M> type_cast(std::index_sequence<I...>) const noexcept
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{
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return {vector<U, M>(columns[I])...};
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}
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/**
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* Type-casts the elements of this matrix using `static_cast`.
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*
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* @tparam U Target element type.
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*
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* @return Matrix containing the type-casted elements.
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*/
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template <class U>
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constexpr inline explicit operator matrix<U, N, M>() const noexcept
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{
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return type_cast<U>(std::make_index_sequence<N>{});
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}
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/// @private
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template <std::size_t P, std::size_t O, std::size_t... I>
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constexpr inline matrix<T, P, O> size_cast(std::index_sequence<I...>) const noexcept
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{
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if constexpr (O == M)
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return {((I < N) ? columns[I] : matrix<T, P, O>::identity()[I]) ...};
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else
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return {((I < N) ? vector<T, O>(columns[I]) : matrix<T, P, O>::identity()[I]) ...};
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}
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/**
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* Size-casts this matrix to a matrix with different dimensions. Casting to greater dimensions causes new elements to be set to identity matrix elements.
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*
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* @tparam P Target number of columns.
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* @tparam O Target number of rows.
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*
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* @return *p* by *o* matrix.
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*/
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template <std::size_t P, std::size_t O>
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constexpr inline explicit operator matrix<T, P, O>() const noexcept
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{
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return size_cast<P, O>(std::make_index_sequence<P>{});
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}
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/// Returns a zero matrix, where every element is equal to zero.
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static constexpr matrix zero() noexcept
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{
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return {};
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}
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/// @private
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template <std::size_t... I>
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static constexpr inline matrix one(std::index_sequence<I...>) noexcept
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{
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//return {column_vector_type::one() ...};
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// MSVC bug workaround (I must be referenced for parameter pack expansion)
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return {(I ? column_vector_type::one() : column_vector_type::one()) ...};
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}
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/// Returns a matrix of ones, where every element is equal to one.
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static constexpr matrix one() noexcept
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{
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return one(std::make_index_sequence<column_count>{});
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}
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/// @private
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template <std::size_t... I>
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static constexpr inline column_vector_type identity_column(std::size_t i, std::index_sequence<I...>) noexcept
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{
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return {(I == i ? T{1} : T{0}) ...};
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}
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/// @private
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template <std::size_t... I>
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static constexpr inline matrix identity(std::index_sequence<I...>) noexcept
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{
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return {identity_column(I, std::make_index_sequence<row_count>{}) ...};
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}
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/// Returns an identity matrix, with ones on the main diagonal and zeros elsewhere.
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static constexpr matrix identity() noexcept
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{
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return identity(std::make_index_sequence<column_count>{});
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}
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};
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/// 2x2 matrix.
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template <typename T>
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using matrix2 = matrix<T, 2, 2>;
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/// 2x2 matrix.
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template <typename T>
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using matrix2x2 = matrix<T, 2, 2>;
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/// 3x3 matrix.
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template <typename T>
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using matrix3 = matrix<T, 3, 3>;
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/// 3x3 matrix.
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template <typename T>
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using matrix3x3 = matrix<T, 3, 3>;
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/// 4x4 matrix.
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template <typename T>
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using matrix4 = matrix<T, 4, 4>;
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/// 4x4 matrix.
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template <typename T>
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using matrix4x4 = matrix<T, 4, 4>;
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/**
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* Adds two matrices.
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*
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* @param a First matrix.
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* @param b Second matrix.
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*
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* @return Sum of the two matrices.
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*/
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template <class T, std::size_t N, std::size_t M>
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constexpr matrix<T, N, M> add(const matrix<T, N, M>& a, const matrix<T, N, M>& b) noexcept;
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/**
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* Adds a matrix and a scalar.
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*
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* @param a Matrix.
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* @param b scalar.
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*
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* @return Sum of the matrix and scalar.
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*/
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template <class T, std::size_t N, std::size_t M>
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constexpr matrix<T, N, M> add(const matrix<T, N, M>& a, T b) noexcept;
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/**
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* Calculates the determinant of a square matrix.
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*
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* @param m Matrix of which to take the determinant.
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*
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* @return Determinant of @p m.
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*
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* @warning Currently only implemented for 2x2, 3x3, and 4x4 matrices.
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*/
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template <class T, std::size_t N>
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constexpr T determinant(const matrix<T, N, N>& m) noexcept;
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/**
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* Calculates the inverse of a square matrix.
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*
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* @param m Square matrix.
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*
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* @return Inverse of matrix @p m.
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*
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* @warning Currently only implemented for 2x2, 3x3, and 4x4 matrices.
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*/
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template <class T, std::size_t N>
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constexpr matrix<T, N, N> inverse(const matrix<T, N, N>& m) noexcept;
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/**
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* Performs a component-wise multiplication of two matrices.
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*
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* @param x First matrix multiplicand.
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* @param y Second matrix multiplicand.
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*
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* @return Product of the component-wise multiplcation.
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*/
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template <class T, std::size_t N, std::size_t M>
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constexpr matrix<T, N, M> componentwise_mul(const matrix<T, N, M>& a, const matrix<T, N, M>& b) noexcept;
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/**
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* Divides a matrix by a matrix.
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*
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* @param a First matrix.
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* @param b Second matrix.
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*
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* @return Result of the division.
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*/
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template <class T, std::size_t N, std::size_t M>
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constexpr matrix<T, N, M> div(const matrix<T, N, M>& a, const matrix<T, N, M>& b) noexcept;
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/**
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* Divides a matrix by a scalar.
