💿🐜 Antkeeper source code https://antkeeper.com
You can not select more than 25 topics Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.

848 lines
24 KiB

/*
* Copyright (C) 2020 Christopher J. Howard
*
* This file is part of Antkeeper source code.
*
* Antkeeper source code is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* Antkeeper source code is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with Antkeeper source code. If not, see <http://www.gnu.org/licenses/>.
*/
#ifndef ANTKEEPER_MATH_MATRIX_FUNCTIONS_HPP
#define ANTKEEPER_MATH_MATRIX_FUNCTIONS_HPP
#include "math/matrix-type.hpp"
#include "math/vector-type.hpp"
#include "math/vector-functions.hpp"
#include <type_traits>
namespace math {
/// @addtogroup matrix
/// @{
/**
* Adds two matrices.
*
* @param x First matrix.
* @param y Second matrix.
* @return Sum of the two matrices.
*/
template <class T>
matrix<T, 2, 2> add(const matrix<T, 2, 2>& x, const matrix<T, 2, 2>& y);
/// @copydoc add(const matrix<T, 2, 2>&, const matrix<T, 2, 2>&)
template <class T>
matrix<T, 3, 3> add(const matrix<T, 3, 3>& x, const matrix<T, 3, 3>& y);
/// @copydoc add(const matrix<T, 2, 2>&, const matrix<T, 2, 2>&)
template <class T>
matrix<T, 4, 4> add(const matrix<T, 4, 4>& x, const matrix<T, 4, 4>& y);
/**
* Reinterprets data as an `NxM` matrix of type `T`.
*
* @tparam N Number of columns.
* @tparam M Number of rows.
* @tparam T Element type.
* @param data Data to reinterpret.
*/
template <std::size_t N, std::size_t M, typename T>
matrix<T, N, M>& as_matrix(T& data);
/**
* Calculates the determinant of a matrix.
*
* @param m Matrix of which to take the determinant.
*/
template <class T>
T determinant(const matrix<T, 2, 2>& m);
/// @copydoc determinant(const matrix<T, 2, 2>&)
template <class T>
T determinant(const matrix<T, 3, 3>& m);
/// @copydoc determinant(const matrix<T, 2, 2>&)
template <class T>
T determinant(const matrix<T, 4, 4>& m);
/**
* Calculates the inverse of a matrix.
*
* @param m Matrix of which to take the inverse.
*/
template <class T>
matrix<T, 2, 2> inverse(const matrix<T, 2, 2>& m);
/// @copydoc inverse(const matrix<T, 2, 2>&)
template <class T>
matrix<T, 3, 3> inverse(const matrix<T, 3, 3>& m);
/// @copydoc inverse(const matrix<T, 2, 2>&)
template <class T>
matrix<T, 4, 4> inverse(const matrix<T, 4, 4>& m);
/**
* Performs a component-wise multiplication of two matrices.
*
* @param x First matrix multiplicand.
* @param y Second matrix multiplicand.
*/
template <class T>
matrix<T, 2, 2> componentwise_mul(const matrix<T, 2, 2>& x, const matrix<T, 2, 2>& y);
/// @copydoc componentwise_mul(const matrix<T, 2, 2>&, const matrix<T, 2, 2>&)
template <class T>
matrix<T, 3, 3> componentwise_mul(const matrix<T, 3, 3>& x, const matrix<T, 3, 3>& y);
/// @copydoc componentwise_mul(const matrix<T, 2, 2>&, const matrix<T, 2, 2>&)
template <class T>
matrix<T, 4, 4> componentwise_mul(const matrix<T, 4, 4>& x, const matrix<T, 4, 4>& y);
/**
* Creates a viewing transformation matrix.
*
* @param position Position of the view point.
* @param target Position of the target.
* @param up Normalized direction of the up vector.
* @return Viewing transformation matrix.
*/
template <class T>
matrix<T, 4, 4> look_at(const vector<T, 3>& position, const vector<T, 3>& target, vector<T, 3> up);
/**
* Multiplies two matrices.
*
* @param x First matrix.
* @param y Second matrix.
* @return Product of the two matrices.
