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gtkradiant/libs/math/matrix.h
spog 55b14badf1 fixed typo in comment 
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/*
Copyright (C) 2001-2006, William Joseph.
All Rights Reserved.
This file is part of GtkRadiant.
GtkRadiant 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 2 of the License, or
(at your option) any later version.
GtkRadiant 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 GtkRadiant; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
*/
#if !defined(INCLUDED_MATH_MATRIX_H)
#define INCLUDED_MATH_MATRIX_H
/// \file
/// \brief Matrix data types and related operations.
#include "math/vector.h"
/// \brief A 4x4 matrix stored in single-precision floating-point.
class Matrix4
{
float m_elements[16];
public:
Matrix4()
{
}
Matrix4(float xx_, float xy_, float xz_, float xw_,
float yx_, float yy_, float yz_, float yw_,
float zx_, float zy_, float zz_, float zw_,
float tx_, float ty_, float tz_, float tw_)
{
xx() = xx_;
xy() = xy_;
xz() = xz_;
xw() = xw_;
yx() = yx_;
yy() = yy_;
yz() = yz_;
yw() = yw_;
zx() = zx_;
zy() = zy_;
zz() = zz_;
zw() = zw_;
tx() = tx_;
ty() = ty_;
tz() = tz_;
tw() = tw_;
}
float& xx()
{
return m_elements[0];
}
const float& xx() const
{
return m_elements[0];
}
float& xy()
{
return m_elements[1];
}
const float& xy() const
{
return m_elements[1];
}
float& xz()
{
return m_elements[2];
}
const float& xz() const
{
return m_elements[2];
}
float& xw()
{
return m_elements[3];
}
const float& xw() const
{
return m_elements[3];
}
float& yx()
{
return m_elements[4];
}
const float& yx() const
{
return m_elements[4];
}
float& yy()
{
return m_elements[5];
}
const float& yy() const
{
return m_elements[5];
}
float& yz()
{
return m_elements[6];
}
const float& yz() const
{
return m_elements[6];
}
float& yw()
{
return m_elements[7];
}
const float& yw() const
{
return m_elements[7];
}
float& zx()
{
return m_elements[8];
}
const float& zx() const
{
return m_elements[8];
}
float& zy()
{
return m_elements[9];
}
const float& zy() const
{
return m_elements[9];
}
float& zz()
{
return m_elements[10];
}
const float& zz() const
{
return m_elements[10];
}
float& zw()
{
return m_elements[11];
}
const float& zw() const
{
return m_elements[11];
}
float& tx()
{
return m_elements[12];
}
const float& tx() const
{
return m_elements[12];
}
float& ty()
{
return m_elements[13];
}
const float& ty() const
{
return m_elements[13];
}
float& tz()
{
return m_elements[14];
}
const float& tz() const
{
return m_elements[14];
}
float& tw()
{
return m_elements[15];
}
const float& tw() const
{
return m_elements[15];
}
Vector4& x()
{
return reinterpret_cast<Vector4&>(xx());
}
const Vector4& x() const
{
return reinterpret_cast<const Vector4&>(xx());
}
Vector4& y()
{
return reinterpret_cast<Vector4&>(yx());
}
const Vector4& y() const
{
return reinterpret_cast<const Vector4&>(yx());
}
Vector4& z()
{
return reinterpret_cast<Vector4&>(zx());
}
const Vector4& z() const
{
return reinterpret_cast<const Vector4&>(zx());
}
Vector4& t()
{
return reinterpret_cast<Vector4&>(tx());
}
const Vector4& t() const
{
return reinterpret_cast<const Vector4&>(tx());
}
const float& index(std::size_t i) const
{
return m_elements[i];
}
float& index(std::size_t i)
{
return m_elements[i];
}
const float& operator[](std::size_t i) const
{
return m_elements[i];
}
float& operator[](std::size_t i)
{
return m_elements[i];
}
const float& index(std::size_t r, std::size_t c) const
{
return m_elements[(r << 2) + c];
}
float& index(std::size_t r, std::size_t c)
{
return m_elements[(r << 2) + c];
}
};
/// \brief The 4x4 identity matrix.
const Matrix4 g_matrix4_identity(
1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1
);
/// \brief Returns true if \p self and \p other are exactly element-wise equal.
inline bool operator==(const Matrix4& self, const Matrix4& other)
{
return self.xx() == other.xx() && self.xy() == other.xy() && self.xz() == other.xz() && self.xw() == other.xw()
&& self.yx() == other.yx() && self.yy() == other.yy() && self.yz() == other.yz() && self.yw() == other.yw()
&& self.zx() == other.zx() && self.zy() == other.zy() && self.zz() == other.zz() && self.zw() == other.zw()
&& self.tx() == other.tx() && self.ty() == other.ty() && self.tz() == other.tz() && self.tw() == other.tw();
}
/// \brief Returns true if \p self and \p other are exactly element-wise equal.
inline bool matrix4_equal(const Matrix4& self, const Matrix4& other)
{
return self == other;
}
/// \brief Returns true if \p self and \p other are element-wise equal within \p epsilon.
inline bool matrix4_equal_epsilon(const Matrix4& self, const Matrix4& other, float epsilon)
{
return float_equal_epsilon(self.xx(), other.xx(), epsilon)
&& float_equal_epsilon(self.xy(), other.xy(), epsilon)
&& float_equal_epsilon(self.xz(), other.xz(), epsilon)
&& float_equal_epsilon(self.xw(), other.xw(), epsilon)
&& float_equal_epsilon(self.yx(), other.yx(), epsilon)
&& float_equal_epsilon(self.yy(), other.yy(), epsilon)
&& float_equal_epsilon(self.yz(), other.yz(), epsilon)
&& float_equal_epsilon(self.yw(), other.yw(), epsilon)
&& float_equal_epsilon(self.zx(), other.zx(), epsilon)
&& float_equal_epsilon(self.zy(), other.zy(), epsilon)
&& float_equal_epsilon(self.zz(), other.zz(), epsilon)
&& float_equal_epsilon(self.zw(), other.zw(), epsilon)
&& float_equal_epsilon(self.tx(), other.tx(), epsilon)
&& float_equal_epsilon(self.ty(), other.ty(), epsilon)
&& float_equal_epsilon(self.tz(), other.tz(), epsilon)
&& float_equal_epsilon(self.tw(), other.tw(), epsilon);
}
/// \brief Returns true if \p self and \p other are exactly element-wise equal.
