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Object-Oriented Graphics Rendering Engine
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Ogre::Matrix3 Class Reference
Core » Math

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
 
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=Real(1e-06)) const
 
Matrix3 Inverse (Real fTolerance=Real(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 operator- (const Matrix3 &rkMatrix) const
 Matrix subtraction. More...
 
bool operator== (const Matrix3 &rkMatrix) const
 Tests 2 matrices for equality. More...
 
Real * operator[] (size_t iRow)
 
const Real * operator[] (size_t iRow) const
 Member access, allows use of construct mat[r][c]. More...
 
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, Degree &rfAngle) const
 
void ToAngleAxis (Vector3 &rkAxis, Radian &rfAngle) const
 Note: Matrix must be orthonormal. More...
 
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
 

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

◆ Determinant()

Real Ogre::Matrix3::Determinant ( ) const

◆ EigenSolveSymmetric()

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

Eigensolver, matrix must be symmetric.

◆ FromAngleAxis()

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

◆ FromAxes()

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

◆ 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 
)

◆ GetColumn()

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

◆ hasScale()

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

Determines if this matrix involves a scaling.

References Ogre::Math::RealEqual().

◆ Inverse() [1/2]

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

◆ Inverse() [2/2]

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

◆ operator!=()

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

Tests 2 matrices for inequality.

References Ogre::operator==().

◆ operator*() [1/3]

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

Matrix concatenation using '*'.

◆ 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.

◆ operator+()

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

Matrix addition.

◆ operator-() [1/2]

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

◆ operator-() [2/2]

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

Matrix subtraction.

◆ operator==()

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

Tests 2 matrices for equality.

◆ operator[]() [1/2]

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

◆ operator[]() [2/2]

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

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

◆ 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)

◆ SetColumn()

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

◆ SingularValueComposition()

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

◆ SingularValueDecomposition()

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

Singular value decomposition.

◆ SpectralNorm()

Real Ogre::Matrix3::SpectralNorm ( ) const

◆ swap()

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

Exchange the contents of this matrix with another.

References std::swap().

◆ TensorProduct()

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

◆ ToAngleAxis() [1/2]

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

◆ ToAngleAxis() [2/2]

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

Note: Matrix must be orthonormal.

◆ 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

◆ Transpose()

Matrix3 Ogre::Matrix3::Transpose ( ) const

Member Data Documentation

◆ EPSILON

const Real Ogre::Matrix3::EPSILON
static

◆ IDENTITY

const Matrix3 Ogre::Matrix3::IDENTITY
static

◆ ZERO

const Matrix3 Ogre::Matrix3::ZERO
static
The documentation for this class was generated from the following file: