A 4x4 matrix class. More...

#include <gz/math/Matrix4.hh>

Public Member Functions
	Matrix4 ()
	Constructor. More...

	Matrix4 (const Matrix4< T > &_m)=default
	Copy constructor. More...

	Matrix4 (const Pose3< T > &_pose)
	Construct Matrix4 from a math::Pose3. More...

	Matrix4 (const Quaternion< T > &_q)
	Construct Matrix4 from a quaternion. More...

constexpr	Matrix4 (T _v00, T _v01, T _v02, T _v03, T _v10, T _v11, T _v12, T _v13, T _v20, T _v21, T _v22, T _v23, T _v30, T _v31, T _v32, T _v33)
	Constructor. More...

	~Matrix4 ()=default
	Destructor. More...

void	Axis (const Vector3< T > &_axis, T _angle)
	Set the upper-left 3x3 matrix from an axis and angle. More...

T	Determinant () const
	Return the determinant of the matrix. More...

bool	Equal (const Matrix4 &_m, const T &_tol) const
	Equality test with tolerance. More...

Vector3< T >	EulerRotation (bool _firstSolution) const
	Get the rotation as a Euler angles. More...

Matrix4< T >	Inverse () const
	Return the inverse matrix. This is a non-destructive operation. More...

bool	IsAffine () const
	Return true if the matrix is affine. More...

bool	operator!= (const Matrix4< T > &_m) const
	Inequality test operator. More...

T &	operator() (const size_t _row, const size_t _col)
	Get a mutable version the value at the specified row, column index. More...

const T &	operator() (const size_t _row, const size_t _col) const
	Get the value at the specified row, column index. More...

Matrix4< T >	operator* (const Matrix4< T > &_m2) const
	Multiplication operator. More...

Vector3< T >	operator* (const Vector3< T > &_vec) const
	Multiplication operator. More...

Matrix4< T >	operator*= (const Matrix4< T > &_m2)
	Multiplication assignment operator. This matrix will become equal to this * _m2. More...

const Matrix4< T > &	operator= (const Matrix3< T > &_mat)
	Equal operator for 3x3 matrix. More...

Matrix4< T > &	operator= (const Matrix4< T > &_mat)=default
	Equal operator. this = _mat. More...

bool	operator== (const Matrix4< T > &_m) const
	Equality operator. More...

Pose3< T >	Pose () const
	Get the transformation as math::Pose. More...

Quaternion< T >	Rotation () const
	Get the rotation as a quaternion. More...

Vector3< T >	Scale () const
	Get the scale values as a Vector3<T> More...

void	Scale (const Vector3< T > &_s)
	Set the scale. More...

void	Scale (T _x, T _y, T _z)
	Set the scale. More...

void	Set (T _v00, T _v01, T _v02, T _v03, T _v10, T _v11, T _v12, T _v13, T _v20, T _v21, T _v22, T _v23, T _v30, T _v31, T _v32, T _v33)
	Change the values. More...

void	SetTranslation (const Vector3< T > &_t)
	Set the translational values [ (0, 3) (1, 3) (2, 3) ]. More...

void	SetTranslation (T _x, T _y, T _z)
	Set the translational values [ (0, 3) (1, 3) (2, 3) ]. More...

bool	TransformAffine (const Vector3< T > &_v, Vector3< T > &_result) const
	Perform an affine transformation. More...

Vector3< T >	Translation () const
	Get the translational values as a Vector3. More...

void	Transpose ()
	Transpose this matrix. More...

Matrix4< T >	Transposed () const
	Return the transpose of this matrix. More...

Static Public Member Functions
static Matrix4< T >	LookAt (const Vector3< T > &_eye, const Vector3< T > &_target, const Vector3< T > &_up=Vector3< T >::UnitZ)
	Get transform which translates to _eye and rotates the X axis so it faces the _target. The rotation is such that Z axis is in the _up direction, if possible. The coordinate system is right-handed,. More...

Static Public Attributes
static const Matrix4< T > &	Identity = detail::gMatrix4Identity<T>
	Identity matrix. More...

static const Matrix4< T > &	Zero = detail::gMatrix4Zero<T>
	Zero matrix. More...