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*
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* @param a Matrix.
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* @param b Scalar.
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*
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* @return Result of the division.
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*/
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template <class T, std::size_t N, std::size_t M>
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constexpr matrix<T, N, M> div(const matrix<T, N, M>& a, T b) noexcept;
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/**
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* Divides a scalar by a matrix.
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*
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* @param a Scalar.
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* @param b Matrix.
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*
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* @return Result of the division.
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*/
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template <class T, std::size_t N, std::size_t M>
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constexpr matrix<T, N, M> div(T a, const matrix<T, N, M>& b) noexcept;
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/**
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* Creates a viewing transformation matrix.
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*
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* @param position Position of the view point.
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* @param target Position of the target.
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* @param up Normalized direction of the up vector.
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*
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* @return Viewing transformation matrix.
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*/
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template <class T>
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constexpr matrix<T, 4, 4> look_at(const vector<T, 3>& position, const vector<T, 3>& target, vector<T, 3> up);
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/**
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* Multiplies two matrices
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*
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* @tparam T Matrix element type.
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* @tparam N Number of columns in matrix @p a, and rows in matrix @p b.
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* @tparam M Number of rows in matrix @p a.
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* @tparam P Number of columns in matrix @p b.
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*
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* @param a First matrix.
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* @param b Second matrix.
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*
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* @return Product of `a * b`.
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*/
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template <typename T, std::size_t N, std::size_t M, std::size_t P>
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constexpr matrix<T, P, M> mul(const matrix<T, N, M>& a, const matrix<T, P, N>& b) noexcept;
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/**
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* Multiplies a matrix by a scalar.
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*
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* @param a Matrix.
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* @param b Scalar.
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*
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* @return Product of the matrix and the scalar.
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*/
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template <class T, std::size_t N, std::size_t M>
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constexpr matrix<T, N, M> mul(const matrix<T, N, M>& a, T b) noexcept;
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/**
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* Calculates the product of a matrix and a row vector.
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*
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* @param a Matrix.
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* @param b Row vector
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*
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* @return Product of the matrix and the row vector.
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*/
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template <typename T, std::size_t N, std::size_t M>
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constexpr typename matrix<T, N, M>::column_vector_type mul(const matrix<T, N, M>& a, const typename matrix<T, N, M>::row_vector_type& b) noexcept;
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/**
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* Calculates the product of a column vector and a matrix.
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*
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* @param a Column vector.
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* @param b Matrix.
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*
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* @return Product of the column vector and the matrix.
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*/
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template <typename T, std::size_t N, std::size_t M>
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constexpr typename matrix<T, N, M>::row_vector_type mul(const typename matrix<T, N, M>::column_vector_type& a, const matrix<T, N, M>& b) noexcept;
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/**
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* Constructs a rotation matrix.
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*
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* @param angle Angle of rotation, in radians.
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* @param axis Axis of rotation.
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*
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* @return Rotation matrix.
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*/
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template <class T>
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matrix<T, 3, 3> rotate(T angle, const vector<T, 3>& axis);
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/**
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* Produces a matrix which rotates Cartesian coordinates about the x-axis by a given angle.
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*
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* @param angle Angle of rotation, in radians.
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*
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* @return Rotation matrix.
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*/
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template <class T>
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matrix3<T> rotate_x(T angle);
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/**
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* Produces a matrix which rotates Cartesian coordinates about the y-axis by a given angle.
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*
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* @param angle Angle of rotation, in radians.
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*
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* @return Rotation matrix.
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*/
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template <class T>
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matrix3<T> rotate_y(T angle);
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/**
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* Produces a matrix which rotates Cartesian coordinates about the z-axis by a given angle.
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*
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* @param angle Angle of rotation, in radians.
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*
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* @return Rotation matrix.
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*/
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template <class T>
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matrix3<T> rotate_z(T angle);
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/**
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* Scales a matrix.
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*
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* @param m Matrix to scale.
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* @param v Scale vector.
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*
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* @return Scaled matrix.
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*/
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template <class T>
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constexpr matrix<T, 4, 4> scale(const matrix<T, 4, 4>& m, const vector<T, 3>& v);
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/**
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* Subtracts a matrix from another matrix.
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*
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* @param a First matrix.
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* @param b Second matrix.
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*
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* @return Difference between the two matrices.
|
|
*/
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr matrix<T, N, M> sub(const matrix<T, N, M>& a, const matrix<T, N, M>& b) noexcept;
|
|
|
|
/**
|
|
* Subtracts a scalar from matrix.
|
|
*
|
|
* @param a Matrix.
|
|
* @param b Scalar.
|
|
*
|
|
* @return Difference between the matrix and scalar.
|
|
*/
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr matrix<T, N, M> sub(const matrix<T, N, M>& a, T b) noexcept;
|
|
|
|
/**
|
|
* Subtracts a matrix from a scalar.
|
|
*
|
|
* @param a Scalar.
|
|
* @param b Matrix.
|
|
*
|
|
* @return Difference between the scalar and matrix.
|
|
*/
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr matrix<T, N, M> sub(T a, const matrix<T, N, M>& b) noexcept;
|
|
|
|
/**
|
|
* Calculates the trace of a square matrix.
|
|
*
|
|
* @param m Square matrix.
|
|
*
|
|
* @return Sum of elements on the main diagonal.
