Ogre::Matrix3 Class Reference
[Math]

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

#include <OgreMatrix3.h>

Public Member Functions
	Matrix3 ()
	Default constructor.
	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)
void	swap (Matrix3 &other)
	Exchange the contents of this matrix with another.
Real *	operator[] (size_t iRow) const
Vector3	GetColumn (size_t iCol) const
void	SetColumn (size_t iCol, const Vector3 &vec)
void	FromAxes (const Vector3 &xAxis, const Vector3 &yAxis, const Vector3 &zAxis)
Matrix3 &	operator= (const Matrix3 &rkMatrix)
bool	operator== (const Matrix3 &rkMatrix) const
	Tests 2 matrices for equality.
bool	operator!= (const Matrix3 &rkMatrix) const
	Tests 2 matrices for inequality.
Matrix3	operator+ (const Matrix3 &rkMatrix) const
	Matrix addition.
Matrix3	operator- (const Matrix3 &rkMatrix) const
	Matrix subtraction.
Matrix3	operator* (const Matrix3 &rkMatrix) const
	Matrix concatenation using '*'.
Matrix3	operator- () const
Vector3	operator* (const Vector3 &rkVector) const
	Matrix * vector [3x3 * 3x1 = 3x1].
Matrix3	operator* (Real fScalar) const
	Matrix * scalar.
Matrix3	Transpose () const
bool	Inverse (Matrix3 &rkInverse, Real fTolerance=1e-06) const
Matrix3	Inverse (Real fTolerance=1e-06) const
Real	Determinant () const
void	SingularValueDecomposition (Matrix3 &rkL, Vector3 &rkS, Matrix3 &rkR) const
void	SingularValueComposition (const Matrix3 &rkL, const Vector3 &rkS, const Matrix3 &rkR)
void	Orthonormalize ()
	Gram-Schmidt orthonormalization (applied to columns of rotation matrix).
void	QDUDecomposition (Matrix3 &rkQ, Vector3 &rkD, Vector3 &rkU) const
	Orthogonal Q, diagonal D, upper triangular U stored as (u01,u02,u12).
Real	SpectralNorm () const
void	ToAngleAxis (Vector3 &rkAxis, Radian &rfAngle) const
void	ToAngleAxis (Vector3 &rkAxis, Degree &rfAngle) const
void	FromAngleAxis (const Vector3 &rkAxis, const Radian &fRadians)
bool	ToEulerAnglesXYZ (Radian &rfYAngle, Radian &rfPAngle, Radian &rfRAngle) const
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
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)
void	EigenSolveSymmetric (Real afEigenvalue[3], Vector3 akEigenvector[3]) const
	Eigensolver, matrix must be symmetric.
bool	hasScale () const
	Determines if this matrix involves a scaling.
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	ZERO
static const Matrix3	IDENTITY
Protected Member Functions
void	Tridiagonal (Real afDiag[3], Real afSubDiag[3])
bool	QLAlgorithm (Real afDiag[3], Real afSubDiag[3])
Static Protected Member Functions
static void	Bidiagonalize (Matrix3 &kA, Matrix3 &kL, Matrix3 &kR)
static void	GolubKahanStep (Matrix3 &kA, Matrix3 &kL, Matrix3 &kR)
static Real	MaxCubicRoot (Real afCoeff[3])
Protected Attributes
Real	m [3][3]
Static Protected Attributes
static const Real	msSvdEpsilon
static const unsigned int	msSvdMaxIterations
Friends
class	Matrix4
_OgreExport friend Vector3	operator* (const Vector3 &rkVector, const Matrix3 &rkMatrix)
	Vector * matrix [1x3 * 3x3 = 1x3].
_OgreExport friend Matrix3	operator* (Real fScalar, const Matrix3 &rkMatrix)
	Scalar * matrix.
_OgreExport friend std::ostream &	operator<< (std::ostream &o, const Matrix3 &mat)
	Function for writing to a stream.

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.

Definition at line 68 of file OgreMatrix3.h.

Constructor & Destructor Documentation

Ogre::Matrix3::Matrix3 ( )

Default constructor.

Note:: It does NOT initialize the matrix for efficiency.

Definition at line 75 of file OgreMatrix3.h.

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

Definition at line 76 of file OgreMatrix3.h.

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

Definition at line 80 of file OgreMatrix3.h.

References m.

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

Definition at line 84 of file OgreMatrix3.h.

Member Function Documentation

static void Ogre::Matrix3::Bidiagonalize	(	Matrix3 &	kA,
		Matrix3 &	kL,
		Matrix3 &	kR
	)			`[static, protected]`

Real Ogre::Matrix3::Determinant ( ) const

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

Eigensolver, matrix must be symmetric.

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

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

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

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

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

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

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

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

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

static void Ogre::Matrix3::GolubKahanStep	(	Matrix3 &	kA,
		Matrix3 &	kL,
		Matrix3 &	kR
	)			`[static, protected]`

bool Ogre::Matrix3::hasScale ( ) const

Determines if this matrix involves a scaling.

Definition at line 231 of file OgreMatrix3.h.

References Ogre::Math::RealEqual().

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

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

static Real Ogre::Matrix3::MaxCubicRoot ( Real afCoeff[3] ) [static, protected]

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

Tests 2 matrices for inequality.

Definition at line 140 of file OgreMatrix3.h.

References Ogre::operator==().

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

Matrix * scalar.

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

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

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

Matrix concatenation using '*'.

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

Matrix addition.

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

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

Matrix subtraction.

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

Definition at line 128 of file OgreMatrix3.h.

References m.

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

Tests 2 matrices for equality.

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

Definition at line 115 of file OgreMatrix3.h.

void Ogre::Matrix3::Orthonormalize ( )

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

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

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

bool Ogre::Matrix3::QLAlgorithm	(	Real	afDiag[3],
		Real	afSubDiag[3]
	)			`[protected]`

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

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

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

Real Ogre::Matrix3::SpectralNorm ( ) const

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

Exchange the contents of this matrix with another.

Definition at line 101 of file OgreMatrix3.h.

References m, and std::swap().

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

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

Definition at line 195 of file OgreMatrix3.h.

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

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

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

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

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

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

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

Matrix3 Ogre::Matrix3::Transpose ( ) const

void Ogre::Matrix3::Tridiagonal	(	Real	afDiag[3],
		Real	afSubDiag[3]
	)			`[protected]`

Friends And Related Function Documentation

friend class Matrix4 [friend]

Definition at line 281 of file OgreMatrix3.h.

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

Scalar * matrix.

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

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

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

Function for writing to a stream.

Definition at line 250 of file OgreMatrix3.h.

Member Data Documentation

const Real Ogre::Matrix3::EPSILON [static]

Definition at line 258 of file OgreMatrix3.h.

const Matrix3 Ogre::Matrix3::IDENTITY [static]

Definition at line 260 of file OgreMatrix3.h.

Real Ogre::Matrix3::m[3][3] [protected]

Definition at line 278 of file OgreMatrix3.h.

Referenced by Ogre::Matrix4::extract3x3Matrix(), Matrix3(), Ogre::Matrix4::operator=(), operator=(), and swap().

const Real Ogre::Matrix3::msSvdEpsilon [static, protected]

Definition at line 268 of file OgreMatrix3.h.

const unsigned int Ogre::Matrix3::msSvdMaxIterations [static, protected]

Definition at line 269 of file OgreMatrix3.h.

const Matrix3 Ogre::Matrix3::ZERO [static]

Definition at line 259 of file OgreMatrix3.h.

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

OgreMatrix3.h

Ogre::Matrix3 Class Reference [Math]

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Static Protected Attributes

Friends