Detailed Description

template<typename T>
class gz::math::Matrix4< T >

A 4x4 matrix class.

Constructor & Destructor Documentation

◆ Matrix4() [1/5]

Matrix4 ( )

inline

Constructor.

◆ Matrix4() [2/5]

Matrix4 ( const Matrix4< T > & _m )

default

Copy constructor.

Parameters

_m	Matrix to copy

◆ Matrix4() [3/5]

constexpr Matrix4	(	T	_v00,
		T	_v01,
		T	_v02,
		T	_v03,
		T	_v10,
		T	_v11,
		T	_v12,
		T	_v13,
		T	_v20,
		T	_v21,
		T	_v22,
		T	_v23,
		T	_v30,
		T	_v31,
		T	_v32,
		T	_v33
	)

inlineconstexpr

Constructor.

Parameters

[in]	_v00	Row 0, Col 0 value
[in]	_v01	Row 0, Col 1 value
[in]	_v02	Row 0, Col 2 value
[in]	_v03	Row 0, Col 3 value
[in]	_v10	Row 1, Col 0 value
[in]	_v11	Row 1, Col 1 value
[in]	_v12	Row 1, Col 2 value
[in]	_v13	Row 1, Col 3 value
[in]	_v20	Row 2, Col 0 value
[in]	_v21	Row 2, Col 1 value
[in]	_v22	Row 2, Col 2 value
[in]	_v23	Row 2, Col 3 value
[in]	_v30	Row 3, Col 0 value
[in]	_v31	Row 3, Col 1 value
[in]	_v32	Row 3, Col 2 value
[in]	_v33	Row 3, Col 3 value

◆ Matrix4() [4/5]

Matrix4 ( const Quaternion< T > & _q )

inlineexplicit

Construct Matrix4 from a quaternion.

Parameters

[in] _q Quaternion.

References Quaternion< T >::Normalize(), Quaternion< T >::W(), Quaternion< T >::X(), Quaternion< T >::Y(), and Quaternion< T >::Z().

◆ Matrix4() [5/5]

Matrix4 ( const Pose3< T > & _pose )

inlineexplicit

Construct Matrix4 from a math::Pose3.

Parameters

[in] _pose Pose.

References Pose3< T >::Pos().

◆ ~Matrix4()

~Matrix4 ( )

default

Destructor.

Member Function Documentation

◆ Axis()

void Axis	(	const Vector3< T > &	_axis,
		T	_angle
	)

inline

Set the upper-left 3x3 matrix from an axis and angle.

Parameters

[in]	_axis	the axis
[in]	_angle	ccw rotation around the axis in radians

References Vector3< T >::X(), Vector3< T >::Y(), and Vector3< T >::Z().

◆ Determinant()

T Determinant ( ) const

inline

Return the determinant of the matrix.

Returns: Determinant of this matrix.

◆ Equal()

bool Equal	(	const Matrix4< T > &	_m,
		const T &	_tol
	)		const

inline

Equality test with tolerance.

Parameters

[in]	_m	the matrix to compare to
[in]	_tol	equality tolerance.

Returns: true if the elements of the matrices are equal within the tolerence specified by _tol.

◆ EulerRotation()

Vector3<T> EulerRotation ( bool _firstSolution ) const

inline

Get the rotation as a Euler angles.

Parameters

[in] _firstSolution True to get the first Euler solution, false to get the second.

Returns: the rotation

References GZ_PI, Vector3< T >::X(), Vector3< T >::Y(), and Vector3< T >::Z().

◆ Inverse()

Matrix4<T> Inverse ( ) const

inline

Return the inverse matrix. This is a non-destructive operation.

Returns: Inverse of this matrix.

Referenced by OrientedBox< T >::Contains().

◆ IsAffine()

bool IsAffine ( ) const

inline

Return true if the matrix is affine.

Returns: true if the matrix is affine, false otherwise

References gz::math::equal().

◆ LookAt()

static Matrix4<T> LookAt	(	const Vector3< T > &	_eye,
		const Vector3< T > &	_target,
		const Vector3< T > &	_up = `Vector3<T>::UnitZ`
	)

inlinestatic

Get transform which translates to _eye and rotates the X axis so it faces the _target. The rotation is such that Z axis is in the _up direction, if possible. The coordinate system is right-handed,.

