mal-math
C++20 mathematics library.
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mat_math.hpp
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1#pragma once
2#include "mat.hpp"
16namespace mal_math
17{
26 template <AnyMat U>
27 constexpr std::istream &operator>>(std::istream &is, U &matrix);
28
37 template <AnyMat U>
38 constexpr std::ostream &operator<<(std::ostream &os, U const &matrix);
39
49 template <AnyMat U, AnyMat V>
50 [[nodiscard]] constexpr auto operator*(U const &lhs, V const &rhs) requires (U::size.x == V::size.y);
51
61 template <AnyVec V, AnyMat M>
62 [[nodiscard]] constexpr auto operator*(V const &left, M const &right) requires (V::size == M::size.y);
63
73 template <AnyMat M, AnyVec V>
74 [[nodiscard]] constexpr auto operator*(M const &left, V const &right) requires (M::size.x == V::size);
75
85 template <AnyMat T, Primitive U>
86 [[nodiscard]] constexpr mat<T::size.x, T::size.y, std::remove_const_t<typename T::type>> operator*(T const &left, U const right);
87
97 template <AnyMat T, Primitive U>
98 [[nodiscard]] constexpr mat<T::size.x, T::size.y, std::remove_const_t<typename T::type>> operator*(U const left, T const &right);
99
109 template <AnyMat T, Primitive U>
110 [[nodiscard]] constexpr mat<T::size.x, T::size.y, std::remove_const_t<typename T::type>> operator-(T const &left, U const right);
111
121 template <AnyMat T, Primitive U>
122 [[nodiscard]] constexpr mat<T::size.x, T::size.y, std::remove_const_t<typename T::type>> operator+(U const left, T const &right);
123
133 template <AnyMat T, AnyMat U>
134 [[nodiscard]] constexpr mat<T::size.x, T::size.y, std::remove_const_t<typename T::type>> operator-(T const left, U const &right) requires(T::size.x == U::size.x && T::size.y == U::size.y);
135
145 template <AnyMat T, AnyMat U>
146 [[nodiscard]] constexpr mat<T::size.x, T::size.y, std::remove_const_t<typename T::type>> operator+(T const &left, U const &right) requires(T::size.x == U::size.x && T::size.y == U::size.y);
147
155 template <AnyMat T>
156 constexpr mat<T::size.y, T::size.x, std::remove_const_t<typename T::type>> transpose(T const &matrix);
157
165 template <AnyMat T>
166 constexpr rmat<T::size.y, T::size.x, typename T::type> rtranspose(T &matrix);
167
175 template <AnyMat T>
176 constexpr rmat<T::size.y, T::size.x, const typename T::type> rctranspose(T const &matrix);
177
185 template <AnyMat T>
186 constexpr typename T::type det(T const &matrix) requires(T::size.x == T::size.y);
187
194 template <AnyMat T>
195 constexpr typename T::type determinant(T const &matrix) requires(T::size.x == T::size.y);
196
203 template <AnyMat T>
204 constexpr mat<T::size.x, T::size.y, std::remove_const_t<typename T::type>> adj(T const &m) requires(T::size.x == T::size.y);
208 template <AnyMat T>
209 constexpr mat<T::size.x, T::size.y, std::remove_const_t<typename T::type>> adjugate(T const &m) requires(T::size.x == T::size.y);
210
217 template <AnyMat T>
218 constexpr mat<T::size.x, T::size.y, std::remove_const_t<typename T::type>> inverse(T const &matrix) requires(T::size.x == T::size.y);
219
228 template <AnyMat T, AnyVec V>
229 constexpr mat<4, 4, std::remove_const_t<typename T::type>> translate(T const &matrix, V const &vec) requires(T::size.x == T::size.y && T::size.x == 4 && V::size == 3);
230
241 template <AnyMat T, Primitive U, AnyVec V>
242 constexpr mat<4, 4, std::remove_const_t<typename T::type>> rotate(T const &matrix, U angle, V const &axis) requires(T::size.x == T::size.y && T::size.x == 4 && V::size == 3);
243
252 template <AnyMat T, AnyVec V>
253 constexpr mat<4, 4, std::remove_const_t<typename T::type>> scale(T const &matrix, V const &scale) requires(T::size.x == T::size.y && T::size.x == 4 && V::size == 3);
254
263 template <AnyVec Position>
264 constexpr mat<4, 4, std::remove_const_t<typename Position::type>> look_at(Position const &eye, Position const &center, Position const &up) requires(Position::size == 3);
274 template <Primitive T>
275 constexpr mat<4, 4, T> perspective(T fov_y, T aspect_ratio, T z_near, T z_far);
276
288 template <Primitive T>
289 constexpr mat<4, 4, T> ortho(T left, T right, T bottom, T top, T zNear, T zFar);
290
297 template <Primitive T>
298 constexpr void invert_orthonormal(mat<4, 4, T> const &src, mat<4, 4, T> &dst);
299
306 template <Primitive T>
307 constexpr void invert_orthogonal(mat<4, 4, T> const &src, mat<4, 4, T> &dst);
308
315 template <Primitive T>
316 constexpr mat<4, 4, T> invert_orthonormal(mat<4, 4, T> const &src);
317
324 template <Primitive T>
325 constexpr mat<4, 4, T> invert_orthogonal(mat<4, 4, T> const &src);
326} // namespace mal_math
327#include "mat_math.inl"
mat.hpp
Provides matrix definitions tailored for various sizes and primitive types.
mat_math.inl
mal_math
Contains mathematical utility functions and classes.
mal_math::det
constexpr T::type det(T const &matrix)
Calculates the determinant of a square matrix.