/// \p self and \p other must be affine.
inline bool matrix4_affine_equal(const Matrix4& self, const Matrix4& other)
{
return self[0] == other[0]
&& self[1] == other[1]
&& self[2] == other[2]
&& self[4] == other[4]
&& self[5] == other[5]
&& self[6] == other[6]
&& self[8] == other[8]
&& self[9] == other[9]
&& self[10] == other[10]
&& self[12] == other[12]
&& self[13] == other[13]
&& self[14] == other[14];
}
enum Matrix4Handedness
{
MATRIX4_RIGHTHANDED = 0,
MATRIX4_LEFTHANDED = 1,
};
/// \brief Returns MATRIX4_RIGHTHANDED if \p self is right-handed, else returns MATRIX4_LEFTHANDED.
inline Matrix4Handedness matrix4_handedness(const Matrix4& self)
{
return (
vector3_dot(
vector3_cross(vector4_to_vector3(self.x()), vector4_to_vector3(self.y())),
vector4_to_vector3(self.z())
)
< 0.0
) ? MATRIX4_LEFTHANDED : MATRIX4_RIGHTHANDED;
}
/// \brief Returns \p self post-multiplied by \p other.
inline Matrix4 matrix4_multiplied_by_matrix4(const Matrix4& self, const Matrix4& other)
{
return Matrix4(
other[0] * self[0] + other[1] * self[4] + other[2] * self[8] + other[3] * self[12],
other[0] * self[1] + other[1] * self[5] + other[2] * self[9] + other[3] * self[13],
other[0] * self[2] + other[1] * self[6] + other[2] * self[10]+ other[3] * self[14],
other[0] * self[3] + other[1] * self[7] + other[2] * self[11]+ other[3] * self[15],
other[4] * self[0] + other[5] * self[4] + other[6] * self[8] + other[7] * self[12],
other[4] * self[1] + other[5] * self[5] + other[6] * self[9] + other[7] * self[13],
other[4] * self[2] + other[5] * self[6] + other[6] * self[10]+ other[7] * self[14],
other[4] * self[3] + other[5] * self[7] + other[6] * self[11]+ other[7] * self[15],
other[8] * self[0] + other[9] * self[4] + other[10]* self[8] + other[11]* self[12],
other[8] * self[1] + other[9] * self[5] + other[10]* self[9] + other[11]* self[13],
other[8] * self[2] + other[9] * self[6] + other[10]* self[10]+ other[11]* self[14],
other[8] * self[3] + other[9] * self[7] + other[10]* self[11]+ other[11]* self[15],
other[12]* self[0] + other[13]* self[4] + other[14]* self[8] + other[15]* self[12],
other[12]* self[1] + other[13]* self[5] + other[14]* self[9] + other[15]* self[13],
other[12]* self[2] + other[13]* self[6] + other[14]* self[10]+ other[15]* self[14],
other[12]* self[3] + other[13]* self[7] + other[14]* self[11]+ other[15]* self[15]
);
}
/// \brief Post-multiplies \p self by \p other in-place.
inline void matrix4_multiply_by_matrix4(Matrix4& self, const Matrix4& other)
{
self = matrix4_multiplied_by_matrix4(self, other);
}
/// \brief Returns \p self pre-multiplied by \p other.
inline Matrix4 matrix4_premultiplied_by_matrix4(const Matrix4& self, const Matrix4& other)
{
#if 1
return matrix4_multiplied_by_matrix4(other, self);
#else
return Matrix4(
self[0] * other[0] + self[1] * other[4] + self[2] * other[8] + self[3] * other[12],
self[0] * other[1] + self[1] * other[5] + self[2] * other[9] + self[3] * other[13],
self[0] * other[2] + self[1] * other[6] + self[2] * other[10]+ self[3] * other[14],
self[0] * other[3] + self[1] * other[7] + self[2] * other[11]+ self[3] * other[15],
self[4] * other[0] + self[5] * other[4] + self[6] * other[8] + self[7] * other[12],
self[4] * other[1] + self[5] * other[5] + self[6] * other[9] + self[7] * other[13],
self[4] * other[2] + self[5] * other[6] + self[6] * other[10]+ self[7] * other[14],
self[4] * other[3] + self[5] * other[7] + self[6] * other[11]+ self[7] * other[15],
self[8] * other[0] + self[9] * other[4] + self[10]* other[8] + self[11]* other[12],
self[8] * other[1] + self[9] * other[5] + self[10]* other[9] + self[11]* other[13],
self[8] * other[2] + self[9] * other[6] + self[10]* other[10]+ self[11]* other[14],
self[8] * other[3] + self[9] * other[7] + self[10]* other[11]+ self[11]* other[15],
self[12]* other[0] + self[13]* other[4] + self[14]* other[8] + self[15]* other[12],
self[12]* other[1] + self[13]* other[5] + self[14]* other[9] + self[15]* other[13],
self[12]* other[2] + self[13]* other[6] + self[14]* other[10]+ self[15]* other[14],
self[12]* other[3] + self[13]* other[7] + self[14]* other[11]+ self[15]* other[15]
);
#endif
}
/// \brief Pre-multiplies \p self by \p other in-place.
inline void matrix4_premultiply_by_matrix4(Matrix4& self, const Matrix4& other)
{
self = matrix4_premultiplied_by_matrix4(self, other);
}
/// \brief returns true if \p transform is affine.
inline bool matrix4_is_affine(const Matrix4& transform)
{
return transform[3] == 0 && transform[7] == 0 && transform[11] == 0 && transform[15] == 1;
}
/// \brief Returns \p self post-multiplied by \p other.
