A 3x3 matrix class. More...

#include <gz/math/Matrix3.hh>

Public Member Functions
	Matrix3 ()
	Default constructor that initializes the matrix3 to zero. More...

	Matrix3 (const Matrix3< T > &_m)=default
	Copy constructor. More...

	Matrix3 (const Quaternion< T > &_q)
	Construct 3x3 rotation Matrix from a quaternion. More...

constexpr	Matrix3 (T _v00, T _v01, T _v02, T _v10, T _v11, T _v12, T _v20, T _v21, T _v22)
	Construct a matrix3 using nine values. More...

	~Matrix3 ()=default
	Desctructor. More...

void	Axes (const Vector3< T > &_xAxis, const Vector3< T > &_yAxis, const Vector3< T > &_zAxis)
	Set the matrix from three axis (1 per column). More...

void	Axis (const Vector3< T > &_axis, T _angle)
	Set as a rotation matrix from an axis and angle. More...

void	Col (unsigned int _c, const Vector3< T > &_v)
	Set a column. More...

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

bool	Equal (const Matrix3 &_m, const T &_tol) const
	Equality test with tolerance. More...

void	From2Axes (const Vector3< T > &_v1, const Vector3< T > &_v2)
	Set as a rotation matrix to represent rotation from vector _v1 to vector _v2, so that _v2.Normalize() == this * _v1.Normalize() holds. More...

Matrix3< T >	Inverse () const
	Return the inverse matrix. More...

bool	operator!= (const Matrix3< T > &_m) const
	Inequality test operator. More...

T &	operator() (size_t _row, size_t _col)
	Array subscript operator. More...

T	operator() (size_t _row, size_t _col) const
	Array subscript operator. More...

Matrix3< T >	operator* (const Matrix3< T > &_m) const
	Matrix multiplication operator. More...

Matrix3< T >	operator* (const T &_s) const
	Scalar multiplication operator. More...

Vector3< T >	operator* (const Vector3< T > &_vec) const
	Multiplication operator with Vector3 on the right treated like a column vector. More...

Matrix3< T >	operator+ (const Matrix3< T > &_m) const
	Addition operation. More...

Matrix3< T >	operator- (const Matrix3< T > &_m) const
	Subtraction operator. More...

Matrix3< T > &	operator= (const Matrix3< T > &_mat)=default
	Equal operator. this = _mat. More...

Matrix3< T > &	operator= (const Quaternion< T > &_q)
	Set as a 3x3 rotation matrix from a quaternion. More...

bool	operator== (const Matrix3< T > &_m) const
	Equality test operator. More...

void	Set (size_t _row, size_t _col, T _v)
	Set a single value. More...

void	Set (T _v00, T _v01, T _v02, T _v10, T _v11, T _v12, T _v20, T _v21, T _v22)
	Set values. More...

void	SetAxes (const Vector3< T > &_xAxis, const Vector3< T > &_yAxis, const Vector3< T > &_zAxis)
	Set the matrix from three axis (1 per column). More...

void	SetCol (unsigned int _c, const Vector3< T > &_v)
	Set a column. More...

void	SetFrom2Axes (const Vector3< T > &_v1, const Vector3< T > &_v2)
	Set as a rotation matrix to represent rotation from vector _v1 to vector _v2, so that _v2.Normalize() == this * _v1.Normalize() holds. More...

void	SetFromAxisAngle (const Vector3< T > &_axis, T _angle)
	Set as a rotation matrix from an axis and angle. More...

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

Matrix3< T >	Transposed () const
	Return the transpose of this matrix. More...

Static Public Attributes
static const Matrix3< T > &	Identity = detail::gMatrix3Identity<T>
	A Matrix3 initialized to identity. This is equivalent to math::Matrix3<T>(1, 0, 0, 0, 1, 0, 0, 0, 1). More...

static const Matrix3< T > &	Zero = detail::gMatrix3Zero<T>
	A Matrix3 initialized to zero. This is equivalent to math::Matrix3<T>(0, 0, 0, 0, 0, 0, 0, 0, 0). More...

Detailed Description

template<typename T>
class gz::math::Matrix3< T >

A 3x3 matrix class.