|
|
*/
|
|
template <class T, std::size_t N>
|
|
constexpr T trace(const matrix<T, N, N>& m) noexcept;
|
|
|
|
/**
|
|
* Translates a matrix.
|
|
*
|
|
* @param m Matrix to translate.
|
|
* @param v Translation vector.
|
|
*
|
|
* @return Translated matrix.
|
|
*/
|
|
template <class T>
|
|
constexpr matrix<T, 4, 4> translate(const matrix<T, 4, 4>& m, const vector<T, 3>& v);
|
|
|
|
/**
|
|
* Calculates the transpose of a matrix.
|
|
*
|
|
* @param m Matrix to transpose.
|
|
*
|
|
* @return Transposed matrix.
|
|
*/
|
|
template <typename T, std::size_t N, std::size_t M>
|
|
constexpr matrix<T, M, N> transpose(const matrix<T, N, M>& m) noexcept;
|
|
|
|
/// @private
|
|
template <class T, std::size_t N, std::size_t M, std::size_t... I>
|
|
constexpr inline matrix<T, N, M> add(const matrix<T, N, M>& a, const matrix<T, N, M>& b, std::index_sequence<I...>) noexcept
|
|
{
|
|
return {(a[I] + b[I]) ...};
|
|
}
|
|
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr matrix<T, N, M> add(const matrix<T, N, M>& a, const matrix<T, N, M>& b) noexcept
|
|
{
|
|
return add(a, b, std::make_index_sequence<N>{});
|
|
}
|
|
|
|
/// @private
|
|
template <class T, std::size_t N, std::size_t M, std::size_t... I>
|
|
constexpr inline matrix<T, N, M> add(const matrix<T, N, M>& a, T b, std::index_sequence<I...>) noexcept
|
|
{
|
|
return {(a[I] + b) ...};
|
|
}
|
|
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr matrix<T, N, M> add(const matrix<T, N, M>& a, T b) noexcept
|
|
{
|
|
return add(a, b, std::make_index_sequence<N>{});
|
|
}
|
|
|
|
template <class T>
|
|
constexpr T determinant(const matrix<T, 2, 2>& m) noexcept
|
|
{
|
|
return
|
|
m[0][0] * m[1][1] -
|
|
m[0][1] * m[1][0];
|
|
}
|
|
|
|
template <class T>
|
|
constexpr T determinant(const matrix<T, 3, 3>& m) noexcept
|
|
{
|
|
return
|
|
m[0][0] * m[1][1] * m[2][2] +
|
|
m[0][1] * m[1][2] * m[2][0] +
|
|
m[0][2] * m[1][0] * m[2][1] -
|
|
m[0][0] * m[1][2] * m[2][1] -
|
|
m[0][1] * m[1][0] * m[2][2] -
|
|
m[0][2] * m[1][1] * m[2][0];
|
|
}
|
|
|
|
template <class T>
|
|
constexpr T determinant(const matrix<T, 4, 4>& m) noexcept
|
|
{
|
|
return
|
|
m[0][3] * m[1][2] * m[2][1] * m[3][0] - m[0][2] * m[1][3] * m[2][1] * m[3][0] -
|
|
m[0][3] * m[1][1] * m[2][2] * m[3][0] + m[0][1] * m[1][3] * m[2][2] * m[3][0] +
|
|
m[0][2] * m[1][1] * m[2][3] * m[3][0] - m[0][1] * m[1][2] * m[2][3] * m[3][0] -
|
|
m[0][3] * m[1][2] * m[2][0] * m[3][1] + m[0][2] * m[1][3] * m[2][0] * m[3][1] +
|
|
m[0][3] * m[1][0] * m[2][2] * m[3][1] - m[0][0] * m[1][3] * m[2][2] * m[3][1] -
|
|
m[0][2] * m[1][0] * m[2][3] * m[3][1] + m[0][0] * m[1][2] * m[2][3] * m[3][1] +
|
|
m[0][3] * m[1][1] * m[2][0] * m[3][2] - m[0][1] * m[1][3] * m[2][0] * m[3][2] -
|
|
m[0][3] * m[1][0] * m[2][1] * m[3][2] + m[0][0] * m[1][3] * m[2][1] * m[3][2] +
|
|
m[0][1] * m[1][0] * m[2][3] * m[3][2] - m[0][0] * m[1][1] * m[2][3] * m[3][2] -
|
|
m[0][2] * m[1][1] * m[2][0] * m[3][3] + m[0][1] * m[1][2] * m[2][0] * m[3][3] +
|
|
m[0][2] * m[1][0] * m[2][1] * m[3][3] - m[0][0] * m[1][2] * m[2][1] * m[3][3] -
|
|
m[0][1] * m[1][0] * m[2][2] * m[3][3] + m[0][0] * m[1][1] * m[2][2] * m[3][3];
|
|
}
|
|
|
|
template <class T>
|
|
constexpr matrix<T, 2, 2> inverse(const matrix<T, 2, 2>& m) noexcept
|
|
{
|
|
const T inv_det = T{1} / determinant(m);
|
|
|
|
return
|
|
{
|
|
m[1][1] * inv_det,
|
|
-m[0][1] * inv_det,
|
|
-m[1][0] * inv_det,
|
|
m[0][0] * inv_det
|
|
};
|
|
}
|
|
|
|
template <class T>
|
|
constexpr matrix<T, 3, 3> inverse(const matrix<T, 3, 3>& m) noexcept
|
|
{
|
|
const T inv_det = T{1} / determinant(m);
|
|
|
|
return
|
|
{
|
|
(m[1][1] * m[2][2] - m[1][2] * m[2][1]) * inv_det,
|
|
(m[0][2] * m[2][1] - m[0][1] * m[2][2]) * inv_det,
|
|
(m[0][1] * m[1][2] - m[0][2] * m[1][1]) * inv_det,
|
|
|
|
(m[1][2] * m[2][0] - m[1][0] * m[2][2]) * inv_det,
|
|
(m[0][0] * m[2][2] - m[0][2] * m[2][0]) * inv_det,
|
|
(m[0][2] * m[1][0] - m[0][0] * m[1][2]) * inv_det,
|
|
|
|
(m[1][0] * m[2][1] - m[1][1] * m[2][0]) * inv_det,