/// \p self and \p other must be affine.
inline Matrix4 matrix4_affine_multiplied_by_matrix4(const Matrix4& self, const Matrix4& other)
{
return Matrix4(
other[0] * self[0] + other[1] * self[4] + other[2] * self[8],
other[0] * self[1] + other[1] * self[5] + other[2] * self[9],
other[0] * self[2] + other[1] * self[6] + other[2] * self[10],
0,
other[4] * self[0] + other[5] * self[4] + other[6] * self[8],
other[4] * self[1] + other[5] * self[5] + other[6] * self[9],
other[4] * self[2] + other[5] * self[6] + other[6] * self[10],
0,
other[8] * self[0] + other[9] * self[4] + other[10]* self[8],
other[8] * self[1] + other[9] * self[5] + other[10]* self[9],
other[8] * self[2] + other[9] * self[6] + other[10]* self[10],
0,
other[12]* self[0] + other[13]* self[4] + other[14]* self[8] + self[12],
other[12]* self[1] + other[13]* self[5] + other[14]* self[9] + self[13],
other[12]* self[2] + other[13]* self[6] + other[14]* self[10]+ self[14],
1
);
}
/// \brief Post-multiplies \p self by \p other in-place.
/// \p self and \p other must be affine.
inline void matrix4_affine_multiply_by_matrix4(Matrix4& self, const Matrix4& other)
{
self = matrix4_affine_multiplied_by_matrix4(self, other);
}
/// \brief Returns \p self pre-multiplied by \p other.
/// \p self and \p other must be affine.
inline Matrix4 matrix4_affine_premultiplied_by_matrix4(const Matrix4& self, const Matrix4& other)
{
#if 1
return matrix4_affine_multiplied_by_matrix4(other, self);
#else
return Matrix4(
self[0] * other[0] + self[1] * other[4] + self[2] * other[8],
self[0] * other[1] + self[1] * other[5] + self[2] * other[9],
self[0] * other[2] + self[1] * other[6] + self[2] * other[10],
0,
self[4] * other[0] + self[5] * other[4] + self[6] * other[8],
self[4] * other[1] + self[5] * other[5] + self[6] * other[9],
self[4] * other[2] + self[5] * other[6] + self[6] * other[10],
0,
self[8] * other[0] + self[9] * other[4] + self[10]* other[8],
self[8] * other[1] + self[9] * other[5] + self[10]* other[9],
self[8] * other[2] + self[9] * other[6] + self[10]* other[10],
0,
self[12]* other[0] + self[13]* other[4] + self[14]* other[8] + other[12],
self[12]* other[1] + self[13]* other[5] + self[14]* other[9] + other[13],
self[12]* other[2] + self[13]* other[6] + self[14]* other[10]+ other[14],
1
)
);
#endif
}
/// \brief Pre-multiplies \p self by \p other in-place.
/// \p self and \p other must be affine.
inline void matrix4_affine_premultiply_by_matrix4(Matrix4& self, const Matrix4& other)
{
self = matrix4_affine_premultiplied_by_matrix4(self, other);
}
/// \brief Returns \p point transformed by \p self.
template<typename Element>
inline BasicVector3<Element> matrix4_transformed_point(const Matrix4& self, const BasicVector3<Element>& point)
{
return BasicVector3<Element>(
static_cast<Element>(self[0] * point[0] + self[4] * point[1] + self[8] * point[2] + self[12]),
static_cast<Element>(self[1] * point[0] + self[5] * point[1] + self[9] * point[2] + self[13]),
static_cast<Element>(self[2] * point[0] + self[6] * point[1] + self[10] * point[2] + self[14])
);
}
/// \brief Transforms \p point by \p self in-place.
template<typename Element>
inline void matrix4_transform_point(const Matrix4& self, BasicVector3<Element>& point)
{
point = matrix4_transformed_point(self, point);
}
/// \brief Returns \p direction transformed by \p self.
template<typename Element>
inline BasicVector3<Element> matrix4_transformed_direction(const Matrix4& self, const BasicVector3<Element>& direction)
{
return BasicVector3<Element>(
static_cast<Element>(self[0] * direction[0] + self[4] * direction[1] + self[8] * direction[2]),
static_cast<Element>(self[1] * direction[0] + self[5] * direction[1] + self[9] * direction[2]),
static_cast<Element>(self[2] * direction[0] + self[6] * direction[1] + self[10] * direction[2])
);
}
/// \brief Transforms \p direction by \p self in-place.
template<typename Element>
inline void matrix4_transform_direction(const Matrix4& self, BasicVector3<Element>& normal)
{
normal = matrix4_transformed_direction(self, normal);
}
/// \brief Returns \p vector4 transformed by \p self.
inline Vector4 matrix4_transformed_vector4(const Matrix4& self, const Vector4& vector4)
{
return Vector4(
self[0] * vector4[0] + self[4] * vector4[1] + self[8] * vector4[2] + self[12] * vector4[3],
self[1] * vector4[0] + self[5] * vector4[1] + self[9] * vector4[2] + self[13] * vector4[3],
self[2] * vector4[0] + self[6] * vector4[1] + self[10] * vector4[2] + self[14] * vector4[3],
self[3] * vector4[0] + self[7] * vector4[1] + self[11] * vector4[2] + self[15] * vector4[3]
);
}
/// \brief Transforms \p vector4 by \p self in-place.
inline void matrix4_transform_vector4(const Matrix4& self, Vector4& vector4)
{
vector4 = matrix4_transformed_vector4(self, vector4);
}
/// \brief Transposes \p self in-place.
inline void matrix4_transpose(Matrix4& self)
{
std::swap(self.xy(), self.yx());
std::swap(self.xz(), self.zx());
std::swap(self.xw(), self.tx());
std::swap(self.yz(), self.zy());
std::swap(self.yw(), self.ty());
std::swap(self.zw(), self.tz());
}
/// \brief Returns \p self transposed.
inline Matrix4 matrix4_transposed(const Matrix4& self)
{
return Matrix4(
self.xx(),
self.yx(),
self.zx(),
self.tx(),
self.xy(),
self.yy(),
self.zy(),
self.ty(),
self.xz(),
self.yz(),
self.zz(),
self.tz(),
self.xw(),
self.yw(),
self.zw(),
self.tw()
);
}
/// \brief Inverts an affine transform in-place.