*/
template <class T>
matrix<T, 2, 2> mul(const matrix<T, 2, 2>& x, const matrix<T, 2, 2>& y);
/// @copydoc mul(const matrix<T, 2, 2>&, const matrix<T, 2, 2>&);
template <class T>
matrix<T, 3, 3> mul(const matrix<T, 3, 3>& x, const matrix<T, 3, 3>& y);
/// @copydoc mul(const matrix<T, 2, 2>&, const matrix<T, 2, 2>&);
template <class T>
matrix<T, 4, 4> mul(const matrix<T, 4, 4>& x, const matrix<T, 4, 4>& y);
/**
* Multiplies a matrix by a scalar.
*
* @param m Matrix.
* @param s Scalar.
* @return Product of the matrix and the scalar..
*/
template <class T, std::size_t N, std::size_t M>
matrix<T, N, M> mul(const matrix<T, N, M>& m, T s);
/**
* Transforms a vector by a matrix.
*
* @param m Matrix.
* @param v Vector.
* @return Transformed vector.
*/
template <class T>
vector<T, 2> mul(const matrix<T, 2, 2>& m, const vector<T, 2>& v);
/// @copydoc mul(const matrix<T, 2, 2>&, const vector<T, 2>&)
template <class T>
vector<T, 3> mul(const matrix<T, 3, 3>& m, const vector<T, 3>& v);
/// @copydoc mul(const matrix<T, 2, 2>&, const vector<T, 2>&)
template <class T>
vector<T, 4> mul(const matrix<T, 4, 4>& m, const vector<T, 4>& v);
/**
* Creates an orthographic projection matrix which will transform the near and far clipping planes to `[-1, 1]`, respectively.
*
* @param left Signed distance to the left clipping plane.
* @param right Signed distance to the right clipping plane.
* @param bottom Signed distance to the bottom clipping plane.
* @param top Signed distance to the top clipping plane.
* @param z_near Signed distance to the near clipping plane.
* @param z_far Signed distance to the far clipping plane.
* @return Orthographic projection matrix.
*/
template <class T>
matrix<T, 4, 4> ortho(T left, T right, T bottom, T top, T z_near, T z_far);
/**
* Creates an orthographic projection matrix which will transform the near and far clipping planes to `[0, 1]`, respectively.
*
* @param left Signed distance to the left clipping plane.
* @param right Signed distance to the right clipping plane.
* @param bottom Signed distance to the bottom clipping plane.
* @param top Signed distance to the top clipping plane.
* @param z_near Signed distance to the near clipping plane.
* @param z_far Signed distance to the far clipping plane.
* @return Orthographic projection matrix.
*/
template <class T>
matrix<T, 4, 4> ortho_half_z(T left, T right, T bottom, T top, T z_near, T z_far);
/**
* Calculates the outer product of a pair of vectors.
*
* @param c Parameter to be treated as a column vector.
* @param r Parameter to be treated as a row vector.
*/
template <class T>
matrix<T, 2, 2> outer_product(const vector<T, 2>& c, const vector<T, 2>& r);
/// @copydoc outer_product(const vector<T, 2>&, const vector<T, 2>&)
template <class T>
matrix<T, 3, 3> outer_product(const vector<T, 3>& c, const vector<T, 3>& r);
/// @copydoc outer_product(const vector<T, 2>&, const vector<T, 2>&)
template <class T>
matrix<T, 4, 4> outer_product(const vector<T, 4>& c, const vector<T, 4> r);
/**
* Creates a perspective projection matrix which will transform the near and far clipping planes to `[-1, 1]`, respectively.
*
* @param vertical_fov Vertical field of view angle, in radians.
* @param aspect_ratio Aspect ratio which determines the horizontal field of view.
* @param z_near Distance to the near clipping plane.
* @param z_far Distance to the far clipping plane.
* @return Perspective projection matrix.
*/
template <class T>
matrix<T, 4, 4> perspective(T vertical_fov, T aspect_ratio, T z_near, T z_far);
/**
* Creates a perspective projection matrix which will transform the near and far clipping planes to `[0, 1]`, respectively.
*
* @param vertical_fov Vertical field of view angle, in radians.
