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G3D::Matrix3

G3D::Matrix3 Class Reference

#include <Matrix3.h>

List of all members.

Public Member Functions

Matrix3 ()

Matrix3 (class BinaryInput &b)

Matrix3 (const float aafEntry[3][3])

Matrix3 (const Matrix3 &rkMatrix)

Matrix3 (float fEntry00, float fEntry01, float fEntry02, float fEntry10, float fEntry11, float fEntry12, float fEntry20, float fEntry21, float fEntry22)

bool fuzzyEq (const Matrix3 &b) const

Matrix3 (const class Quat &q)

void serialize (class BinaryOutput &b) const

void deserialize (class BinaryInput &b)

void set (float fEntry00, float fEntry01, float fEntry02, float fEntry10, float fEntry11, float fEntry12, float fEntry20, float fEntry21, float fEntry22)

float * operator[] (int iRow)

const float * operator[] (int iRow) const

operator float * ()

operator const float * () const

Vector3 getColumn (int iCol) const

Vector3 getRow (int iRow) const

void setColumn (int iCol, const Vector3 &vector)

void setRow (int iRow, const Vector3 &vector)

Matrix3 & operator= (const Matrix3 &rkMatrix)

bool operator== (const Matrix3 &rkMatrix) const

bool operator!= (const Matrix3 &rkMatrix) const

Matrix3 operator+ (const Matrix3 &rkMatrix) const

Matrix3 operator- (const Matrix3 &rkMatrix) const

Matrix3 operator * (const Matrix3 &rkMatrix) const

Matrix3 operator- () const

Matrix3 & operator+= (const Matrix3 &rkMatrix)

Matrix3 & operator-= (const Matrix3 &rkMatrix)

Matrix3 & operator *= (const Matrix3 &rkMatrix)

Vector3 operator * (const Vector3 &v) const

Matrix3 operator * (float fScalar) const

bool isOrthonormal () const

Matrix3 transpose () const

bool inverse (Matrix3 &rkInverse, float fTolerance=1e-06) const

Matrix3 inverse (float fTolerance=1e-06) const

float determinant () const

void singularValueDecomposition (Matrix3 &rkL, Vector3 &rkS, Matrix3 &rkR) const

void singularValueComposition (const Matrix3 &rkL, const Vector3 &rkS, const Matrix3 &rkR)

void orthonormalize ()

void qDUDecomposition (Matrix3 &rkQ, Vector3 &rkD, Vector3 &rkU) const

float spectralNorm () const

void toAxisAngle (Vector3 &rkAxis, float &rfRadians) const

bool toEulerAnglesXYZ (float &rfYAngle, float &rfPAngle, float &rfRAngle) const

bool toEulerAnglesXZY (float &rfYAngle, float &rfPAngle, float &rfRAngle) const

bool toEulerAnglesYXZ (float &rfYAngle, float &rfPAngle, float &rfRAngle) const

bool toEulerAnglesYZX (float &rfYAngle, float &rfPAngle, float &rfRAngle) const

bool toEulerAnglesZXY (float &rfYAngle, float &rfPAngle, float &rfRAngle) const

bool toEulerAnglesZYX (float &rfYAngle, float &rfPAngle, float &rfRAngle) const

void eigenSolveSymmetric (float afEigenvalue[3], Vector3 akEigenvector[3]) const

std::string toString () const

Static Public Member Functions

static void mul (const Matrix3 &A, const Matrix3 &B, Matrix3 &out)

static void transpose (const Matrix3 &A, Matrix3 &out)

static Matrix3 fromAxisAngle (const Vector3 &rkAxis, float fRadians)

static Matrix3 fromEulerAnglesXYZ (float fYAngle, float fPAngle, float fRAngle)

static Matrix3 fromEulerAnglesXZY (float fYAngle, float fPAngle, float fRAngle)

static Matrix3 fromEulerAnglesYXZ (float fYAngle, float fPAngle, float fRAngle)

static Matrix3 fromEulerAnglesYZX (float fYAngle, float fPAngle, float fRAngle)

static Matrix3 fromEulerAnglesZXY (float fYAngle, float fPAngle, float fRAngle)

static Matrix3 fromEulerAnglesZYX (float fYAngle, float fPAngle, float fRAngle)

static void tensorProduct (const Vector3 &rkU, const Vector3 &rkV, Matrix3 &rkProduct)

static const Matrix3 & zero ()

static const Matrix3 & identity ()

Static Public Attributes

static const float EPSILON

static const Matrix3 ZERO

static const Matrix3 IDENTITY

Protected Member Functions

void tridiagonal (float afDiag[3], float afSubDiag[3])

bool qLAlgorithm (float afDiag[3], float 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 float maxCubicRoot (float afCoeff[3])

Static Protected Attributes

static const float ms_fSvdEpsilon

static const int ms_iSvdMaxIterations

Friends

Vector3 operator * (const Vector3 &rkVector, const Matrix3 &rkMatrix)

Matrix3 operator * (double fScalar, const Matrix3 &rkMatrix)

Matrix3 operator * (float fScalar, const Matrix3 &rkMatrix)

Matrix3 operator * (int fScalar, const Matrix3 &rkMatrix)

Detailed Description

3x3 matrix. Do not subclass.