/// Adapted from Graphics Gems 2.
inline Matrix4 matrix4_affine_inverse(const Matrix4& self)
{
Matrix4 result;
// determinant of rotation submatrix
double det
= self[0] * ( self[5]*self[10] - self[9]*self[6] )
- self[1] * ( self[4]*self[10] - self[8]*self[6] )
+ self[2] * ( self[4]*self[9] - self[8]*self[5] );
// throw exception here if (det*det < 1e-25)
// invert rotation submatrix
det = 1.0 / det;
result[0] = ( (self[5]*self[10]- self[6]*self[9] )*det);
result[1] = (- (self[1]*self[10]- self[2]*self[9] )*det);
result[2] = ( (self[1]*self[6] - self[2]*self[5] )*det);
result[3] = 0;
result[4] = (- (self[4]*self[10]- self[6]*self[8] )*det);
result[5] = ( (self[0]*self[10]- self[2]*self[8] )*det);
result[6] = (- (self[0]*self[6] - self[2]*self[4] )*det);
result[7] = 0;
result[8] = ( (self[4]*self[9] - self[5]*self[8] )*det);
result[9] = (- (self[0]*self[9] - self[1]*self[8] )*det);
result[10]= ( (self[0]*self[5] - self[1]*self[4] )*det);
result[11] = 0;
// multiply translation part by rotation
result[12] = - (self[12] * result[0] +
self[13] * result[4] +
self[14] * result[8]);
result[13] = - (self[12] * result[1] +
self[13] * result[5] +
self[14] * result[9]);
result[14] = - (self[12] * result[2] +
self[13] * result[6] +
self[14] * result[10]);
result[15] = 1;
return result;
}
inline void matrix4_affine_invert(Matrix4& self)
{
self = matrix4_affine_inverse(self);
}
/// \brief A compile-time-constant integer.
template<int VALUE_>
struct IntegralConstant
{
enum unnamed_{ VALUE = VALUE_ };
};
/// \brief A compile-time-constant row/column index into a 4x4 matrix.
template<typename Row, typename Col>
class Matrix4Index
{
public:
typedef IntegralConstant<Row::VALUE> r;
typedef IntegralConstant<Col::VALUE> c;
typedef IntegralConstant<(r::VALUE * 4) + c::VALUE> i;
};
/// \brief A functor which returns the cofactor of a 3x3 submatrix obtained by ignoring a given row and column of a 4x4 matrix.
/// \param Row Defines the compile-time-constant integers x, y and z with values corresponding to the indices of the three rows to use.
/// \param Col Defines the compile-time-constant integers x, y and z with values corresponding to the indices of the three columns to use.
template<typename Row, typename Col>
class Matrix4Cofactor
{
public:
typedef typename Matrix4Index<typename Row::x, typename Col::x>::i xx;
typedef typename Matrix4Index<typename Row::x, typename Col::y>::i xy;
typedef typename Matrix4Index<typename Row::x, typename Col::z>::i xz;
typedef typename Matrix4Index<typename Row::y, typename Col::x>::i yx;
typedef typename Matrix4Index<typename Row::y, typename Col::y>::i yy;
typedef typename Matrix4Index<typename Row::y, typename Col::z>::i yz;
typedef typename Matrix4Index<typename Row::z, typename Col::x>::i zx;
typedef typename Matrix4Index<typename Row::z, typename Col::y>::i zy;
typedef typename Matrix4Index<typename Row::z, typename Col::z>::i zz;
static double apply(const Matrix4& self)
{
return self[xx::VALUE] * ( self[yy::VALUE]*self[zz::VALUE] - self[zy::VALUE]*self[yz::VALUE] )
- self[xy::VALUE] * ( self[yx::VALUE]*self[zz::VALUE] - self[zx::VALUE]*self[yz::VALUE] )
+ self[xz::VALUE] * ( self[yx::VALUE]*self[zy::VALUE] - self[zx::VALUE]*self[yy::VALUE] );
}
};
/// \brief The cofactor element indices for a 4x4 matrix row or column.
/// \param Element The index of the element to ignore.
template<int Element>
class Cofactor4
{
public:
typedef IntegralConstant<(Element <= 0) ? 1 : 0> x;
typedef IntegralConstant<(Element <= 1) ? 2 : 1> y;
typedef IntegralConstant<(Element <= 2) ? 3 : 2> z;
};
/// \brief Returns the determinant of \p self.
inline double matrix4_determinant(const Matrix4& self)
{
return self.xx() * Matrix4Cofactor< Cofactor4<0>, Cofactor4<0> >::apply(self)
- self.xy() * Matrix4Cofactor< Cofactor4<0>, Cofactor4<1> >::apply(self)
+ self.xz() * Matrix4Cofactor< Cofactor4<0>, Cofactor4<2> >::apply(self)
- self.xw() * Matrix4Cofactor< Cofactor4<0>, Cofactor4<3> >::apply(self);
}
/// \brief Returns the inverse of \p self using the Adjoint method.
/// \todo Throw an exception if the determinant is zero.
