libcruft-util/matrix.hpp

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/*
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* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
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* Copyright 2011-2015 Danny Robson <danny@nerdcruft.net>
*/
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#ifndef __UTIL_MATRIX_HPP
#define __UTIL_MATRIX_HPP
#include "point.hpp"
#include "range.hpp"
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#include <ostream>
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#include <cstdlib>
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namespace util {
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template <size_t Rows, size_t Cols, typename T>
struct matrix {
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static constexpr auto rows = Rows;
static constexpr auto cols = Cols;
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T values[Rows][Cols];
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///////////////////////////////////////////////////////////////////////
// index operators return a pointer into the data array so that
// multidimensional array syntax can be used transparently on this
// type.
constexpr T*
operator[] (size_t idx) noexcept
{
return this->values[idx];
}
//---------------------------------------------------------------------
constexpr const T*
operator[] (size_t idx) const noexcept
{
return this->values[idx];
}
//---------------------------------------------------------------------
constexpr T*
data (void) noexcept
{
return begin ();
}
//---------------------------------------------------------------------
constexpr const T*
data (void) const noexcept
{
return begin ();
}
//---------------------------------------------------------------------
constexpr const T*
begin (void) const noexcept
{
return &(*this)[0][0];
}
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//---------------------------------------------------------------------
constexpr const T*
end (void) const noexcept
{
return &(*this)[Rows][0];
}
//---------------------------------------------------------------------
constexpr T*
begin (void) noexcept
{
return &(*this)[0][0];
}
//---------------------------------------------------------------------
constexpr T*
end (void) noexcept
{
return &(*this)[Rows][0];
}
//---------------------------------------------------------------------
constexpr auto
cbegin (void) const noexcept
{
return begin ();
}
//---------------------------------------------------------------------
constexpr auto
cend (void) const noexcept
{
return end ();
}
///////////////////////////////////////////////////////////////////////
T determinant (void) const;
matrix inverse (void) const;
matrix
inverse_affine (void) const
{
// TODO: ensure we have specialisations for typical dimensions
return inverse ();
}
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///////////////////////////////////////////////////////////////////////
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vector<Rows,T> operator* (const vector<Rows,T>&) const;
point<Rows,T> operator* (const point<Rows,T> &) const;
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bool is_affine (void) const;
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template <typename U>
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matrix<Rows,Cols,U>
cast (void) const
{
util::matrix<Rows,Cols,T> out;
std::copy (cbegin (), cend (), std::begin (out));
return out;
}
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// Perspective matrices
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static matrix<4,4,T> ortho (T left, T right, T bottom, T top, T near, T far);
static matrix<4,4,T> ortho2D (T left, T right, T bottom, T top);
static matrix<4,4,T> perspective (T fov, T aspect, range<T> Z);
static matrix<4,4,T> look_at (point<3,T> eye, point<3,T> target, vector<3,T> up);
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// Affine matrices
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static matrix<4,4,T> translation (util::vector<2,T>);
static matrix<4,4,T> translation (util::vector<3,T>);
static matrix<4,4,T> scale (util::vector<3,T>);
static matrix<4,4,T> scale (T);
static matrix<4,4,T> rotation (T angle, util::vector<3,T> about);
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// Constant matrices
static constexpr matrix identity ();
static constexpr matrix zeroes ();
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};
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///////////////////////////////////////////////////////////////////////////
// Convert an affine rotation matrix to euler angles.
//
// Results are undefined if the matrix is not purely a rotation matrix,
// or if the dimension is not 3x3 or 4x4.