Parameters

[in]	_eye	Coordinate frame translation.
[in]	_target	Point which the X axis should face. If _target is equal to _eye, the X axis won't be rotated.
[in]	_up	Direction in which the Z axis should point. If _up is zero or parallel to X, it will be set to +Z.

Returns: Transformation matrix.

References Vector3< T >::Normalize(), Vector3< T >::X(), Vector3< T >::Y(), and Vector3< T >::Z().

◆ operator!=()

bool operator!= ( const Matrix4< T > & _m ) const

inline

Inequality test operator.

Parameters

[in] _m Matrix4<T> to test

Returns: True if not equal (using the default tolerance of 1e-6)

◆ operator()() [1/2]

T& operator()	(	const size_t	_row,
		const size_t	_col
	)

inline

Get a mutable version the value at the specified row, column index.

Parameters

[in]	_col	The column index. Index values are clamped to a range of [0, 3].
[in]	_row	the row index. Index values are clamped to a range of [0, 3].

Returns: The value at the specified index

References gz::math::clamp(), gz::math::GZ_THREE_SIZE_T, and gz::math::GZ_ZERO_SIZE_T.

◆ operator()() [2/2]

const T& operator()	(	const size_t	_row,
		const size_t	_col
	)		const

inline

Get the value at the specified row, column index.

Parameters

[in]	_col	The column index. Index values are clamped to a range of [0, 3].
[in]	_row	the row index. Index values are clamped to a range of [0, 3].

Returns: The value at the specified index

References gz::math::clamp(), gz::math::GZ_THREE_SIZE_T, and gz::math::GZ_ZERO_SIZE_T.

◆ operator*() [1/2]

Matrix4<T> operator* ( const Matrix4< T > & _m2 ) const

inline

Multiplication operator.

Parameters

[in] _m2 Incoming matrix

Returns: This matrix * _mat

◆ operator*() [2/2]

Vector3<T> operator* ( const Vector3< T > & _vec ) const

inline

Multiplication operator.

Parameters

_vec Vector3

Returns: Resulting vector from multiplication

References Vector3< T >::X(), Vector3< T >::Y(), and Vector3< T >::Z().

◆ operator*=()

Matrix4<T> operator*= ( const Matrix4< T > & _m2 )

inline

Multiplication assignment operator. This matrix will become equal to this * _m2.

Parameters

[in] _m2 Incoming matrix.

Returns: This matrix * _mat.

◆ operator=() [1/2]

const Matrix4<T>& operator= ( const Matrix3< T > & _mat )

inline

Equal operator for 3x3 matrix.

Parameters

_mat	Incoming matrix

Returns: itself

◆ operator=() [2/2]

Matrix4<T>& operator= ( const Matrix4< T > & _mat )

default

Equal operator. this = _mat.

Parameters

_mat	Incoming matrix

Returns: itself

◆ operator==()

bool operator== ( const Matrix4< T > & _m ) const

inline

Equality operator.

Parameters

[in] _m Matrix3 to test

Returns: true if the 2 matrices are equal (using the tolerance 1e-6), false otherwise

◆ Pose()

Pose3<T> Pose ( ) const

inline

Get the transformation as math::Pose.

Returns: the pose

◆ Rotation()

Quaternion<T> Rotation ( ) const

inline

Get the rotation as a quaternion.

Returns: the rotation

algorithm from Ogre::Quaternion<T> source, which in turn is based on Ken Shoemake's article "Quaternion Calculus and Fast Animation".

References Quaternion< T >::SetW(), Quaternion< T >::SetX(), Quaternion< T >::SetY(), and Quaternion< T >::SetZ().

◆ Scale() [1/3]

Vector3<T> Scale ( ) const

inline

Get the scale values as a Vector3<T>

Returns: x,y,z scale values

◆ Scale() [2/3]

void Scale ( const Vector3< T > & _s )

inline

Set the scale.

Parameters

[in] _s scale

References Vector3< T >::X(), Vector3< T >::Y(), and Vector3< T >::Z().

◆ Scale() [3/3]

void Scale	(	T	_x,
		T	_y,
		T	_z
	)

inline

Set the scale.

Parameters

[in]	_x	X scale value.
[in]	_y	Y scale value.
[in]	_z	Z scale value.

◆ Set()

void Set	(	T	_v00,
		T	_v01,
		T	_v02,
		T	_v03,
		T	_v10,
		T	_v11,
		T	_v12,
		T	_v13,
		T	_v20,
		T	_v21,
		T	_v22,
		T	_v23,
		T	_v30,
		T	_v31,
		T	_v32,
		T	_v33
	)

inline

Change the values.

Parameters

[in]	_v00	Row 0, Col 0 value
[in]	_v01	Row 0, Col 1 value
[in]	_v02	Row 0, Col 2 value
[in]	_v03	Row 0, Col 3 value
[in]	_v10	Row 1, Col 0 value
[in]	_v11	Row 1, Col 1 value
[in]	_v12	Row 1, Col 2 value
[in]	_v13	Row 1, Col 3 value
[in]	_v20	Row 2, Col 0 value
[in]	_v21	Row 2, Col 1 value
[in]	_v22	Row 2, Col 2 value
[in]	_v23	Row 2, Col 3 value
[in]	_v30	Row 3, Col 0 value
[in]	_v31	Row 3, Col 1 value
[in]	_v32	Row 3, Col 2 value
[in]	_v33	Row 3, Col 3 value

◆ SetTranslation() [1/2]

void SetTranslation ( const Vector3< T > & _t )

inline

Set the translational values [ (0, 3) (1, 3) (2, 3) ].

Parameters

[in] _t Values to set

References Vector3< T >::X(), Vector3< T >::Y(), and Vector3< T >::Z().

◆ SetTranslation() [2/2]

void SetTranslation	(	T	_x,
		T	_y,
		T	_z
	)

inline

Set the translational values [ (0, 3) (1, 3) (2, 3) ].

Parameters

[in]	_x	X translation value.
[in]	_y	Y translation value.
[in]	_z	Z translation value.

◆ TransformAffine()

bool TransformAffine	(	const Vector3< T > &	_v,
		Vector3< T > &	_result
	)		const

inline

Perform an affine transformation.

Parameters

[in]	_v	Vector3 value for the transformation
[out]	_result	The result of the transformation. _result is not changed if this matrix is not affine.

Returns: True if this matrix is affine, false otherwise.

References Vector3< T >::Set(), Vector3< T >::X(), Vector3< T >::Y(), and Vector3< T >::Z().

◆ Translation()

Vector3<T> Translation ( ) const

inline

Get the translational values as a Vector3.

Returns: x,y,z translation values

◆ Transpose()

void Transpose ( )

inline

Transpose this matrix.

References std::swap().

◆ Transposed()

Matrix4<T> Transposed ( ) const

inline

Return the transpose of this matrix.

Returns: Transpose of this matrix.

Member Data Documentation

◆ Identity

const Matrix4< T > & Identity = detail::gMatrix4Identity<T>

static

Identity matrix.

◆ Zero

const Matrix4< T > & Zero = detail::gMatrix4Zero<T>

static

Zero matrix.

The documentation for this class was generated from the following file:

gz/math/Matrix4.hh

Public Member Functions

Static Public Member Functions

Static Public Attributes

Detailed Description

template<typename T> class gz::math::Matrix4< T >

Constructor & Destructor Documentation

◆ Matrix4() [1/5]

◆ Matrix4() [2/5]

◆ Matrix4() [3/5]

◆ Matrix4() [4/5]

◆ Matrix4() [5/5]

◆ ~Matrix4()

Member Function Documentation

◆ Axis()

◆ Determinant()

◆ Equal()

◆ EulerRotation()

◆ Inverse()

◆ IsAffine()

◆ LookAt()

◆ operator!=()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator*=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ Pose()

◆ Rotation()

◆ Scale() [1/3]

◆ Scale() [2/3]

◆ Scale() [3/3]

◆ Set()

◆ SetTranslation() [1/2]

◆ SetTranslation() [2/2]

◆ TransformAffine()

◆ Translation()

◆ Transpose()

◆ Transposed()

Member Data Documentation

◆ Identity

◆ Zero

template<typename T>
class gz::math::Matrix4< T >