inline Matrix4 matrix4_full_inverse(const Matrix4& self)
{
double determinant = 1.0 / matrix4_determinant(self);
return Matrix4(
static_cast<float>( Matrix4Cofactor< Cofactor4<0>, Cofactor4<0> >::apply(self) * determinant),
static_cast<float>(-Matrix4Cofactor< Cofactor4<1>, Cofactor4<0> >::apply(self) * determinant),
static_cast<float>( Matrix4Cofactor< Cofactor4<2>, Cofactor4<0> >::apply(self) * determinant),
static_cast<float>(-Matrix4Cofactor< Cofactor4<3>, Cofactor4<0> >::apply(self) * determinant),
static_cast<float>(-Matrix4Cofactor< Cofactor4<0>, Cofactor4<1> >::apply(self) * determinant),
static_cast<float>( Matrix4Cofactor< Cofactor4<1>, Cofactor4<1> >::apply(self) * determinant),
static_cast<float>(-Matrix4Cofactor< Cofactor4<2>, Cofactor4<1> >::apply(self) * determinant),
static_cast<float>( Matrix4Cofactor< Cofactor4<3>, Cofactor4<1> >::apply(self) * determinant),
static_cast<float>( Matrix4Cofactor< Cofactor4<0>, Cofactor4<2> >::apply(self) * determinant),
static_cast<float>(-Matrix4Cofactor< Cofactor4<1>, Cofactor4<2> >::apply(self) * determinant),
static_cast<float>( Matrix4Cofactor< Cofactor4<2>, Cofactor4<2> >::apply(self) * determinant),
static_cast<float>(-Matrix4Cofactor< Cofactor4<3>, Cofactor4<2> >::apply(self) * determinant),
static_cast<float>(-Matrix4Cofactor< Cofactor4<0>, Cofactor4<3> >::apply(self) * determinant),
static_cast<float>( Matrix4Cofactor< Cofactor4<1>, Cofactor4<3> >::apply(self) * determinant),
static_cast<float>(-Matrix4Cofactor< Cofactor4<2>, Cofactor4<3> >::apply(self) * determinant),
static_cast<float>( Matrix4Cofactor< Cofactor4<3>, Cofactor4<3> >::apply(self) * determinant)
);
}
/// \brief Inverts \p self in-place using the Adjoint method.
inline void matrix4_full_invert(Matrix4& self)
{
self = matrix4_full_inverse(self);
}
/// \brief Constructs a pure-translation matrix from \p translation.
inline Matrix4 matrix4_translation_for_vec3(const Vector3& translation)
{
return Matrix4(
1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
translation[0], translation[1], translation[2], 1
);
}
/// \brief Returns the translation part of \p self.
inline Vector3 matrix4_get_translation_vec3(const Matrix4& self)
{
return vector4_to_vector3(self.t());
}
/// \brief Concatenates \p self with \p translation.
/// The concatenated \p translation occurs before \p self.
inline void matrix4_translate_by_vec3(Matrix4& self, const Vector3& translation)
{
matrix4_multiply_by_matrix4(self, matrix4_translation_for_vec3(translation));
}
/// \brief Returns \p self Concatenated with \p translation.
/// The concatenated translation occurs before \p self.
inline Matrix4 matrix4_translated_by_vec3(const Matrix4& self, const Vector3& translation)
{
return matrix4_multiplied_by_matrix4(self, matrix4_translation_for_vec3(translation));
}
#include "math/pi.h"
/// \brief Returns \p angle modulated by the range [0, 360).
/// \p angle must be in the range [-360, 360).
inline float angle_modulate_degrees_range(float angle)
{
return static_cast<float>(float_mod_range(angle, 360.0));
}
/// \brief Returns \p euler angles converted from radians to degrees.
inline Vector3 euler_radians_to_degrees(const Vector3& euler)
{
return Vector3(
static_cast<float>(radians_to_degrees(euler.x())),
static_cast<float>(radians_to_degrees(euler.y())),
static_cast<float>(radians_to_degrees(euler.z()))
);
}
/// \brief Returns \p euler angles converted from degrees to radians.
inline Vector3 euler_degrees_to_radians(const Vector3& euler)
{
return Vector3(
static_cast<float>(degrees_to_radians(euler.x())),
static_cast<float>(degrees_to_radians(euler.y())),
static_cast<float>(degrees_to_radians(euler.z()))
);
}
/// \brief Constructs a pure-rotation matrix about the x axis from sin \p s and cosine \p c of an angle.
inline Matrix4 matrix4_rotation_for_sincos_x(float s, float c)
{
return Matrix4(
1, 0, 0, 0,
0, c, s, 0,
0,-s, c, 0,
0, 0, 0, 1
);
}
/// \brief Constructs a pure-rotation matrix about the x axis from an angle in radians.
inline Matrix4 matrix4_rotation_for_x(double x)
{
return matrix4_rotation_for_sincos_x(static_cast<float>(sin(x)), static_cast<float>(cos(x)));
}
/// \brief Constructs a pure-rotation matrix about the x axis from an angle in degrees.
inline Matrix4 matrix4_rotation_for_x_degrees(float x)
{
return matrix4_rotation_for_x(degrees_to_radians(x));
}
/// \brief Constructs a pure-rotation matrix about the y axis from sin \p s and cosine \p c of an angle.
inline Matrix4 matrix4_rotation_for_sincos_y(float s, float c)
{
return Matrix4(
c, 0,-s, 0,
0, 1, 0, 0,
s, 0, c, 0,
0, 0, 0, 1
);
}
/// \brief Constructs a pure-rotation matrix about the y axis from an angle in radians.
inline Matrix4 matrix4_rotation_for_y(double y)
{
return matrix4_rotation_for_sincos_y(static_cast<float>(sin(y)), static_cast<float>(cos(y)));
}
/// \brief Constructs a pure-rotation matrix about the y axis from an angle in degrees.
inline Matrix4 matrix4_rotation_for_y_degrees(float y)
{
return matrix4_rotation_for_y(degrees_to_radians(y));
}
/// \brief Constructs a pure-rotation matrix about the z axis from sin \p s and cosine \p c of an angle.
inline Matrix4 matrix4_rotation_for_sincos_z(float s, float c)
{
return Matrix4(
c, s, 0, 0,
-s, c, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1
);
}
/// \brief Constructs a pure-rotation matrix about the z axis from an angle in radians.
inline Matrix4 matrix4_rotation_for_z(double z)
{
return matrix4_rotation_for_sincos_z(static_cast<float>(sin(z)), static_cast<float>(cos(z)));
}
/// \brief Constructs a pure-rotation matrix about the z axis from an angle in degrees.
inline Matrix4 matrix4_rotation_for_z_degrees(float z)
{
return matrix4_rotation_for_z(degrees_to_radians(z));
}
/// \brief Constructs a pure-rotation matrix from a set of euler angles (radians) in the order (x, y, z).
