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

Real	Determinant () const

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	hasNegativeScale () const
	Determines if this matrix involves a negative scaling. More...

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

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

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

Matrix3	inverse () const

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

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

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	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

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...

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() [1/3]

Ogre::Matrix3::Matrix3 ( )

inline

Default constructor.

Note: It does NOT initialize the matrix for efficiency.

◆ Matrix3() [2/3]

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

inlineexplicit

◆ Matrix3() [3/3]

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

◆ 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

References Ogre::operator==().

◆ 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==()

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*(), Ogre::operator+(), 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*() [1/2]

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

Matrix concatenation using '*'.

◆ operator-() [2/2]

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

◆ operator*() [2/2]

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-06f`
	)		const

◆ Inverse() [2/2]

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

◆ Determinant()

Real Ogre::Matrix3::Determinant ( ) const

◆ transpose()

Matrix3 Ogre::Matrix3::transpose ( ) const

inline

◆ inverse()

Matrix3 Ogre::Matrix3::inverse ( ) const

inline

◆ determinant()

Real Ogre::Matrix3::determinant ( ) const

inline

◆ hasNegativeScale()

bool Ogre::Matrix3::hasNegativeScale ( ) const

inline

Determines if this matrix involves a negative scaling.

◆ 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<<

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

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() [1/3]

◆ Matrix3() [2/3]

◆ Matrix3() [3/3]

Member Function Documentation

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ GetColumn()

◆ SetColumn()

◆ FromAxes()

◆ operator==()

◆ operator!=()

◆ operator+()

◆ operator-() [1/2]

◆ operator*() [1/2]

◆ operator-() [2/2]

◆ operator*() [2/2]

◆ Transpose()

◆ Inverse() [1/2]

◆ Inverse() [2/2]

◆ Determinant()

◆ transpose()

◆ inverse()

◆ determinant()

◆ hasNegativeScale()

◆ 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