A 3x3 matrix which can represent rotations around axes. More...

#include <OgreMatrix3.h>

Public Member Functions
	Matrix3 ()
	Default constructor. More...

	Matrix3 (const Real arr[3][3])

	Matrix3 (const Matrix3 &rkMatrix)

	Matrix3 (Real fEntry00, Real fEntry01, Real fEntry02, Real fEntry10, Real fEntry11, Real fEntry12, Real fEntry20, Real fEntry21, Real fEntry22)

Real	Determinant () const

void	EigenSolveSymmetric (Real afEigenvalue[3], Vector3 akEigenvector[3]) const
	Eigensolver, matrix must be symmetric. More...

void	FromAngleAxis (const Vector3 &rkAxis, const Radian &fRadians)

void	FromAxes (const Vector3 &xAxis, const Vector3 &yAxis, const Vector3 &zAxis)

void	FromEulerAnglesXYZ (const Radian &fYAngle, const Radian &fPAngle, const Radian &fRAngle)

void	FromEulerAnglesXZY (const Radian &fYAngle, const Radian &fPAngle, const Radian &fRAngle)

void	FromEulerAnglesYXZ (const Radian &fYAngle, const Radian &fPAngle, const Radian &fRAngle)

void	FromEulerAnglesYZX (const Radian &fYAngle, const Radian &fPAngle, const Radian &fRAngle)

void	FromEulerAnglesZXY (const Radian &fYAngle, const Radian &fPAngle, const Radian &fRAngle)

void	FromEulerAnglesZYX (const Radian &fYAngle, const Radian &fPAngle, const Radian &fRAngle)

Vector3	GetColumn (size_t iCol) const

bool	hasScale () const
	Determines if this matrix involves a scaling. More...

bool	Inverse (Matrix3 &rkInverse, Real fTolerance=1e-06) const

Matrix3	Inverse (Real fTolerance=1e-06) const

bool	operator!= (const Matrix3 &rkMatrix) const
	Tests 2 matrices for inequality. More...

Matrix3	operator* (const Matrix3 &rkMatrix) const
	Matrix concatenation using '*'. More...

Vector3	operator* (const Vector3 &rkVector) const
	Matrix * vector [3x3 * 3x1 = 3x1]. More...

Matrix3	operator* (Real fScalar) const
	Matrix * scalar. More...

Matrix3	operator+ (const Matrix3 &rkMatrix) const
	Matrix addition. More...

Matrix3	operator- (const Matrix3 &rkMatrix) const
	Matrix subtraction. More...

Matrix3	operator- () const

Matrix3 &	operator= (const Matrix3 &rkMatrix)
	Assignment and comparison. More...

bool	operator== (const Matrix3 &rkMatrix) const
	Tests 2 matrices for equality. More...

const Real *	operator[] (size_t iRow) const
	Member access, allows use of construct mat[r][c]. More...

Real *	operator[] (size_t iRow)

void	Orthonormalize ()
	Gram-Schmidt orthonormalization (applied to columns of rotation matrix) More...

void	QDUDecomposition (Matrix3 &rkQ, Vector3 &rkD, Vector3 &rkU) const
	Orthogonal Q, diagonal D, upper triangular U stored as (u01,u02,u12) More...

void	SetColumn (size_t iCol, const Vector3 &vec)

void	SingularValueComposition (const Matrix3 &rkL, const Vector3 &rkS, const Matrix3 &rkR)

void	SingularValueDecomposition (Matrix3 &rkL, Vector3 &rkS, Matrix3 &rkR) const
	Singular value decomposition. More...

Real	SpectralNorm () const

void	swap (Matrix3 &other)
	Exchange the contents of this matrix with another. More...

void	ToAngleAxis (Vector3 &rkAxis, Radian &rfAngle) const
	Note: Matrix must be orthonormal. More...

void	ToAngleAxis (Vector3 &rkAxis, Degree &rfAngle) const

bool	ToEulerAnglesXYZ (Radian &rfYAngle, Radian &rfPAngle, Radian &rfRAngle) const
	The matrix must be orthonormal. More...