/*! \verbatim
clockwise rotation around X, Y, Z, facing along axis
1 0 0 cy 0 -sy cz sz 0
0 cx sx 0 1 0 -sz cz 0
0 -sx cx sy 0 cy 0 0 1
rows of Z by cols of Y
cy*cz -sy*cz+sz -sy*sz+cz
-sz*cy -sz*sy+cz
.. or something like that..
final rotation is Z * Y * X
cy*cz -sx*-sy*cz+cx*sz cx*-sy*sz+sx*cz
-cy*sz sx*sy*sz+cx*cz -cx*-sy*sz+sx*cz
sy -sx*cy cx*cy
transposed
cy.cz + 0.sz + sy.0 cy.-sz + 0 .cz + sy.0 cy.0 + 0 .0 + sy.1 |
sx.sy.cz + cx.sz + -sx.cy.0 sx.sy.-sz + cx.cz + -sx.cy.0 sx.sy.0 + cx.0 + -sx.cy.1 |
-cx.sy.cz + sx.sz + cx.cy.0 -cx.sy.-sz + sx.cz + cx.cy.0 -cx.sy.0 + 0 .0 + cx.cy.1 |
\endverbatim */
inline Matrix4 matrix4_rotation_for_euler_xyz(const Vector3& euler)
{
#if 1
double cx = cos(euler[0]);
double sx = sin(euler[0]);
double cy = cos(euler[1]);
double sy = sin(euler[1]);
double cz = cos(euler[2]);
double sz = sin(euler[2]);
return Matrix4(
static_cast<float>(cy*cz),
static_cast<float>(cy*sz),
static_cast<float>(-sy),
0,
static_cast<float>(sx*sy*cz + cx*-sz),
static_cast<float>(sx*sy*sz + cx*cz),
static_cast<float>(sx*cy),
0,
static_cast<float>(cx*sy*cz + sx*sz),
static_cast<float>(cx*sy*sz + -sx*cz),
static_cast<float>(cx*cy),
0,
0,
0,
0,
1
);
#else
return matrix4_premultiply_by_matrix4(
matrix4_premultiply_by_matrix4(
matrix4_rotation_for_x(euler[0]),
matrix4_rotation_for_y(euler[1])
),
matrix4_rotation_for_z(euler[2])
);
#endif
}
/// \brief Constructs a pure-rotation matrix from a set of euler angles (degrees) in the order (x, y, z).
inline Matrix4 matrix4_rotation_for_euler_xyz_degrees(const Vector3& euler)
{
return matrix4_rotation_for_euler_xyz(euler_degrees_to_radians(euler));
}
/// \brief Concatenates \p self with the rotation transform produced by \p euler angles (degrees) in the order (x, y, z).
/// The concatenated rotation occurs before \p self.
inline void matrix4_rotate_by_euler_xyz_degrees(Matrix4& self, const Vector3& euler)
{
matrix4_multiply_by_matrix4(self, matrix4_rotation_for_euler_xyz_degrees(euler));
}
/// \brief Constructs a pure-rotation matrix from a set of euler angles (radians) in the order (y, z, x).
inline Matrix4 matrix4_rotation_for_euler_yzx(const Vector3& euler)
{
return matrix4_premultiplied_by_matrix4(
matrix4_premultiplied_by_matrix4(
matrix4_rotation_for_y(euler[1]),
matrix4_rotation_for_z(euler[2])
),
matrix4_rotation_for_x(euler[0])
);
}
/// \brief Constructs a pure-rotation matrix from a set of euler angles (degrees) in the order (y, z, x).
inline Matrix4 matrix4_rotation_for_euler_yzx_degrees(const Vector3& euler)
{
return matrix4_rotation_for_euler_yzx(euler_degrees_to_radians(euler));
}
/// \brief Constructs a pure-rotation matrix from a set of euler angles (radians) in the order (x, z, y).
inline Matrix4 matrix4_rotation_for_euler_xzy(const Vector3& euler)
{
return matrix4_premultiplied_by_matrix4(
matrix4_premultiplied_by_matrix4(
matrix4_rotation_for_x(euler[0]),
matrix4_rotation_for_z(euler[2])
),
matrix4_rotation_for_y(euler[1])
);
}
/// \brief Constructs a pure-rotation matrix from a set of euler angles (degrees) in the order (x, z, y).
inline Matrix4 matrix4_rotation_for_euler_xzy_degrees(const Vector3& euler)
{
return matrix4_rotation_for_euler_xzy(euler_degrees_to_radians(euler));
}
/// \brief Constructs a pure-rotation matrix from a set of euler angles (radians) in the order (y, x, z).
/*! \verbatim
| cy.cz + sx.sy.-sz + -cx.sy.0 0.cz + cx.-sz + sx.0 sy.cz + -sx.cy.-sz + cx.cy.0 |
| cy.sz + sx.sy.cz + -cx.sy.0 0.sz + cx.cz + sx.0 sy.sz + -sx.cy.cz + cx.cy.0 |
| cy.0 + sx.sy.0 + -cx.sy.1 0.0 + cx.0 + sx.1 sy.0 + -sx.cy.0 + cx.cy.1 |
\endverbatim */
inline Matrix4 matrix4_rotation_for_euler_yxz(const Vector3& euler)
{
#if 1
double cx = cos(euler[0]);
double sx = sin(euler[0]);
double cy = cos(euler[1]);
double sy = sin(euler[1]);
double cz = cos(euler[2]);
double sz = sin(euler[2]);
return Matrix4(
static_cast<float>(cy*cz + sx*sy*-sz),
static_cast<float>(cy*sz + sx*sy*cz),
static_cast<float>(-cx*sy),
0,
static_cast<float>(cx*-sz),
static_cast<float>(cx*cz),
static_cast<float>(sx),
0,
static_cast<float>(sy*cz + -sx*cy*-sz),
static_cast<float>(sy*sz + -sx*cy*cz),
static_cast<float>(cx*cy),
0,
0,
0,
0,
1
);
#else
return matrix4_premultiply_by_matrix4(
matrix4_premultiply_by_matrix4(
matrix4_rotation_for_y(euler[1]),
matrix4_rotation_for_x(euler[0])
),
matrix4_rotation_for_z(euler[2])
);
#endif
}
/// \brief Constructs a pure-rotation matrix from a set of euler angles (degrees) in the order (y, x, z).
inline Matrix4 matrix4_rotation_for_euler_yxz_degrees(const Vector3& euler)
{
return matrix4_rotation_for_euler_yxz(euler_degrees_to_radians(euler));
}
/// \brief Returns \p self concatenated with the rotation transform produced by \p euler angles (degrees) in the order (y, x, z).
