Public Member Functions | Static Public Member Functions | Static Public Attributes | Protected Member Functions | Static Protected Member Functions | Protected Attributes | Static Protected Attributes | Friends | List of all members
Ogre::Matrix3 Class Reference

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
 
Matrix3operator= (const Matrix3 &rkMatrix)
 Assignment and comparison. More...
 
bool operator== (const Matrix3 &rkMatrix) const
 Tests 2 matrices for equality. More...
 
const Realoperator[] (size_t iRow) const
 Member access, allows use of construct mat[r][c]. More...
 
Realoperator[] (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
 

Protected Member Functions

bool QLAlgorithm (Real afDiag[3], Real afSubDiag[3])
 
void Tridiagonal (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]. 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.

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 
)
staticprotected
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 
)
staticprotected
bool Ogre::Matrix3::hasScale ( ) const

Determines if this matrix involves a scaling.

Definition at line 239 of file OgreMatrix3.h.

References Ogre::Math::RealEqual().

bool Ogre::Matrix3::Inverse ( Matrix3 rkInverse,
Real  fTolerance = 1e-06 
) const
Matrix3 Ogre::Matrix3::Inverse ( Real  fTolerance = 1e-06) const
static Real Ogre::Matrix3::MaxCubicRoot ( Real  afCoeff[3])
staticprotected
bool Ogre::Matrix3::operator!= ( const Matrix3 rkMatrix) const

Tests 2 matrices for inequality.

Definition at line 148 of file OgreMatrix3.h.

References Ogre::operator==().

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

Matrix concatenation using '*'.

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

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

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

Matrix * scalar.

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

Matrix addition.

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

Matrix subtraction.

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

Assignment and comparison.

Definition at line 136 of file OgreMatrix3.h.

References m.

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

Tests 2 matrices for equality.

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

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

Definition at line 115 of file OgreMatrix3.h.

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

Definition at line 120 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

Singular value decomposition.

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,
Radian rfAngle 
) const

Note: Matrix must be orthonormal.

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

Definition at line 203 of file OgreMatrix3.h.

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.

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 289 of file OgreMatrix3.h.

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

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

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

Scalar * matrix.

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

Function for writing to a stream.

Definition at line 258 of file OgreMatrix3.h.

Member Data Documentation

const Real Ogre::Matrix3::EPSILON
static

Definition at line 266 of file OgreMatrix3.h.

const Matrix3 Ogre::Matrix3::IDENTITY
static

Definition at line 268 of file OgreMatrix3.h.

Real Ogre::Matrix3::m[3][3]
protected
const Real Ogre::Matrix3::msSvdEpsilon
staticprotected

Definition at line 276 of file OgreMatrix3.h.

const unsigned int Ogre::Matrix3::msSvdMaxIterations
staticprotected

Definition at line 277 of file OgreMatrix3.h.

const Matrix3 Ogre::Matrix3::ZERO
static

Definition at line 267 of file OgreMatrix3.h.


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

Copyright © 2013 Torus Knot Software Ltd
Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License.
Last modified Sat Dec 14 2013 14:36:25