|
|
(m[0][1] * m[2][0] - m[0][0] * m[2][1]) * inv_det,
|
|
(m[0][0] * m[1][1] - m[0][1] * m[1][0]) * inv_det
|
|
};
|
|
}
|
|
|
|
template <class T>
|
|
constexpr matrix<T, 4, 4> inverse(const matrix<T, 4, 4>& m) noexcept
|
|
{
|
|
const T inv_det = T{1} / determinant(m);
|
|
|
|
return
|
|
{
|
|
(m[1][2] * m[2][3] * m[3][1] - m[1][3] * m[2][2] * m[3][1] + m[1][3] * m[2][1] * m[3][2] - m[1][1] * m[2][3] * m[3][2] - m[1][2] * m[2][1] * m[3][3] + m[1][1] * m[2][2] * m[3][3]) * inv_det,
|
|
(m[0][3] * m[2][2] * m[3][1] - m[0][2] * m[2][3] * m[3][1] - m[0][3] * m[2][1] * m[3][2] + m[0][1] * m[2][3] * m[3][2] + m[0][2] * m[2][1] * m[3][3] - m[0][1] * m[2][2] * m[3][3]) * inv_det,
|
|
(m[0][2] * m[1][3] * m[3][1] - m[0][3] * m[1][2] * m[3][1] + m[0][3] * m[1][1] * m[3][2] - m[0][1] * m[1][3] * m[3][2] - m[0][2] * m[1][1] * m[3][3] + m[0][1] * m[1][2] * m[3][3]) * inv_det,
|
|
(m[0][3] * m[1][2] * m[2][1] - m[0][2] * m[1][3] * m[2][1] - m[0][3] * m[1][1] * m[2][2] + m[0][1] * m[1][3] * m[2][2] + m[0][2] * m[1][1] * m[2][3] - m[0][1] * m[1][2] * m[2][3]) * inv_det,
|
|
|
|
(m[1][3] * m[2][2] * m[3][0] - m[1][2] * m[2][3] * m[3][0] - m[1][3] * m[2][0] * m[3][2] + m[1][0] * m[2][3] * m[3][2] + m[1][2] * m[2][0] * m[3][3] - m[1][0] * m[2][2] * m[3][3]) * inv_det,
|
|
(m[0][2] * m[2][3] * m[3][0] - m[0][3] * m[2][2] * m[3][0] + m[0][3] * m[2][0] * m[3][2] - m[0][0] * m[2][3] * m[3][2] - m[0][2] * m[2][0] * m[3][3] + m[0][0] * m[2][2] * m[3][3]) * inv_det,
|
|
(m[0][3] * m[1][2] * m[3][0] - m[0][2] * m[1][3] * m[3][0] - m[0][3] * m[1][0] * m[3][2] + m[0][0] * m[1][3] * m[3][2] + m[0][2] * m[1][0] * m[3][3] - m[0][0] * m[1][2] * m[3][3]) * inv_det,
|
|
(m[0][2] * m[1][3] * m[2][0] - m[0][3] * m[1][2] * m[2][0] + m[0][3] * m[1][0] * m[2][2] - m[0][0] * m[1][3] * m[2][2] - m[0][2] * m[1][0] * m[2][3] + m[0][0] * m[1][2] * m[2][3]) * inv_det,
|
|
|
|
(m[1][1] * m[2][3] * m[3][0] - m[1][3] * m[2][1] * m[3][0] + m[1][3] * m[2][0] * m[3][1] - m[1][0] * m[2][3] * m[3][1] - m[1][1] * m[2][0] * m[3][3] + m[1][0] * m[2][1] * m[3][3]) * inv_det,
|
|
(m[0][3] * m[2][1] * m[3][0] - m[0][1] * m[2][3] * m[3][0] - m[0][3] * m[2][0] * m[3][1] + m[0][0] * m[2][3] * m[3][1] + m[0][1] * m[2][0] * m[3][3] - m[0][0] * m[2][1] * m[3][3]) * inv_det,
|
|
(m[0][1] * m[1][3] * m[3][0] - m[0][3] * m[1][1] * m[3][0] + m[0][3] * m[1][0] * m[3][1] - m[0][0] * m[1][3] * m[3][1] - m[0][1] * m[1][0] * m[3][3] + m[0][0] * m[1][1] * m[3][3]) * inv_det,
|
|
(m[0][3] * m[1][1] * m[2][0] - m[0][1] * m[1][3] * m[2][0] - m[0][3] * m[1][0] * m[2][1] + m[0][0] * m[1][3] * m[2][1] + m[0][1] * m[1][0] * m[2][3] - m[0][0] * m[1][1] * m[2][3]) * inv_det,
|
|
|
|
(m[1][2] * m[2][1] * m[3][0] - m[1][1] * m[2][2] * m[3][0] - m[1][2] * m[2][0] * m[3][1] + m[1][0] * m[2][2] * m[3][1] + m[1][1] * m[2][0] * m[3][2] - m[1][0] * m[2][1] * m[3][2]) * inv_det,
|
|
(m[0][1] * m[2][2] * m[3][0] - m[0][2] * m[2][1] * m[3][0] + m[0][2] * m[2][0] * m[3][1] - m[0][0] * m[2][2] * m[3][1] - m[0][1] * m[2][0] * m[3][2] + m[0][0] * m[2][1] * m[3][2]) * inv_det,
|
|
(m[0][2] * m[1][1] * m[3][0] - m[0][1] * m[1][2] * m[3][0] - m[0][2] * m[1][0] * m[3][1] + m[0][0] * m[1][2] * m[3][1] + m[0][1] * m[1][0] * m[3][2] - m[0][0] * m[1][1] * m[3][2]) * inv_det,
|
|
(m[0][1] * m[1][2] * m[2][0] - m[0][2] * m[1][1] * m[2][0] + m[0][2] * m[1][0] * m[2][1] - m[0][0] * m[1][2] * m[2][1] - m[0][1] * m[1][0] * m[2][2] + m[0][0] * m[1][1] * m[2][2]) * inv_det
|
|
};
|
|
}
|
|
|
|
/// @private
|
|
template <class T, std::size_t N, std::size_t M, std::size_t... I>
|
|
constexpr inline matrix<T, N, M> componentwise_mul(const matrix<T, N, M>& a, const matrix<T, N, M>& b, std::index_sequence<I...>) noexcept
|
|
{
|
|
return {(a[I] * b[I]) ...};
|
|
}
|
|
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr matrix<T, N, M> componentwise_mul(const matrix<T, N, M>& a, const matrix<T, N, M>& b) noexcept
|
|
{
|
|
return componentwise_mul(a, b, std::make_index_sequence<N>{});
|
|
}
|
|
|
|