bool	ToEulerAnglesXZY (Radian &rfYAngle, Radian &rfPAngle, Radian &rfRAngle) const

bool	ToEulerAnglesYXZ (Radian &rfYAngle, Radian &rfPAngle, Radian &rfRAngle) const

bool	ToEulerAnglesYZX (Radian &rfYAngle, Radian &rfPAngle, Radian &rfRAngle) const

bool	ToEulerAnglesZXY (Radian &rfYAngle, Radian &rfPAngle, Radian &rfRAngle) const

bool	ToEulerAnglesZYX (Radian &rfYAngle, Radian &rfPAngle, Radian &rfRAngle) const

Matrix3	Transpose () const

Static Public Member Functions
static void	TensorProduct (const Vector3 &rkU, const Vector3 &rkV, Matrix3 &rkProduct)

Static Public Attributes
static const Real	EPSILON

static const Matrix3	IDENTITY

static const Matrix3	ZERO

Friends
class	Matrix4

_OgreExport friend Vector3	operator* (const Vector3 &rkVector, const Matrix3 &rkMatrix)
	Vector * matrix [1x3 * 3x3 = 1x3]. More...

_OgreExport friend Matrix3	operator* (Real fScalar, const Matrix3 &rkMatrix)
	Scalar * matrix. More...

_OgreExport friend std::ostream &	operator<< (std::ostream &o, const Matrix3 &mat)
	Function for writing to a stream. More...

Detailed Description

A 3x3 matrix which can represent rotations around axes.

Note: All the code is adapted from the Wild Magic 0.2 Matrix library (http://www.geometrictools.com/).

: The coordinate system is assumed to be right-handed.

Constructor & Destructor Documentation

◆ Matrix3() [1/4]

Ogre::Matrix3::Matrix3 ( )

inline

Default constructor.

Note: It does NOT initialize the matrix for efficiency.

◆ Matrix3() [2/4]

Ogre::Matrix3::Matrix3 ( const Real arr[3][3] )

inlineexplicit

◆ Matrix3() [3/4]

Ogre::Matrix3::Matrix3 ( const Matrix3 & rkMatrix )

inline

◆ Matrix3() [4/4]

Ogre::Matrix3::Matrix3	(	Real	fEntry00,
		Real	fEntry01,
		Real	fEntry02,
		Real	fEntry10,
		Real	fEntry11,
		Real	fEntry12,
		Real	fEntry20,
		Real	fEntry21,
		Real	fEntry22
	)

inline

Member Function Documentation

◆ swap()

void Ogre::Matrix3::swap ( Matrix3 & other )

inline

Exchange the contents of this matrix with another.

References std::swap().

◆ operator[]() [1/2]

const Real* Ogre::Matrix3::operator[] ( size_t iRow ) const

inline

Member access, allows use of construct mat[r][c].

◆ operator[]() [2/2]

Real* Ogre::Matrix3::operator[] ( size_t iRow )

inline

◆ GetColumn()

Vector3 Ogre::Matrix3::GetColumn ( size_t iCol ) const

◆ SetColumn()

void Ogre::Matrix3::SetColumn	(	size_t	iCol,
		const Vector3 &	vec
	)

◆ FromAxes()

void Ogre::Matrix3::FromAxes	(	const Vector3 &	xAxis,
		const Vector3 &	yAxis,
		const Vector3 &	zAxis
	)

◆ operator=()

Matrix3& Ogre::Matrix3::operator= ( const Matrix3 & rkMatrix )

inline

Assignment and comparison.

References Ogre::operator==().

◆ operator==()

bool Ogre::Matrix3::operator== ( const Matrix3 & rkMatrix ) const

Tests 2 matrices for equality.

◆ operator!=()

bool Ogre::Matrix3::operator!= ( const Matrix3 & rkMatrix ) const

inline

Tests 2 matrices for inequality.

References Ogre::operator*(), and Ogre::operator==().

◆ operator+()

Matrix3 Ogre::Matrix3::operator+ ( const Matrix3 & rkMatrix ) const

Matrix addition.

◆ operator-() [1/2]

Matrix3 Ogre::Matrix3::operator- ( const Matrix3 & rkMatrix ) const

Matrix subtraction.

◆ operator*() [1/3]

Matrix3 Ogre::Matrix3::operator* ( const Matrix3 & rkMatrix ) const

Matrix concatenation using '*'.

◆ operator-() [2/2]

Matrix3 Ogre::Matrix3::operator- ( ) const

◆ operator*() [2/3]

Vector3 Ogre::Matrix3::operator* ( const Vector3 & rkVector ) const

Matrix * vector [3x3 * 3x1 = 3x1].