* @param aspect_ratio Aspect ratio which determines the horizontal field of view.
* @param z_near Distance to the near clipping plane.
* @param z_far Distance to the far clipping plane.
* @return Perspective projection matrix.
*/
template <class T>
matrix<T, 4, 4> perspective_half_z(T vertical_fov, T aspect_ratio, T z_near, T z_far);
/**
* Resizes a matrix. Any new elements will be set to `1` if in the diagonal, and `0` otherwise.
*
* @param m Matrix to resize.
* @return Resized matrix.
*/
template <std::size_t N1, std::size_t M1, class T, std::size_t N0, std::size_t M0>
matrix<T, N1, M1> resize(const matrix<T, N0, M0>& m);
/**
* Rotates a matrix.
*
* @param m Matrix to rotate.
* @param angle Angle of rotation (in radians).
* @param axis Axis of rotation
* @return Rotated matrix.
*/
template <class T>
matrix<T, 4, 4> rotate(const matrix<T, 4, 4>& m, T angle, const vector<T, 3>& axis);
/**
* Scales a matrix.
*
* @param m Matrix to scale.
* @param v Scale vector.
* @return Scaled matrix.
*/
template <class T>
matrix<T, 4, 4> scale(const matrix<T, 4, 4>& m, const vector<T, 3>& v);
/**
* Subtracts a matrix from another matrix.
*
* @param x First matrix.
* @param y Second matrix.
* @return Difference between the two matrices.
*/
template <class T>
matrix<T, 2, 2> sub(const matrix<T, 2, 2>& x, const matrix<T, 2, 2>& y);
/// @copydoc sub(const matrix<T, 2, 2>&, const matrix<T, 2, 2>&)
template <class T>
matrix<T, 3, 3> sub(const matrix<T, 3, 3>& x, const matrix<T, 3, 3>& y);
/// @copydoc sub(const matrix<T, 2, 2>&, const matrix<T, 2, 2>&)
template <class T>
matrix<T, 4, 4> sub(const matrix<T, 4, 4>& x, const matrix<T, 4, 4>& y);
/**
* Translates a matrix.
*
* @param m Matrix to translate.
* @param v Translation vector.
* @return Translated matrix.
*/
template <class T>
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 of which to take the transpose.
*/
template <class T>
matrix<T, 2, 2> transpose(const matrix<T, 2, 2>& m);
/// @copydoc transpose(const matrix<T, 2, 2>&)
template <class T>
matrix<T, 3, 3> transpose(const matrix<T, 3, 3>& m);
/// @copydoc transpose(const matrix<T, 2, 2>&)
template <class T>
matrix<T, 4, 4> transpose(const matrix<T, 4, 4>& m);
template <class T>
matrix<T, 2, 2> add(const matrix<T, 2, 2>& x, const matrix<T, 2, 2>& y)
{
return
{{
x[0] + y[0],
x[1] + y[1]
}};
}
template <class T>
matrix<T, 3, 3> add(const matrix<T, 3, 3>& x, const matrix<T, 3, 3>& y)
{
return
{{
x[0] + y[0],
x[1] + y[1],
x[2] + y[2]
}};
}
template <class T>
matrix<T, 4, 4> add(const matrix<T, 4, 4>& x, const matrix<T, 4, 4>& y)
{
return
{{
x[0] + y[0],
x[1] + y[1],
x[2] + y[2],
x[3] + y[3]
}};
}
template <std::size_t N, std::size_t M, typename T>
inline matrix<T, N, M>& as_matrix(T& data)
{
static_assert(std::is_pod<matrix<T, N, M>>::value);
return reinterpret_cast<matrix<T, N, M>&>(data);
}
template <class T>
T determinant(const matrix<T, 2, 2>& m)
{
return m[0][0] * m[1][1] - m[0][1] * m[1][0];
}
template <class T>
T determinant(const matrix<T, 3, 3>& m)
{
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>