/// @private
|
|
template <class T, std::size_t N, std::size_t M, std::size_t... I>
|
|
constexpr inline matrix<T, N, M> div(const matrix<T, N, M>& a, const matrix<T, N, M>& b, std::index_sequence<I...>) noexcept
|
|
{
|
|
return {(a[I] / b[I]) ...};
|
|
}
|
|
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr matrix<T, N, M> div(const matrix<T, N, M>& a, const matrix<T, N, M>& b) noexcept
|
|
{
|
|
return div(a, b, std::make_index_sequence<N>{});
|
|
}
|
|
|
|
/// @private
|
|
template <class T, std::size_t N, std::size_t M, std::size_t... I>
|
|
constexpr inline matrix<T, N, M> div(const matrix<T, N, M>& a, T b, std::index_sequence<I...>) noexcept
|
|
{
|
|
return {(a[I] / b) ...};
|
|
}
|
|
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr matrix<T, N, M> div(const matrix<T, N, M>& a, T b) noexcept
|
|
{
|
|
return div(a, b, std::make_index_sequence<N>{});
|
|
}
|
|
|
|
/// @private
|
|
template <class T, std::size_t N, std::size_t M, std::size_t... I>
|
|
constexpr inline matrix<T, N, M> div(T a, const matrix<T, N, M>& b, std::index_sequence<I...>) noexcept
|
|
{
|
|
return {(a / b[I]) ...};
|
|
}
|
|
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr matrix<T, N, M> div(T a, const matrix<T, N, M>& b) noexcept
|
|
{
|
|
return div(a, b, std::make_index_sequence<N>{});
|
|
}
|
|
|
|
template <class T>
|
|
constexpr matrix<T, 4, 4> look_at(const vector<T, 3>& position, const vector<T, 3>& target, vector<T, 3> up)
|
|
{
|
|
vector<T, 3> forward = normalize(sub(target, position));
|
|
vector<T, 3> right = normalize(cross(forward, up));
|
|
up = cross(right, forward);
|
|
|
|
matrix<T, 4, 4> m =
|
|
{{
|
|
{right[0], up[0], -forward[0], T(0)},
|
|
{right[1], up[1], -forward[1], T(0)},
|
|
{right[2], up[2], -forward[2], T(0)},
|
|
{T(0), T(0), T(0), T(1)}
|
|
}};
|
|
|
|
return translate(m, negate(position));
|
|
}
|
|
|
|
template <typename T, std::size_t N, std::size_t M, std::size_t P>
|
|
constexpr matrix<T, P, M> mul(const matrix<T, N, M>& a, const matrix<T, P, N>& b) noexcept
|
|
{
|
|
matrix<T, P, M> c = matrix<T, P, M>::zero();
|
|
|
|
for (std::size_t i = 0; i < P; ++i)
|
|
{
|
|
for (std::size_t j = 0; j < M; ++j)
|
|
{
|
|
for (std::size_t k = 0; k < N; ++k)
|
|
{
|
|
c[i][j] += a[k][j] * b[i][k];
|
|
}
|
|
}
|
|
}
|
|
|
|
return c;
|
|
}
|
|
|
|
/// @private
|
|
template <class T, std::size_t N, std::size_t M, std::size_t... I>
|
|
constexpr inline matrix<T, N, M> mul(const matrix<T, N, M>& a, T b, std::index_sequence<I...>) noexcept
|
|
{
|
|
return {(a[I] * b) ...};
|
|
}
|
|
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr matrix<T, N, M> mul(const matrix<T, N, M>& a, T b) noexcept
|
|
{
|
|
return mul(a, b, std::make_index_sequence<N>{});
|
|
}
|
|
|
|
/// @private
|
|
template <typename T, std::size_t N, std::size_t M, std::size_t... I>
|
|
constexpr inline typename matrix<T, N, M>::column_vector_type mul(const matrix<T, N, M>& a, const typename matrix<T, N, M>::row_vector_type& b, std::index_sequence<I...>) noexcept
|
|
{
|
|
return ((a[I] * b[I]) + ...);
|
|
}
|
|
|
|
template <typename T, std::size_t N, std::size_t M>
|
|
constexpr typename matrix<T, N, M>::column_vector_type mul(const matrix<T, N, M>& a, const typename matrix<T, N, M>::row_vector_type& b) noexcept
|
|
{
|
|
return mul(a, b, std::make_index_sequence<N>{});
|
|
}
|
|
|
|
/// @private
|
|
template <typename T, std::size_t N, std::size_t M, std::size_t... I>
|
|
constexpr inline typename matrix<T, N, M>::row_vector_type mul(const typename matrix<T, N, M>::column_vector_type& a, const matrix<T, N, M>& b, std::index_sequence<I...>) noexcept
|
|
{
|
|
return {dot(a, b[I]) ...};
|
|
}
|
|
|
|
template <typename T, std::size_t N, std::size_t M>
|
|
constexpr typename matrix<T, N, M>::row_vector_type mul(const typename matrix<T, N, M>::column_vector_type& a, const matrix<T, N, M>& b) noexcept
|
|
{
|
|
return mul(a, b, std::make_index_sequence<N>{});
|
|
}
|
|
|
|
template <class T>
|
|