The following two type definitions are provided:

Matrix3i : Equivalent to Matrix3<int>
Matrix3f : Equivalent to Matrix3<float>
Matrix3d : Equivalent to Matrix3<double>

Examples

C++

#include <iostream>
#include <gz/math/Matrix3.hh>
 
int main(int argc, char **argv)
{
  // Construct a default matrix3.
  gz::math::Matrix3d m;
  std::cout << "The default constructed matrix m has the following values.\n\t"
    << m << std::endl;
 
  // Set the first column of the matrix.
  m.SetCol(0, gz::math::Vector3d(3, 4, 5));
  std::cout << "Setting the first column of the matrix m to 3, 4, 5.\n\t"
    << m << std::endl;
 
  // Transpose the matrix.
  gz::math::Matrix3d t = m.Transposed();
  std::cout << "The transposed matrix t has the values.\n\t"
    << t << std::endl;
 
  // Multiply the two matrices.
  std::cout << "m * t = " << m * t << std::endl;
}

Ruby
# Modify the RUBYLIB environment variable to include the Gazebo Math

# library install path. For example, if you install to /user:

#

# $ export RUBYLIB=/usr/lib/ruby:$RUBYLIB

#

require 'gz/math'

# Construct a default matrix3.

m = Gz::Math::Matrix3d.new

printf("The default constructed matrix m has the following "+

"values.\n\t" +

"%2.1f %2.1f %2.1f %2.1f %2.1f %2.1f %2.1f %2.1f %2.1f\n",

m.(0, 0), m.(0, 1), m.(0, 2),

m.(1, 0), m.(1, 1), m.(1, 2),

m.(2, 0), m.(2, 1), m.(2, 2))

# Set the first column of the matrix.

m.SetCol(0, Gz::Math::Vector3d.new(3, 4, 5))

printf("Setting the first column of the matrix m to 3, 4, 5.\n\t" +

"%2.1f %2.1f %2.1f %2.1f %2.1f %2.1f %2.1f %2.1f %2.1f\n",

m.(0, 0), m.(0, 1), m.(0, 2),

m.(1, 0), m.(1, 1), m.(1, 2),

m.(2, 0), m.(2, 1), m.(2, 2))

# Transpose the matrix.

t = m.Transposed()

printf("The transposed matrix t has the values.\n\t"+

"%2.1f %2.1f %2.1f %2.1f %2.1f %2.1f %2.1f %2.1f %2.1f\n",

t.(0, 0), t.(0, 1), t.(0, 2),

t.(1, 0), t.(1, 1), t.(1, 2),

t.(2, 0), t.(2, 1), t.(2, 2))

# Multiply the two matrices.

m = m * t

printf("m * t = " +

"%2.1f %2.1f %2.1f %2.1f %2.1f %2.1f %2.1f %2.1f %2.1f\n",

m.(0, 0), m.(0, 1), m.(0, 2),

m.(1, 0), m.(1, 1), m.(1, 2),

m.(2, 0), m.(2, 1), m.(2, 2))

Constructor & Destructor Documentation

◆ Matrix3() [1/4]

Matrix3 ( )

inline

Default constructor that initializes the matrix3 to zero.

References std::memset().

◆ Matrix3() [2/4]

Matrix3 ( const Matrix3< T > & _m )

default

Copy constructor.

Parameters

_m	Matrix to copy

◆ Matrix3() [3/4]

constexpr Matrix3	(	T	_v00,
		T	_v01,
		T	_v02,
		T	_v10,
		T	_v11,
		T	_v12,
		T	_v20,
		T	_v21,
		T	_v22
	)

inlineconstexpr

Construct a matrix3 using nine values.

Parameters

[in]	_v00	Row 0, Col 0 value
[in]	_v01	Row 0, Col 1 value
[in]	_v02	Row 0, Col 2 value
[in]	_v10	Row 1, Col 0 value
[in]	_v11	Row 1, Col 1 value
[in]	_v12	Row 1, Col 2 value
[in]	_v20	Row 2, Col 0 value
[in]	_v21	Row 2, Col 1 value
[in]	_v22	Row 2, Col 2 value

◆ Matrix3() [4/4]

Matrix3 ( const Quaternion< T > & _q )

inlineexplicit

Construct 3x3 rotation Matrix from a quaternion.

Parameters

[in] _q Quaternion to set the Matrix3 from.

References Quaternion::Normalize(), Matrix3< T >::Set(), Quaternion::W(), Quaternion::X(), Quaternion::Y(), and Quaternion::Z().

◆ ~Matrix3()

~Matrix3 ( )

default

Desctructor.

Member Function Documentation

◆ Axes()

void Axes	(	const Vector3< T > &	_xAxis,
		const Vector3< T > &	_yAxis,
		const Vector3< T > &	_zAxis
	)

inline

Set the matrix from three axis (1 per column).