/// The concatenated rotation occurs before \p self.
inline Matrix4 matrix4_rotated_by_euler_yxz_degrees(const Matrix4& self, const Vector3& euler)
{
return matrix4_multiplied_by_matrix4(self, matrix4_rotation_for_euler_yxz_degrees(euler));
}
/// \brief Concatenates \p self with the rotation transform produced by \p euler angles (degrees) in the order (y, x, z).
/// The concatenated rotation occurs before \p self.
inline void matrix4_rotate_by_euler_yxz_degrees(Matrix4& self, const Vector3& euler)
{
self = matrix4_rotated_by_euler_yxz_degrees(self, euler);
}
/// \brief Constructs a pure-rotation matrix from a set of euler angles (radians) in the order (z, x, y).
inline Matrix4 matrix4_rotation_for_euler_zxy(const Vector3& euler)
{
#if 1
return matrix4_premultiplied_by_matrix4(
matrix4_premultiplied_by_matrix4(
matrix4_rotation_for_z(euler[2]),
matrix4_rotation_for_x(euler[0])
),
matrix4_rotation_for_y(euler[1])
);
#else
double cx = cos(euler[0]);
double sx = sin(euler[0]);
double cy = cos(euler[1]);
double sy = sin(euler[1]);
double cz = cos(euler[2]);
double sz = sin(euler[2]);
return Matrix4(
static_cast<float>(cz * cy + sz * sx * sy),
static_cast<float>(sz * cx),
static_cast<float>(cz * -sy + sz * sx * cy),
0,
static_cast<float>(-sz * cy + cz * sx * sy),
static_cast<float>(cz * cx),
static_cast<float>(-sz * -sy + cz * cx * cy),
0,
static_cast<float>(cx* sy),
static_cast<float>(-sx),
static_cast<float>(cx* cy),
0,
0,
0,
0,
1
);
#endif
}
/// \brief Constructs a pure-rotation matrix from a set of euler angles (degres=es) in the order (z, x, y).
inline Matrix4 matrix4_rotation_for_euler_zxy_degrees(const Vector3& euler)
{
return matrix4_rotation_for_euler_zxy(euler_degrees_to_radians(euler));
}
/// \brief Returns \p self concatenated with the rotation transform produced by \p euler angles (degrees) in the order (z, x, y).
/// The concatenated rotation occurs before \p self.
inline Matrix4 matrix4_rotated_by_euler_zxy_degrees(const Matrix4& self, const Vector3& euler)
{
return matrix4_multiplied_by_matrix4(self, matrix4_rotation_for_euler_zxy_degrees(euler));
}
/// \brief Concatenates \p self with the rotation transform produced by \p euler angles (degrees) in the order (z, x, y).
/// The concatenated rotation occurs before \p self.
inline void matrix4_rotate_by_euler_zxy_degrees(Matrix4& self, const Vector3& euler)
{
self = matrix4_rotated_by_euler_zxy_degrees(self, euler);
}
/// \brief Constructs a pure-rotation matrix from a set of euler angles (radians) in the order (z, y, x).
inline Matrix4 matrix4_rotation_for_euler_zyx(const Vector3& euler)
{
#if 1
double cx = cos(euler[0]);
double sx = sin(euler[0]);
double cy = cos(euler[1]);
double sy = sin(euler[1]);
double cz = cos(euler[2]);
double sz = sin(euler[2]);
return Matrix4(
static_cast<float>(cy*cz),
static_cast<float>(sx*sy*cz + cx*sz),
static_cast<float>(cx*-sy*cz + sx*sz),
0,
static_cast<float>(cy*-sz),
static_cast<float>(sx*sy*-sz + cx*cz),
static_cast<float>(cx*-sy*-sz + sx*cz),
0,
static_cast<float>(sy),
static_cast<float>(-sx*cy),
static_cast<float>(cx*cy),
0,
0,
0,
0,
1
);
#else
return matrix4_premultiply_by_matrix4(
matrix4_premultiply_by_matrix4(
matrix4_rotation_for_z(euler[2]),
matrix4_rotation_for_y(euler[1])
),
matrix4_rotation_for_x(euler[0])
);
#endif
}
/// \brief Constructs a pure-rotation matrix from a set of euler angles (degrees) in the order (z, y, x).
inline Matrix4 matrix4_rotation_for_euler_zyx_degrees(const Vector3& euler)
{
return matrix4_rotation_for_euler_zyx(euler_degrees_to_radians(euler));
}
/// \brief Calculates and returns a set of euler angles that produce the rotation component of \p self when applied in the order (x, y, z).
/// \p self must be affine and orthonormal (unscaled) to produce a meaningful result.
inline Vector3 matrix4_get_rotation_euler_xyz(const Matrix4& self)
{
double a = asin(-self[2]);
double ca = cos(a);
if (fabs(ca) > 0.005) // Gimbal lock?
{
return Vector3(
static_cast<float>(atan2(self[6] / ca, self[10] / ca)),
static_cast<float>(a),
static_cast<float>(atan2(self[1] / ca, self[0]/ ca))
);
}
else // Gimbal lock has occurred
{
return Vector3(
static_cast<float>(atan2(-self[9], self[5])),
static_cast<float>(a),
0
);
}
}
/// \brief \copydoc matrix4_get_rotation_euler_xyz(const Matrix4&)
inline Vector3 matrix4_get_rotation_euler_xyz_degrees(const Matrix4& self)
{
return euler_radians_to_degrees(matrix4_get_rotation_euler_xyz(self));
}
/// \brief Calculates and returns a set of euler angles that produce the rotation component of \p self when applied in the order (y, x, z).