matrix<T, 3, 3> rotate(T angle, const vector<T, 3>& axis)
|
|
{
|
|
const T c = std::cos(angle);
|
|
const T s = std::sin(angle);
|
|
const vector<T, 3> temp = mul(axis, T(1) - c);
|
|
|
|
matrix<T, 3, 3> rotation;
|
|
rotation[0][0] = axis[0] * temp[0] + c;
|
|
rotation[0][1] = axis[1] * temp[0] + axis[2] * s;
|
|
rotation[0][2] = axis[2] * temp[0] - axis[1] * s;
|
|
rotation[1][0] = axis[0] * temp[1] - axis[2] * s;
|
|
rotation[1][1] = axis[1] * temp[1] + c;
|
|
rotation[1][2] = axis[2] * temp[1] + axis[0] * s;
|
|
rotation[2][0] = axis[0] * temp[2] + axis[1] * s;
|
|
rotation[2][1] = axis[1] * temp[2] - axis[0] * s;
|
|
rotation[2][2] = axis[2] * temp[2] + c;
|
|
|
|
return rotation;
|
|
}
|
|
|
|
template <class T>
|
|
matrix3<T> rotate_x(T angle)
|
|
{
|
|
const T c = std::cos(angle);
|
|
const T s = std::sin(angle);
|
|
|
|
return matrix3<T>
|
|
{
|
|
T(1), T(0), T(0),
|
|
T(0), c, s,
|
|
T(0), -s, c
|
|
};
|
|
}
|
|
|
|
template <class T>
|
|
matrix3<T> rotate_y(T angle)
|
|
{
|
|
const T c = std::cos(angle);
|
|
const T s = std::sin(angle);
|
|
|
|
return matrix3<T>
|
|
{
|
|
c, T(0), -s,
|
|
T(0), T(1), T(0),
|
|
s, T(0), c
|
|
};
|
|
}
|
|
|
|
template <class T>
|
|
matrix3<T> rotate_z(T angle)
|
|
{
|
|
const T c = std::cos(angle);
|
|
const T s = std::sin(angle);
|
|
|
|
return matrix3<T>
|
|
{
|
|
c, s, T(0),
|
|
-s, c, T(0),
|
|
T(0), T(0), T(1)
|
|
};
|
|
}
|
|
|
|
template <class T>
|
|
constexpr matrix<T, 4, 4> scale(const matrix<T, 4, 4>& m, const vector<T, 3>& v)
|
|
{
|
|
return mul(m, matrix<T, 4, 4>
|
|
{{
|
|
{v[0], T(0), T(0), T(0)},
|
|
{T(0), v[1], T(0), T(0)},
|
|
{T(0), T(0), v[2], T(0)},
|
|
{T(0), T(0), T(0), T(1)}
|
|
}});
|
|
}
|
|
|
|
/// @private
|
|
template <class T, std::size_t N, std::size_t M, std::size_t... I>
|
|
constexpr inline matrix<T, N, M> sub(const matrix<T, N, M>& a, const matrix<T, N, M>& b, std::index_sequence<I...>) noexcept
|
|
{
|
|
return {(a[I] - b[I]) ...};
|
|
}
|
|
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr matrix<T, N, M> sub(const matrix<T, N, M>& a, const matrix<T, N, M>& b) noexcept
|
|
{
|
|
return sub(a, b, std::make_index_sequence<N>{});
|
|
}
|
|
|
|
/// @private
|
|
template <class T, std::size_t N, std::size_t M, std::size_t... I>
|
|
constexpr inline matrix<T, N, M> sub(const matrix<T, N, M>& a, T b, std::index_sequence<I...>) noexcept
|
|
{
|
|
return {(a[I] - b) ...};
|
|
}
|
|
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr matrix<T, N, M> sub(const matrix<T, N, M>& a, T b) noexcept
|
|
{
|
|
return sub(a, b, std::make_index_sequence<N>{});
|
|
}
|
|
|
|
/// @private
|
|
template <class T, std::size_t N, std::size_t M, std::size_t... I>
|
|
constexpr inline matrix<T, N, M> sub(T a, const matrix<T, N, M>& b, std::index_sequence<I...>) noexcept
|
|
{
|
|
return {(a - b[I]) ...};
|
|
}
|
|
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr matrix<T, N, M> sub(T a, const matrix<T, N, M>& b) noexcept
|
|
{
|
|
return sub(a, b, std::make_index_sequence<N>{});
|
|
}
|
|
|
|
/// @private
|
|
template <class T, std::size_t N, std::size_t... I>
|
|
constexpr inline T trace(const matrix<T, N, N>& m, std::index_sequence<I...>) noexcept
|
|
{
|
|
return ((m[I][I]) + ...);
|
|
}
|
|
|
|
template <class T, std::size_t N>
|
|
constexpr T trace(const matrix<T, N, N>& m) noexcept
|
|
{
|
|
return trace(m, std::make_index_sequence<N>{});
|
|
}
|
|
|
|
template <class T>
|
|
constexpr matrix<T, 4, 4> translate(const matrix<T, 4, 4>& m, const vector<T, 3>& v)
|
|
{
|
|
return mul(m, matrix<T, 4, 4>
|
|
{{
|
|
{T(1), T(0), T(0), T(0)},
|
|
{T(0), T(1), T(0), T(0)},
|
|
{T(0), T(0), T(1), T(0)},
|
|
{v[0], v[1], v[2], T(1)}
|
|
}});
|
|
}
|
|
|
|
/// @private
|
|
template <typename T, std::size_t N, std::size_t M, std::size_t... I>
|
|
constexpr inline typename matrix<T, M, N>::column_vector_type transpose_column(const matrix<T, N, M>& m, std::size_t i, std::index_sequence<I...>) noexcept
|
|
{
|
|
return {m[I][i] ...};
|
|
}
|
|
|
|
/// @private
|
|
template <typename T, std::size_t N, std::size_t M, std::size_t... I>
|
|
constexpr inline matrix<T, M, N> transpose(const matrix<T, N, M>& m, std::index_sequence<I...>) noexcept
|
|
{
|
|
return {transpose_column(m, I, std::make_index_sequence<N>{}) ...};
|
|
}
|
|
|
|
template <typename T, std::size_t N, std::size_t M>
|
|
constexpr matrix<T, M, N> transpose(const matrix<T, N, M>& m) noexcept
|
|
{
|
|
return transpose(m, std::make_index_sequence<M>{});
|
|
}
|
|
|
|
namespace operators {
|
|
|
|
/// @copydoc add(const matrix<T, N, M>&, const matrix<T, N, M>&)
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr inline matrix<T, N, M> operator+(const matrix<T, N, M>& a, const matrix<T, N, M>& b) noexcept
|
|
{
|
|
return add(a, b);
|
|
}
|
|
|
|
/// @copydoc add(const matrix<T, N, M>&, T)
|
|
/// @{
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr inline matrix<T, N, M> operator+(const matrix<T, N, M>& a, T b) noexcept
|
|
{
|
|
return add(a, b);
|
|
}
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr inline matrix<T, N, M> operator+(T a, const matrix<T, N, M>& b) noexcept
|
|
{
|
|
return add(b, a);
|
|
}
|
|
/// @}
|
|
|
|
/// @copydoc div(const matrix<T, N, M>&, const matrix<T, N, M>&)
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr inline matrix<T, N, M> operator/(const matrix<T, N, M>& a, const matrix<T, N, M>& b) noexcept
|
|
{
|
|
return div(a, b);
|
|
}
|
|
|
|
/// @copydoc div(const matrix<T, N, M>&, T)
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr inline matrix<T, N, M> operator/(const matrix<T, N, M>& a, T b) noexcept
|
|
{
|
|
return div(a, b);
|
|
}
|
|
|
|
/// @copydoc div(T, const matrix<T, N, M>&)
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr inline matrix<T, N, M> operator/(T a, const matrix<T, N, M>& b) noexcept
|
|
{
|
|
return div(a, b);
|
|
}
|
|
|
|
/// @copydoc mul(const matrix<T, N, M>&, const matrix<T, P, N>&)
|
|
template <typename T, std::size_t N, std::size_t M, std::size_t P>
|
|
constexpr inline matrix<T, P, M> operator*(const matrix<T, N, M>& a, const matrix<T, P, N>& b) noexcept
|
|
{
|
|
return mul(a, b);
|
|
}
|
|
|
|
/// @copydoc mul(const matrix<T, N, M>&, T)
|
|
/// @{
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr inline matrix<T, N, M> operator*(const matrix<T, N, M>& a, T b) noexcept
|
|
{
|
|
return mul(a, b);
|
|
}
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr inline matrix<T, N, M> operator*(T a, const matrix<T, N, M>& b) noexcept
|
|
{
|
|
return mul(b, a);
|
|
}
|
|
/// @}
|
|
|
|
/// @copydoc mul(const matrix<T, N, M>&, const typename matrix<T, N, M>::row_vector_type&)
|
|
template <typename T, std::size_t N, std::size_t M>
|
|
constexpr inline typename matrix<T, N, M>::column_vector_type operator*(const matrix<T, N, M>& a, const typename matrix<T, N, M>::row_vector_type& b) noexcept
|
|
{
|
|
return mul(a, b);
|
|
}
|
|
|
|
/// @copydoc mul(const typename matrix<T, N, M>::column_vector_type&, const matrix<T, N, M>&)
|
|
template <typename T, std::size_t N, std::size_t M>
|
|
constexpr inline typename matrix<T, N, M>::row_vector_type operator*(const typename matrix<T, N, M>::column_vector_type& a, const matrix<T, N, M>& b) noexcept
|
|
{
|
|
return mul(a, b);
|
|
}
|
|
|
|
/// @copydoc sub(const matrix<T, N, M>&, const matrix<T, N, M>&)
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr inline matrix<T, N, M> operator-(const matrix<T, N, M>& a, const matrix<T, N, M>& b) noexcept
|
|
{
|
|
return sub(a, b);
|
|
}
|
|
|
|
/// @copydoc sub(const matrix<T, N, M>&, T)
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr inline matrix<T, N, M> operator-(const matrix<T, N, M>& a, T b) noexcept
|
|
{
|
|
return sub(a, b);
|
|
}
|
|
|
|
/// @copydoc sub(T, const matrix<T, N, M>&)
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr inline matrix<T, N, M> operator-(T a, const matrix<T, N, M>& b) noexcept
|
|
{
|
|
return sub(a, b);
|
|
}
|
|
|
|
/**
|
|
* Adds two values and stores the result in the first value.