◆ operator*() [3/3]

Matrix3 Ogre::Matrix3::operator* ( Real fScalar ) const

Matrix * scalar.

◆ Transpose()

Matrix3 Ogre::Matrix3::Transpose ( ) const

◆ Inverse() [1/2]

bool Ogre::Matrix3::Inverse	(	Matrix3 &	rkInverse,
		Real	fTolerance = `1e-06`
	)		const

◆ Inverse() [2/2]

Matrix3 Ogre::Matrix3::Inverse ( Real fTolerance = 1e-06 ) const

◆ Determinant()

Real Ogre::Matrix3::Determinant ( ) const

◆ SingularValueDecomposition()

void Ogre::Matrix3::SingularValueDecomposition	(	Matrix3 &	rkL,
		Vector3 &	rkS,
		Matrix3 &	rkR
	)		const

Singular value decomposition.

◆ SingularValueComposition()

void Ogre::Matrix3::SingularValueComposition	(	const Matrix3 &	rkL,
		const Vector3 &	rkS,
		const Matrix3 &	rkR
	)

◆ Orthonormalize()

void Ogre::Matrix3::Orthonormalize ( )

Gram-Schmidt orthonormalization (applied to columns of rotation matrix)

◆ QDUDecomposition()

void Ogre::Matrix3::QDUDecomposition	(	Matrix3 &	rkQ,
		Vector3 &	rkD,
		Vector3 &	rkU
	)		const

Orthogonal Q, diagonal D, upper triangular U stored as (u01,u02,u12)

◆ SpectralNorm()

Real Ogre::Matrix3::SpectralNorm ( ) const

◆ ToAngleAxis() [1/2]

void Ogre::Matrix3::ToAngleAxis	(	Vector3 &	rkAxis,
		Radian &	rfAngle
	)		const

Note: Matrix must be orthonormal.

◆ ToAngleAxis() [2/2]

void Ogre::Matrix3::ToAngleAxis	(	Vector3 &	rkAxis,
		Degree &	rfAngle
	)		const

inline

◆ FromAngleAxis()

void Ogre::Matrix3::FromAngleAxis	(	const Vector3 &	rkAxis,
		const Radian &	fRadians
	)

◆ ToEulerAnglesXYZ()

bool Ogre::Matrix3::ToEulerAnglesXYZ	(	Radian &	rfYAngle,
		Radian &	rfPAngle,
		Radian &	rfRAngle
	)		const

The matrix must be orthonormal.

The decomposition is yaw*pitch*roll where yaw is rotation about the Up vector, pitch is rotation about the Right axis, and roll is rotation about the Direction axis.

◆ ToEulerAnglesXZY()

bool Ogre::Matrix3::ToEulerAnglesXZY	(	Radian &	rfYAngle,
		Radian &	rfPAngle,
		Radian &	rfRAngle
	)		const

◆ ToEulerAnglesYXZ()

bool Ogre::Matrix3::ToEulerAnglesYXZ	(	Radian &	rfYAngle,
		Radian &	rfPAngle,
		Radian &	rfRAngle
	)		const

◆ ToEulerAnglesYZX()

bool Ogre::Matrix3::ToEulerAnglesYZX	(	Radian &	rfYAngle,
		Radian &	rfPAngle,
		Radian &	rfRAngle
	)		const

◆ ToEulerAnglesZXY()

bool Ogre::Matrix3::ToEulerAnglesZXY	(	Radian &	rfYAngle,
		Radian &	rfPAngle,
		Radian &	rfRAngle
	)		const

◆ ToEulerAnglesZYX()

bool Ogre::Matrix3::ToEulerAnglesZYX	(	Radian &	rfYAngle,
		Radian &	rfPAngle,
		Radian &	rfRAngle
	)		const

◆ FromEulerAnglesXYZ()

void Ogre::Matrix3::FromEulerAnglesXYZ	(	const Radian &	fYAngle,
		const Radian &	fPAngle,
		const Radian &	fRAngle
	)

◆ FromEulerAnglesXZY()

void Ogre::Matrix3::FromEulerAnglesXZY	(	const Radian &	fYAngle,
		const Radian &	fPAngle,
		const Radian &	fRAngle
	)