T determinant(const matrix<T, 4, 4>& m)
{
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>
matrix<T, 2, 2> inverse(const matrix<T, 2, 2>& m)
{
static_assert(std::is_floating_point<T>::value);
const T rd(T(1) / determinant(m));
return
{{
{ m[1][1] * rd, -m[0][1] * rd},
{-m[1][0] * rd, m[0][0] * rd}
}};
}
template <class T>
matrix<T, 3, 3> inverse(const matrix<T, 3, 3>& m)
{
static_assert(std::is_floating_point<T>::value);
const T rd(T(1) / determinant(m));
return
{{
{
(m[1][1] * m[2][2] - m[1][2] * m[2][1]) * rd,
(m[0][2] * m[2][1] - m[0][1] * m[2][2]) * rd,
(m[0][1] * m[1][2] - m[0][2] * m[1][1]) * rd
},
{
(m[1][2] * m[2][0] - m[1][0] * m[2][2]) * rd,
(m[0][0] * m[2][2] - m[0][2] * m[2][0]) * rd,
(m[0][2] * m[1][0] - m[0][0] * m[1][2]) * rd
},
{
(m[1][0] * m[2][1] - m[1][1] * m[2][0]) * rd,
(m[0][1] * m[2][0] - m[0][0] * m[2][1]) * rd,
(m[0][0] * m[1][1] - m[0][1] * m[1][0]) * rd
}
}};
}
template <class T>
matrix<T, 4, 4> inverse(const matrix<T, 4, 4>& m)
{
static_assert(std::is_floating_point<T>::value);
const T rd(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]) * rd,
(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]) * rd,
(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]) * rd,
(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]) * rd
},
{
(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]) * rd,
(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]) * rd,
(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]) * rd,
(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]) * rd
},
{
(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]) * rd,
(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]) * rd,
(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]) * rd,
(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]) * rd
},
{
(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]) * rd,
(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]) * rd,
(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]) * rd,
(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]) * rd
}
}};
}
template <class T>
matrix<T, 2, 2> componentwise_mul(const matrix<T, 2, 2>& x, const matrix<T, 2, 2>& y)
{
return
{{
{x[0][0] * y[0][0], x[0][1] * y[0][1]},
{x[1][0] * y[1][0], x[1][1] * y[1][1]}
}};
}
template <class T>
matrix<T, 3, 3> componentwise_mul(const matrix<T, 3, 3>& x, const matrix<T, 3, 3>& y)
{
return
{{
{x[0][0] * y[0][0], x[0][1] * y[0][1], x[0][2] * y[0][2]},
{x[1][0] * y[1][0], x[1][1] * y[1][1], x[1][2] * y[1][2]},
{x[2][0] * y[2][0], x[2][1] * y[2][1], x[2][2] * y[2][2]}
}};
}
template <class T>
matrix<T, 4, 4> componentwise_mul(const matrix<T, 4, 4>& x, const matrix<T, 4, 4>& y)
{
return
{{
{x[0][0] * y[0][0], x[0][1] * y[0][1], x[0][2] * y[0][2], x[0][3] * y[0][3]},
{x[1][0] * y[1][0], x[1][1] * y[1][1], x[1][2] * y[1][2], x[1][3] * y[1][3]},
{x[2][0] * y[2][0], x[2][1] * y[2][1], x[2][2] * y[2][2], x[2][3] * y[2][3]},
{x[3][0] * y[3][0], x[3][1] * y[3][1], x[3][2] * y[3][2], x[3][3] * y[3][3]}
}};
}
template <class T>
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 <class T>