|
|
*
|
|
* @param a First value.
|
|
* @param b Second value.
|
|
*
|
|
* @return Reference to the first value.
|
|
*/
|
|
/// @{
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr inline matrix<T, N, M>& operator+=(matrix<T, N, M>& a, const matrix<T, N, M>& b) noexcept
|
|
{
|
|
return (a = a + b);
|
|
}
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr inline matrix<T, N, M>& operator+=(matrix<T, N, M>& a, T b) noexcept
|
|
{
|
|
return (a = a + b);
|
|
}
|
|
/// @}
|
|
|
|
/**
|
|
* Subtracts the first value by the second value and stores the result in the first value.
|
|
*
|
|
* @param a First value.
|
|
* @param b Second value.
|
|
*
|
|
* @return Reference to the first value.
|
|
*/
|
|
/// @{
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr inline matrix<T, N, M>& operator-=(matrix<T, N, M>& a, const matrix<T, N, M>& b) noexcept
|
|
{
|
|
return (a = a - b);
|
|
}
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr inline matrix<T, N, M>& operator-=(matrix<T, N, M>& a, T b) noexcept
|
|
{
|
|
return (a = a - b);
|
|
}
|
|
/// @}
|
|
|
|
/**
|
|
* Multiplies two values and stores the result in the first value.
|
|
*
|
|
* @param a First value.
|
|
* @param b Second value.
|
|
*
|
|
* @return Reference to the first value.
|
|
*/
|
|
/// @{
|
|
template <class T, std::size_t N>
|
|
constexpr inline matrix<T, N, N>& operator*=(matrix<T, N, N>& a, const matrix<T, N, N>& b) noexcept
|
|
{
|
|
return (a = a * b);
|
|
}
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr inline matrix<T, N, M>& operator*=(matrix<T, N, M>& a, T b) noexcept
|
|
{
|
|
return (a = a * b);
|
|
}
|
|
/// @}
|
|
|
|
/**
|
|
* Divides the first value by the second value and stores the result in the first value.
|
|
*
|
|
* @param a First value.
|
|
* @param b Second value.
|
|
*
|
|
* @return Reference to the first value.
|
|
*/
|
|
/// @{
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr inline matrix<T, N, M>& operator/=(matrix<T, N, M>& a, const matrix<T, N, M>& b) noexcept
|
|
{
|
|
return (a = a / b);
|
|
}
|
|
template <class T, std::size_t N, std::size_t M>
|
|
constexpr inline matrix<T, N, M>& operator/=(matrix<T, N, M>& a, T b) noexcept
|
|
{
|
|
return (a = a / b);
|
|
}
|
|
/// @}
|
|
|
|
/**
|
|
* Writes the elements of a matrix to an output stream, with each element delimeted by a space.
|
|
*
|
|
* @param os Output stream.
|
|
* @param m Matrix.
|
|
*
|
|
* @return Output stream.
|
|
*/
|
|
template <class T, std::size_t N, std::size_t M>
|
|
std::ostream& operator<<(std::ostream& os, const matrix<T, N, M>& m)
|
|
{
|
|
for (std::size_t i = 0; i < m.size(); ++i)
|
|
{
|
|
if (i)
|
|
os << ' ';
|
|
os << m.element(i);
|
|
}
|
|
|
|
return os;
|
|
}
|
|
|
|
/**
|
|
* Reads the elements of a matrix from an input stream, with each element delimeted by a space.
|
|
*
|
|
* @param is Input stream.
|
|
* @param m Matrix.
|
|
*
|
|
* @return Input stream.
|
|
*/
|
|
template <class T, std::size_t N, std::size_t M>
|
|
std::istream& operator>>(std::istream& is, matrix<T, N, M>& m)
|
|
{
|
|
for (std::size_t i = 0; i < m.size(); ++i)
|
|
is >> m.element(i);
|
|
|
|
return is;
|
|
}
|
|
|
|
} // namespace operators
|
|
|
|
} // namespace math
|
|
|
|
using namespace math::operators;
|
|
|
|
#endif // ANTKEEPER_MATH_MATRIX_HPP
|