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template <size_t Rows, size_t Cols, typename T>
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vector<3,T>
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to_euler (const matrix<Rows, Cols, T>&);
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///////////////////////////////////////////////////////////////////////////
// logical operations
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template <size_t Rows, size_t Cols, typename T>
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constexpr
bool
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operator== (const matrix<Rows,Cols,T>&, const matrix<Rows,Cols,T>&);
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template <size_t Rows, size_t Cols, typename T>
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constexpr
bool
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operator!= (const matrix<Rows,Cols,T>&, const matrix<Rows,Cols,T>&);
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///////////////////////////////////////////////////////////////////////////
// element operations
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template <size_t Rows, size_t Cols, typename T>
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constexpr
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matrix<Rows,Cols,T>
operator+ (const matrix<Rows,Cols,T>&, const matrix<Rows,Cols,T>&);
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template <size_t Rows, size_t Cols, typename T>
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constexpr
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matrix<Rows,Cols,T>
operator- (const matrix<Rows,Cols,T>&, const matrix<Rows,Cols,T>&);
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///////////////////////////////////////////////////////////////////////////
// scalar operations
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template <size_t R, size_t C, typename T> constexpr matrix<R,C,T> operator* (const matrix<R,C,T>&, T);
template <size_t R, size_t C, typename T> constexpr matrix<R,C,T> operator/ (const matrix<R,C,T>&, T);
template <size_t R, size_t C, typename T> constexpr matrix<R,C,T> operator+ (const matrix<R,C,T>&, T);
template <size_t R, size_t C, typename T> constexpr matrix<R,C,T> operator- (const matrix<R,C,T>&, T);
template <size_t R, size_t C, typename T> constexpr matrix<R,C,T> operator* (T, const matrix<R,C,T>&);
template <size_t R, size_t C, typename T> constexpr matrix<R,C,T> operator/ (T, const matrix<R,C,T>&);
template <size_t R, size_t C, typename T> constexpr matrix<R,C,T> operator+ (T, const matrix<R,C,T>&);
template <size_t R, size_t C, typename T> constexpr matrix<R,C,T> operator- (T, const matrix<R,C,T>&);
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template <size_t R, size_t C, typename T> constexpr matrix<R,C,T>& operator*= (matrix<R,C,T>&, T);
template <size_t R, size_t C, typename T> constexpr matrix<R,C,T>& operator/= (matrix<R,C,T>&, T);
template <size_t R, size_t C, typename T> constexpr matrix<R,C,T>& operator+= (matrix<R,C,T>&, T);
template <size_t R, size_t C, typename T> constexpr matrix<R,C,T>& operator-= (matrix<R,C,T>&, T);
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///////////////////////////////////////////////////////////////////////////
// matrix operations
template <
size_t R1, size_t C1,
size_t R2, size_t C2,
typename T
>
constexpr
matrix<R1,C2,T>
operator* (const matrix<R1,C1,T>&, const matrix<R2,C2,T>&);
//-------------------------------------------------------------------------
template <
size_t R1, size_t C1,
size_t R2, size_t C2,
typename T
>
constexpr
matrix<R1,C2,T>&
operator*= (matrix<R1,C1,T> &a, const matrix<R2,C2,T> &b)
{ return a = a * b; };
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///////////////////////////////////////////////////////////////////////////
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template <size_t Rows, size_t Cols, typename T>
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T
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determinant (const matrix<Rows,Cols,T>&);
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template <size_t Rows, size_t Cols, typename T>
matrix<Rows,Cols,T>
inverse (const matrix<Rows,Cols,T>&);
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template <size_t Rows, size_t Cols, typename T>
matrix<Cols,Rows,T>
transposed (const matrix<Rows,Cols,T>&);
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///////////////////////////////////////////////////////////////////////////
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template <size_t Rows, size_t Cols, typename T>
matrix<Rows,Cols,T>
abs (const matrix<Rows,Cols,T>&);
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template <size_t Rows, size_t Cols, typename T>
constexpr
T
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sum (const matrix<Rows,Cols,T>&);
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///////////////////////////////////////////////////////////////////////////
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template <typename T> using matrix3 = matrix<3,3,T>;
template <typename T> using matrix4 = matrix<4,4,T>;
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template <size_t Rows, size_t Cols> using matrixf = matrix<Rows,Cols,float>;
template <size_t Rows, size_t Cols> using matrixd = matrix<Rows,Cols,double>;
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typedef matrix<2,2,float> matrix2f;
typedef matrix<2,2,double> matrix2d;
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typedef matrix<3,3,float> matrix3f;
typedef matrix<3,3,double> matrix3d;
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typedef matrix<4,4,float> matrix4f;
typedef matrix<4,4,double> matrix4d;
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///////////////////////////////////////////////////////////////////////////
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template <size_t Rows, size_t Cols, typename T>
std::ostream& operator<< (std::ostream&, const matrix<Rows,Cols,T>&);
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}
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#include "matrix.ipp"
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#endif