Definition mat_math.inl:191
mal_math::invert_orthonormal
constexpr void invert_orthonormal(mat< 4, 4, T > const &src, mat< 4, 4, T > &dst)
Inverts an orthonormal matrix in-place and stores the result in a destination matrix.
Definition mat_math.inl:349
mal_math::perspective
constexpr mat< 4, 4, T > perspective(T fov_y, T aspect_ratio, T z_near, T z_far)
Generates a perspective projection matrix.
Definition mat_math.inl:319
mal_math::rotate
constexpr mat< 4, 4, std::remove_const_t< typename T::type > > rotate(T const &matrix, U angle, V const &axis)
Rotates a matrix by a given angle around a given axis.
Definition mat_math.inl:256
mal_math::rtranspose
constexpr rmat< T::size.y, T::size.x, typename T::type > rtranspose(T &matrix)
Transposes a matrix and returns a reference to it.
Definition mat_math.inl:134
mal_math::translate
constexpr mat< 4, 4, std::remove_const_t< typename T::type > > translate(T const &matrix, V const &vec)
Translates a matrix by a given vector.
Definition mat_math.inl:246
mal_math::invert_orthogonal
constexpr void invert_orthogonal(mat< 4, 4, T > const &src, mat< 4, 4, T > &dst)
Inverts an orthogonal matrix in-place and stores the result in a destination matrix.
Definition mat_math.inl:369
mal_math::operator-
constexpr mat< T::size.x, T::size.y, std::remove_const_t< typename T::type > > operator-(T const &left, U const right)
Subtracts a matrix from a primitive.
Definition mat_math.inl:100
mal_math::angle
constexpr T angle(qua< T > const &quaternion) noexcept
Computes the angle (or magnitude) of a quaternion.
Definition quaternion.inl:238
mal_math::ortho
constexpr mat< 4, 4, T > ortho(T left, T right, T bottom, T top, T zNear, T zFar)
Generates an orthographic projection matrix.
Definition mat_math.inl:336
mal_math::operator*
constexpr auto operator*(U const &lhs, V const &rhs)
Multiplies two matrices.
Definition mat_math.inl:33
mal_math::adj
constexpr mat< T::size.x, T::size.y, std::remove_const_t< typename T::type > > adj(T const &m)
Computes the adjoint (or adjugate) of a square matrix.
Definition mat_math.inl:209
mal_math::determinant
constexpr T::type determinant(T const &matrix)
Calculates the determinant of a square matrix.
Definition mat_math.inl:203
mal_math::operator>>
constexpr std::istream & operator>>(std::istream &is, U &matrix)
Reads a matrix from an input stream.
Definition mat_math.inl:8
mal_math::inverse
constexpr mat< T::size.x, T::size.y, std::remove_const_t< typename T::type > > inverse(T const &matrix)
Calculates the inverse of a square matrix.
Definition mat_math.inl:240
mal_math::operator<<
constexpr std::ostream & operator<<(std::ostream &os, U const &matrix)
Writes a matrix to an output stream.
Definition mat_math.inl:20
mal_math::transpose
constexpr mat< T::size.y, T::size.x, std::remove_const_t< typename T::type > > transpose(T const &matrix)
Transposes a matrix.
Definition mat_math.inl:121
mal_math::scale
constexpr mat< 4, 4, std::remove_const_t< typename T::type > > scale(T const &matrix, V const &scale)
Scales a matrix by a given vector.
Definition mat_math.inl:287
mal_math::operator+
constexpr mat< T::size.x, T::size.y, std::remove_const_t< typename T::type > > operator+(U const left, T const &right)
Adds a matrix to a primitive.
Definition mat_math.inl:105
mal_math::adjugate
constexpr mat< T::size.x, T::size.y, std::remove_const_t< typename T::type > > adjugate(T const &m)
Alias for the adj() function to compute the adjugate of a matrix.
Definition mat_math.inl:234
mal_math::look_at
constexpr mat< 4, 4, std::remove_const_t< typename Position::type > > look_at(Position const &eye, Position const &center, Position const &up)
Generates a look-at matrix for camera positioning.
Definition mat_math.inl:298
mal_math::rctranspose
constexpr rmat< T::size.y, T::size.x, const typename T::type > rctranspose(T const &matrix)
Transposes a constant matrix and returns a constant reference to it.
Definition mat_math.inl:147