matrix<T, 2, 2> mul(const matrix<T, 2, 2>& x, const matrix<T, 2, 2>& y)
{
return
{{
x[0] * y[0][0] + x[1] * y[0][1],
x[0] * y[1][0] + x[1] * y[1][1]
}};
}
template <class T>
matrix<T, 3, 3> mul(const matrix<T, 3, 3>& x, const matrix<T, 3, 3>& y)
{
return
{{
x[0] * y[0][0] + x[1] * y[0][1] + x[2] * y[0][2],
x[0] * y[1][0] + x[1] * y[1][1] + x[2] * y[1][2],
x[0] * y[2][0] + x[1] * y[2][1] + x[2] * y[2][2]
}};
}
template <class T>
matrix<T, 4, 4> mul(const matrix<T, 4, 4>& x, const matrix<T, 4, 4>& y)
{
return
{{
x[0] * y[0][0] + x[1] * y[0][1] + x[2] * y[0][2] + x[3] * y[0][3],
x[0] * y[1][0] + x[1] * y[1][1] + x[2] * y[1][2] + x[3] * y[1][3],
x[0] * y[2][0] + x[1] * y[2][1] + x[2] * y[2][2] + x[3] * y[2][3],
x[0] * y[3][0] + x[1] * y[3][1] + x[2] * y[3][2] + x[3] * y[3][3]
}};
}
/// @private
template <class T, std::size_t N, std::size_t M, std::size_t... I>
inline matrix<T, N, M> mul(const matrix<T, N, M>& m, T s, std::index_sequence<I...>)
{
return {{(m[I] * s)...}};
}
template <class T, std::size_t N, std::size_t M>
inline matrix<T, N, M> mul(const matrix<T, N, M>& m, T s)
{
return mul(m, s, std::make_index_sequence<N>{});
}
template <class T>
vector<T, 2> mul(const matrix<T, 2, 2>& m, const vector<T, 2>& v)
{
return
{
m[0][0] * v[0] + m[1][0] * v[1],
m[0][1] * v[0] + m[1][1] * v[1]
};
}
template <class T>
vector<T, 3> mul(const matrix<T, 3, 3>& m, const vector<T, 3>& v)
{
return
{
m[0][0] * v[0] + m[1][0] * v[1] + m[2][0] * v[2],
m[0][1] * v[0] + m[1][1] * v[1] + m[2][1] * v[2],
m[0][2] * v[0] + m[1][2] * v[1] + m[2][2] * v[2]
};
}
template <class T>
vector<T, 4> mul(const matrix<T, 4, 4>& m, const vector<T, 4>& v)
{
return
{
m[0][0] * v[0] + m[1][0] * v[1] + m[2][0] * v[2] + m[3][0] * v[3],
m[0][1] * v[0] + m[1][1] * v[1] + m[2][1] * v[2] + m[3][1] * v[3],
m[0][2] * v[0] + m[1][2] * v[1] + m[2][2] * v[2] + m[3][2] * v[3],
m[0][3] * v[0] + m[1][3] * v[1] + m[2][3] * v[2] + m[3][3] * v[3]
};
}
template <class T>
matrix<T, 4, 4> ortho(T left, T right, T bottom, T top, T z_near, T z_far)
{
return
{{
{T(2) / (right - left), T(0), T(0), T(0)},
{T(0), T(2) / (top - bottom), T(0), T(0)},
{T(0), T(0), T(-2) / (z_far - z_near), T(0)},
{-((right + left) / (right - left)), -((top + bottom) / (top - bottom)), -((z_far + z_near) / (z_far - z_near)), T(1)}
}};
}
template <class T>
matrix<T, 4, 4> ortho_half_z(T left, T right, T bottom, T top, T z_near, T z_far)
{
return
{{
{T(2) / (right - left), T(0), T(0), T(0)},
{T(0), T(2) / (top - bottom), T(0), T(0)},
{T(0), T(0), T(-1) / (z_far - z_near), T(0)},
{-((right + left) / (right - left)), -((top + bottom) / (top - bottom)), -z_near / (z_far - z_near), T(1)}
}};
}
template <class T>
matrix<T, 2, 2> outer_product(const vector<T, 2>& c, const vector<T, 2>& r)
{
return
{{
{c[0] * r[0], c[1] * r[0]},
{c[0] * r[1], c[1] * r[1]}
}};
}
template <class T>
matrix<T, 3, 3> outer_product(const vector<T, 3>& c, const vector<T, 3>& r)
{
return
{{
{c[0] * r[0], c[1] * r[0], c[2] * r[0]},
{c[0] * r[1], c[1] * r[1], c[2] * r[1]},
{c[0] * r[2], c[1] * r[2], c[2] * r[2]}
}};
}
template <class T>
matrix<T, 4, 4> outer_product(const vector<T, 4>& c, const vector<T, 4> r)
{
return
{{
{c[0] * r[0], c[1] * r[0], c[2] * r[0], c[3] * r[0]},
{c[0] * r[1], c[1] * r[1], c[2] * r[1], c[3] * r[1]},
{c[0] * r[2], c[1] * r[2], c[2] * r[2], c[3] * r[2]},
{c[0] * r[3], c[1] * r[3], c[2] * r[3], c[3] * r[3]}
}};
}
template <class T>
matrix<T, 4, 4> perspective(T vertical_fov, T aspect_ratio, T z_near, T z_far)
{
T half_fov = vertical_fov * T(0.5);
T f = std::cos(half_fov) / std::sin(half_fov);
return
{{
{f / aspect_ratio, T(0), T(0), T(0)},
{T(0), f, T(0), T(0)},
{T(0), T(0), (z_far + z_near) / (z_near - z_far), T(-1)},
{T(0), T(0), (T(2) * z_far * z_near) / (z_near - z_far), T(0)}
}};
}
template <class T>
matrix<T, 4, 4> perspective_half_z(T vertical_fov, T aspect_ratio, T z_near, T z_far)
{
T half_fov = vertical_fov * T(0.5);
T f = std::cos(half_fov) / std::sin(half_fov);
return
{{
{f / aspect_ratio, T(0), T(0), T(0)},
{T(0), f, T(0), T(0)},
{T(0), T(0), z_far / (z_near - z_far), T(-1)},
{T(0), T(0), -(z_far * z_near) / (z_far - z_near), T(0)}
}};
}
template <std::size_t N1, std::size_t M1, class T, std::size_t N0, std::size_t M0>
matrix<T, N1, M1> resize(const matrix<T, N0, M0>& m)
{
matrix<T, N1, M1> resized;
for (std::size_t i = 0; i < N1; ++i)
{
for (std::size_t j = 0; j < M1; ++j)
{
resized[i][j] = (i < N0 && j < M0) ? m[i][j] : ((i == j) ? T(1) : T(0));
}
}
return resized;
}
template <class T>
matrix<T, 4, 4> rotate(const matrix<T, 4, 4>& m, 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, 4, 4> 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[0][3] = T(0);
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[1][3] = T(0);
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
rotation[2][3] = T(0);
rotation[3][0] = T(0);
rotation[3][1] = T(0);
rotation[3][2] = T(0);
rotation[3][3] = T(1);
return mul(m, rotation);
}
template <class T>
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)}
}});
}
template <class T>
matrix<T, 2, 2> sub(const matrix<T, 2, 2>& x, const matrix<T, 2, 2>& y)
{
return
{{
x[0] - y[0],
x[1] - y[1]
}};
}
template <class T>
matrix<T, 3, 3> sub(const matrix<T, 3, 3>& x, const matrix<T, 3, 3>& y)
{
return
{{
x[0] - y[0],
x[1] - y[1],
x[2] - y[2]
}};
}
template <class T>
matrix<T, 4, 4> sub(const matrix<T, 4, 4>& x, const matrix<T, 4, 4>& y)
{
return
{{
x[0] - y[0],
x[1] - y[1],
x[2] - y[2],
x[3] - y[3]
}};
}
template <class T>
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)}
}});
}
template <class T>
matrix<T, 2, 2> transpose(const matrix<T, 2, 2>& m)
{
return
{{
{
m[0][0], m[1][0]
},
{
m[0][1], m[1][1]
}
}};
}
template <class T>
matrix<T, 3, 3> transpose(const matrix<T, 3, 3>& m)
{
return
{{
{
m[0][0], m[1][0], m[2][0]
},
{
m[0][1], m[1][1], m[2][1]
},
{
m[0][2], m[1][2], m[2][2]
}
}};
}
template <class T>
matrix<T, 4, 4> transpose(const matrix<T, 4, 4>& m)
{
return
{{
{
m[0][0], m[1][0], m[2][0], m[3][0]
},
{
m[0][1], m[1][1], m[2][1], m[3][1]
},
{
m[0][2], m[1][2], m[2][2], m[3][2]
},
{
m[0][3], m[1][3], m[2][3], m[3][3]
}
}};
}
/// @}
} // namespace math
#endif // ANTKEEPER_MATH_MATRIX_FUNCTIONS_HPP