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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
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-06) const
Matrix3 | Inverse (Real fTolerance=1e-06) 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] | ) |
| inline explicit

## ◆ 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

## ◆ 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==().

## ◆ 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-06`
| ) |  | const

## ◆ Inverse() [2/2]

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