◆ FromEulerAnglesYXZ()

void Ogre::Matrix3::FromEulerAnglesYXZ	(	const Radian &	fYAngle,
		const Radian &	fPAngle,
		const Radian &	fRAngle
	)

◆ FromEulerAnglesYZX()

void Ogre::Matrix3::FromEulerAnglesYZX	(	const Radian &	fYAngle,
		const Radian &	fPAngle,
		const Radian &	fRAngle
	)

◆ FromEulerAnglesZXY()

void Ogre::Matrix3::FromEulerAnglesZXY	(	const Radian &	fYAngle,
		const Radian &	fPAngle,
		const Radian &	fRAngle
	)

◆ FromEulerAnglesZYX()

void Ogre::Matrix3::FromEulerAnglesZYX	(	const Radian &	fYAngle,
		const Radian &	fPAngle,
		const Radian &	fRAngle
	)

◆ EigenSolveSymmetric()

void Ogre::Matrix3::EigenSolveSymmetric	(	Real	afEigenvalue[3],
		Vector3	akEigenvector[3]
	)		const

Eigensolver, matrix must be symmetric.

◆ TensorProduct()

static void Ogre::Matrix3::TensorProduct	(	const Vector3 &	rkU,
		const Vector3 &	rkV,
		Matrix3 &	rkProduct
	)

static

◆ hasScale()

bool Ogre::Matrix3::hasScale ( ) const

inline

Determines if this matrix involves a scaling.

References Ogre::Math::RealEqual().

Friends And Related Function Documentation

◆ Matrix4

friend class Matrix4

friend

◆ operator* [1/2]

_OgreExport friend Vector3 operator*	(	const Vector3 &	rkVector,
		const Matrix3 &	rkMatrix
	)

friend

Vector * matrix [1x3 * 3x3 = 1x3].

◆ operator* [2/2]

_OgreExport friend Matrix3 operator*	(	Real	fScalar,
		const Matrix3 &	rkMatrix
	)

friend

Scalar * matrix.

◆ operator<<

_OgreExport friend std::ostream& operator<<	(	std::ostream &	o,
		const Matrix3 &	mat
	)

friend

Function for writing to a stream.

Member Data Documentation

◆ EPSILON

const Real Ogre::Matrix3::EPSILON

static

◆ ZERO

const Matrix3 Ogre::Matrix3::ZERO

static

◆ IDENTITY

const Matrix3 Ogre::Matrix3::IDENTITY

static

Referenced by Ogre::StringConverter::parseAngle().

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

OgreMatrix3.h

Public Member Functions

Static Public Member Functions

Static Public Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Matrix3() [1/4]

◆ Matrix3() [2/4]

◆ Matrix3() [3/4]

◆ Matrix3() [4/4]

Member Function Documentation

◆ swap()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ GetColumn()

◆ SetColumn()

◆ FromAxes()

◆ operator=()

◆ operator==()

◆ operator!=()

◆ operator+()

◆ operator-() [1/2]

◆ operator*() [1/3]

◆ operator-() [2/2]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ Transpose()

◆ Inverse() [1/2]

◆ Inverse() [2/2]

◆ Determinant()

◆ SingularValueDecomposition()

◆ SingularValueComposition()

◆ Orthonormalize()

◆ QDUDecomposition()

◆ SpectralNorm()

◆ ToAngleAxis() [1/2]

◆ ToAngleAxis() [2/2]

◆ FromAngleAxis()

◆ ToEulerAnglesXYZ()

◆ ToEulerAnglesXZY()

◆ ToEulerAnglesYXZ()

◆ ToEulerAnglesYZX()

◆ ToEulerAnglesZXY()

◆ ToEulerAnglesZYX()

◆ FromEulerAnglesXYZ()

◆ FromEulerAnglesXZY()

◆ FromEulerAnglesYXZ()

◆ FromEulerAnglesYZX()

◆ FromEulerAnglesZXY()

◆ FromEulerAnglesZYX()

◆ EigenSolveSymmetric()

◆ TensorProduct()

◆ hasScale()

Friends And Related Function Documentation

◆ Matrix4

◆ operator* [1/2]

◆ operator* [2/2]

◆ operator<<

Member Data Documentation

◆ EPSILON

◆ ZERO

◆ IDENTITY