Parameters

[in]	_xAxis	The x axis, the first column of the matrix.
[in]	_yAxis	The y axis, the second column of the matrix.
[in]	_zAxis	The z axis, the third column of the matrix.

Deprecated:: Use SetAxes(const Vector3<T> &, const Vector3<T> &, const Vector3<T> &,)

References Matrix3< T >::SetAxes().

◆ Axis()

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

inline

Set as a rotation matrix from an axis and angle.

Parameters

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

Deprecated:: Use SetFromAxisAngle(const Vector3<T> &, T)

References Matrix3< T >::SetFromAxisAngle().

◆ Col()

void Col	(	unsigned int	_c,
		const Vector3< T > &	_v
	)

inline

Set a column.

Parameters

[in]	_c	The colum index [0, 1, 2]. _col is clamped to the range [0, 2].
[in]	_v	The value to set in each row of the column.

Deprecated:: Use SetCol(unsigned int _c, const Vector3<T> &_v)

References Matrix3< T >::SetCol().

◆ Determinant()

T Determinant ( ) const

inline

Return the determinant of the matrix.

Returns: Determinant of this matrix.

◆ Equal()

bool Equal	(	const Matrix3< 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.

Referenced by Matrix3< T >::operator==().

◆ From2Axes()

void From2Axes	(	const Vector3< T > &	_v1,
		const Vector3< T > &	_v2
	)

inline

Set as a rotation matrix to represent rotation from vector _v1 to vector _v2, so that _v2.Normalize() == this * _v1.Normalize() holds.

Parameters

[in]	_v1	The first vector
[in]	_v2	The second vector

Deprecated:: Use SetFrom2Axes(const Vector3<T> &, const Vector3<T> &)

References Matrix3< T >::SetFrom2Axes().

◆ Inverse()

Matrix3<T> Inverse ( ) const

inline

Return the inverse matrix.

Returns: Inverse of this matrix.

◆ operator!=()

bool operator!= ( const Matrix3< T > & _m ) const

inline

Inequality test operator.

Parameters

[in] _m Matrix3<T> to test.

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

◆ operator()() [1/2]

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

inline

Array subscript operator.

Parameters

[in]	_row	row index. _row is clamped to the range [0,2]
[in]	_col	column index. _col is clamped to the range [0,2]

Returns: a pointer to the row

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

◆ operator()() [2/2]

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

inline

Array subscript operator.

Parameters

[in]	_row	row index. _row is clamped to the range [0,2]
[in]	_col	column index. _col is clamped to the range [0,2]

Returns: a pointer to the row

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

◆ operator*() [1/3]

Matrix3<T> operator* ( const Matrix3< T > & _m ) const

inline

Matrix multiplication operator.

Parameters

[in] _m Matrix3<T> to multiply

Returns: Product of this * _m

◆ operator*() [2/3]

Matrix3<T> operator* ( const T & _s ) const

inline

Scalar multiplication operator.

Parameters

[in] _s Value to multiply.

Returns: The element wise scalar multiplication.

◆ operator*() [3/3]

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

inline

Multiplication operator with Vector3 on the right treated like a column vector.

Parameters

_vec Vector3

Returns: Resulting vector from multiplication

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

◆ operator+()

Matrix3<T> operator+ ( const Matrix3< T > & _m ) const

inline

Addition operation.

Parameters

[in] _m Matrix to add.

Returns: The element wise sum of two matrices

◆ operator-()

Matrix3<T> operator- ( const Matrix3< T > & _m ) const

inline

Subtraction operator.

Parameters

[in] _m Matrix to subtract.

Returns: The element wise difference of two matrices.

◆ operator=() [1/2]

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

default

Equal operator. this = _mat.

Parameters

_mat	Matrix to copy.

Returns: This matrix.

◆ operator=() [2/2]

Matrix3<T>& operator= ( const Quaternion< T > & _q )

inline

Set as a 3x3 rotation matrix from a quaternion.

Parameters

[in] _q Quaternion to set the matrix3 from.

Returns: Reference to the new matrix3 object.

◆ operator==()

bool operator== ( const Matrix3< T > & _m ) const

inline

Equality test operator.

Parameters

[in] _m Matrix3<T> to test.

Returns: True if equal (using the default tolerance of 1e-6).

References Matrix3< T >::Equal().

◆ Set() [1/2]

void Set	(	size_t	_row,
		size_t	_col,
		T	_v
	)

inline

Set a single value.