/// \p self must be affine and orthonormal (unscaled) to produce a meaningful result.
inline Vector3 matrix4_get_rotation_euler_yxz(const Matrix4& self)
{
double a = asin(self[6]);
double ca = cos(a);
if (fabs(ca) > 0.005) // Gimbal lock?
{
return Vector3(
static_cast<float>(a),
static_cast<float>(atan2(-self[2] / ca, self[10]/ ca)),
static_cast<float>(atan2(-self[4] / ca, self[5] / ca))
);
}
else // Gimbal lock has occurred
{
return Vector3(
static_cast<float>(a),
static_cast<float>(atan2(self[8], self[0])),
0
);
}
}
/// \brief \copydoc matrix4_get_rotation_euler_yxz(const Matrix4&)
inline Vector3 matrix4_get_rotation_euler_yxz_degrees(const Matrix4& self)
{
return euler_radians_to_degrees(matrix4_get_rotation_euler_yxz(self));
}
/// \brief Calculates and returns a set of euler angles that produce the rotation component of \p self when applied in the order (z, x, y).
/// \p self must be affine and orthonormal (unscaled) to produce a meaningful result.
inline Vector3 matrix4_get_rotation_euler_zxy(const Matrix4& self)
{
double a = asin(-self[9]);
double ca = cos(a);
if (fabs(ca) > 0.005) // Gimbal lock?
{
return Vector3(
static_cast<float>(a),
static_cast<float>(atan2(self[8] / ca, self[10] / ca)),
static_cast<float>(atan2(self[1] / ca, self[5]/ ca))
);
}
else // Gimbal lock has occurred
{
return Vector3(
static_cast<float>(a),
0,
static_cast<float>(atan2(-self[4], self[0]))
);
}
}
/// \brief \copydoc matrix4_get_rotation_euler_zxy(const Matrix4&)
inline Vector3 matrix4_get_rotation_euler_zxy_degrees(const Matrix4& self)
{
return euler_radians_to_degrees(matrix4_get_rotation_euler_zxy(self));
}
/// \brief Calculates and returns a set of euler angles that produce the rotation component of \p self when applied in the order (z, y, x).
/// \p self must be affine and orthonormal (unscaled) to produce a meaningful result.
inline Vector3 matrix4_get_rotation_euler_zyx(const Matrix4& self)
{
double a = asin(self[8]);
double ca = cos(a);
if (fabs(ca) > 0.005) // Gimbal lock?
{
return Vector3(
static_cast<float>(atan2(-self[9] / ca, self[10]/ ca)),
static_cast<float>(a),
static_cast<float>(atan2(-self[4] / ca, self[0] / ca))
);
}
else // Gimbal lock has occurred
{
return Vector3(
0,
static_cast<float>(a),
static_cast<float>(atan2(self[1], self[5]))
);
}
}
/// \brief \copydoc matrix4_get_rotation_euler_zyx(const Matrix4&)
inline Vector3 matrix4_get_rotation_euler_zyx_degrees(const Matrix4& self)
{
return euler_radians_to_degrees(matrix4_get_rotation_euler_zyx(self));
}
/// \brief Rotate \p self by \p euler angles (degrees) applied in the order (x, y, z), using \p pivotpoint.
inline void matrix4_pivoted_rotate_by_euler_xyz_degrees(Matrix4& self, const Vector3& euler, const Vector3& pivotpoint)
{
matrix4_translate_by_vec3(self, pivotpoint);
matrix4_rotate_by_euler_xyz_degrees(self, euler);
matrix4_translate_by_vec3(self, vector3_negated(pivotpoint));
}
/// \brief Constructs a pure-scale matrix from \p scale.
inline Matrix4 matrix4_scale_for_vec3(const Vector3& scale)
{
return Matrix4(
scale[0], 0, 0, 0,
0, scale[1], 0, 0,
0, 0, scale[2], 0,
0, 0, 0, 1
);
}
/// \brief Calculates and returns the (x, y, z) scale values that produce the scale component of \p self.
/// \p self must be affine and orthogonal to produce a meaningful result.
inline Vector3 matrix4_get_scale_vec3(const Matrix4& self)
{
return Vector3(
static_cast<float>(vector3_length(vector4_to_vector3(self.x()))),
static_cast<float>(vector3_length(vector4_to_vector3(self.y()))),
static_cast<float>(vector3_length(vector4_to_vector3(self.z())))
);
}
/// \brief Scales \p self by \p scale.
inline void matrix4_scale_by_vec3(Matrix4& self, const Vector3& scale)
{
matrix4_multiply_by_matrix4(self, matrix4_scale_for_vec3(scale));
}
/// \brief Scales \p self by \p scale, using \p pivotpoint.
inline void matrix4_pivoted_scale_by_vec3(Matrix4& self, const Vector3& scale, const Vector3& pivotpoint)
{
matrix4_translate_by_vec3(self, pivotpoint);
matrix4_scale_by_vec3(self, scale);
matrix4_translate_by_vec3(self, vector3_negated(pivotpoint));
}
/// \brief Transforms \p self by \p translation, \p euler and \p scale.
/// The transforms are combined in the order: scale, rotate-z, rotate-y, rotate-x, translate.
inline void matrix4_transform_by_euler_xyz_degrees(Matrix4& self, const Vector3& translation, const Vector3& euler, const Vector3& scale)
{
matrix4_translate_by_vec3(self, translation);
matrix4_rotate_by_euler_xyz_degrees(self, euler);
matrix4_scale_by_vec3(self, scale);
}
/// \brief Transforms \p self by \p translation, \p euler and \p scale, using \p pivotpoint.
inline void matrix4_pivoted_transform_by_euler_xyz_degrees(Matrix4& self, const Vector3& translation, const Vector3& euler, const Vector3& scale, const Vector3& pivotpoint)
{
matrix4_translate_by_vec3(self, pivotpoint + translation);
matrix4_rotate_by_euler_xyz_degrees(self, euler);
matrix4_scale_by_vec3(self, scale);
matrix4_translate_by_vec3(self, vector3_negated(pivotpoint));
}
#endif
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