Parameters

[in]	_row	row index. _row is clamped to the range [0,2]
[in]	_col	column index. _col is clamped to the range [0,2]
[in]	_v	New value.

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

Referenced by Matrix3< T >::Matrix3(), and Matrix3< T >::SetFrom2Axes().

◆ Set() [2/2]

void Set	(	T	_v00,
		T	_v01,
		T	_v02,
		T	_v10,
		T	_v11,
		T	_v12,
		T	_v20,
		T	_v21,
		T	_v22
	)

inline

Set values.

Parameters

[in]	_v00	Row 0, Col 0 value
[in]	_v01	Row 0, Col 1 value
[in]	_v02	Row 0, Col 2 value
[in]	_v10	Row 1, Col 0 value
[in]	_v11	Row 1, Col 1 value
[in]	_v12	Row 1, Col 2 value
[in]	_v20	Row 2, Col 0 value
[in]	_v21	Row 2, Col 1 value
[in]	_v22	Row 2, Col 2 value

◆ SetAxes()

void SetAxes	(	const Vector3< T > &	_xAxis,
		const Vector3< T > &	_yAxis,
		const Vector3< T > &	_zAxis
	)

inline

Set the matrix from three axis (1 per column).

Parameters

[in]	_xAxis	The x axis, the first column of the matrix.
[in]	_yAxis	The y axis, the second column of the matrix.
[in]	_zAxis	The z axis, the third column of the matrix.

References Matrix3< T >::SetCol().

Referenced by Matrix3< T >::Axes().

◆ SetCol()

void SetCol	(	unsigned int	_c,
		const Vector3< T > &	_v
	)

inline

Set a column.

Parameters

[in]	_c	The colum index [0, 1, 2]. _col is clamped to the range [0, 2].
[in]	_v	The value to set in each row of the column.

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

Referenced by Matrix3< T >::Col(), and Matrix3< T >::SetAxes().

◆ SetFrom2Axes()

void SetFrom2Axes	(	const Vector3< T > &	_v1,
		const Vector3< T > &	_v2
	)

inline

Set as a rotation matrix to represent rotation from vector _v1 to vector _v2, so that _v2.Normalize() == this * _v1.Normalize() holds.

Parameters

[in]	_v1	The first vector
[in]	_v2	The second vector

References Vector3< T >::Cross(), Vector3< T >::Dot(), Matrix3< T >::Set(), Matrix3< T >::SetFromAxisAngle(), and Vector3< T >::SquaredLength().

Referenced by Matrix3< T >::From2Axes().

◆ SetFromAxisAngle()

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

inline

Set as a rotation 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().

Referenced by Matrix3< T >::Axis(), and Matrix3< T >::SetFrom2Axes().

◆ Transpose()

void Transpose ( )

inline

Transpose this matrix.

References std::swap().

◆ Transposed()

Matrix3<T> Transposed ( ) const

inline

Return the transpose of this matrix.

Returns: Transpose of this matrix.

Referenced by MassMatrix3< T >::SetFromBox(), and MassMatrix3< T >::SetFromCylinderZ().

Member Data Documentation

◆ Identity

const Matrix3< T > & Identity = detail::gMatrix3Identity<T>

static

A Matrix3 initialized to identity. This is equivalent to math::Matrix3<T>(1, 0, 0, 0, 1, 0, 0, 0, 1).

◆ Zero

const Matrix3< T > & Zero = detail::gMatrix3Zero<T>

static

A Matrix3 initialized to zero. This is equivalent to math::Matrix3<T>(0, 0, 0, 0, 0, 0, 0, 0, 0).

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

gz/math/Matrix3.hh

Public Member Functions

Static Public Attributes

Detailed Description

template<typename T> class gz::math::Matrix3< T >

Examples

Constructor & Destructor Documentation

◆ Matrix3() [1/4]

◆ Matrix3() [2/4]

◆ Matrix3() [3/4]

◆ Matrix3() [4/4]

◆ ~Matrix3()

Member Function Documentation

◆ Axes()

◆ Axis()

◆ Col()

◆ Determinant()

◆ Equal()

◆ From2Axes()

◆ Inverse()

◆ operator!=()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator+()

◆ operator-()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ Set() [1/2]

◆ Set() [2/2]

◆ SetAxes()

◆ SetCol()

◆ SetFrom2Axes()

◆ SetFromAxisAngle()

◆ Transpose()

◆ Transposed()

Member Data Documentation

◆ Identity

◆ Zero

template<typename T>
class gz::math::Matrix3< T >