Constructor & Destructor Documentation

G3D::Matrix3::Matrix3 ( ) [inline]

Initial values are undefined for performance. See also Matrix3::zero(), Matrix3::identity(), Matrix3::fromAxisAngle, etc.

G3D::Matrix3::Matrix3 ( class BinaryInput & b )

G3D::Matrix3::Matrix3 ( const float aafEntry[3][3] )

G3D::Matrix3::Matrix3 ( const Matrix3 & rkMatrix )

G3D::Matrix3::Matrix3 ( float fEntry00,

float fEntry01,

float fEntry02,

float fEntry10,

float fEntry11,

float fEntry12,

float fEntry20,

float fEntry21,

float fEntry22

)

G3D::Matrix3::Matrix3 ( const class Quat & q )

Constructs a matrix from a quaternion.
Referenced Code:
Graphics Gems II, p. 351--354

Referenced Code:
Implementation from Watt and Watt, pg 362

Member Function Documentation

static void G3D::Matrix3::bidiagonalize ( Matrix3 & kA,

Matrix3 & kL,

Matrix3 & kR

) [static, protected]

void G3D::Matrix3::deserialize ( class BinaryInput & b )

float G3D::Matrix3::determinant ( ) const

void G3D::Matrix3::eigenSolveSymmetric ( float afEigenvalue[3],

Vector3 akEigenvector[3]

) const

eigensolver, matrix must be symmetric

static Matrix3 G3D::Matrix3::fromAxisAngle ( const Vector3 & rkAxis,

float fRadians

) [static]

static Matrix3 G3D::Matrix3::fromEulerAnglesXYZ ( float fYAngle,

float fPAngle,

float fRAngle

) [static]

static Matrix3 G3D::Matrix3::fromEulerAnglesXZY ( float fYAngle,

float fPAngle,

float fRAngle

) [static]

static Matrix3 G3D::Matrix3::fromEulerAnglesYXZ ( float fYAngle,

float fPAngle,

float fRAngle

) [static]

static Matrix3 G3D::Matrix3::fromEulerAnglesYZX ( float fYAngle,

float fPAngle,

float fRAngle

) [static]

static Matrix3 G3D::Matrix3::fromEulerAnglesZXY ( float fYAngle,

float fPAngle,

float fRAngle

) [static]

static Matrix3 G3D::Matrix3::fromEulerAnglesZYX ( float fYAngle,

float fPAngle,

float fRAngle

) [static]

bool G3D::Matrix3::fuzzyEq ( const Matrix3 & b ) const

Vector3 G3D::Matrix3::getColumn ( int iCol ) const

Vector3 G3D::Matrix3::getRow ( int iRow ) const

static void G3D::Matrix3::golubKahanStep ( Matrix3 & kA,

Matrix3 & kL,

Matrix3 & kR

) [static, protected]

static const Matrix3& G3D::Matrix3::identity ( ) [static]

Matrix3 G3D::Matrix3::inverse ( float fTolerance = 1e-06 ) const

bool G3D::Matrix3::inverse ( Matrix3 & rkInverse,

float fTolerance = 1e-06

) const

bool G3D::Matrix3::isOrthonormal ( ) const

Returns true if the rows and column L2 norms are 1.0 and the rows are orthogonal.

static float G3D::Matrix3::maxCubicRoot ( float afCoeff[3] ) [static, protected]

static void G3D::Matrix3::mul ( const Matrix3 & A,

const Matrix3 & B,

Matrix3 & out

) [inline, static]

Optimized implementation of out = A * B. It is safe (but slow) to call with A, B, and out possibly pointer equal to one another.

Matrix3 G3D::Matrix3::operator * ( float fScalar ) const

matrix * scalar

Vector3 G3D::Matrix3::operator * ( const Vector3 & v ) const [inline]

matrix * vector [3x3 * 3x1 = 3x1]

Matrix3 G3D::Matrix3::operator * ( const Matrix3 & rkMatrix ) const

Matrix-matrix multiply

Matrix3& G3D::Matrix3::operator *= ( const Matrix3 & rkMatrix )

G3D::Matrix3::operator const float * ( ) const [inline]

G3D::Matrix3::operator float * ( ) [inline]

bool G3D::Matrix3::operator!= ( const Matrix3 & rkMatrix ) const

Matrix3 G3D::Matrix3::operator+ ( const Matrix3 & rkMatrix ) const

Matrix3& G3D::Matrix3::operator+= ( const Matrix3 & rkMatrix )

Matrix3 G3D::Matrix3::operator- ( ) const

Matrix3 G3D::Matrix3::operator- ( const Matrix3 & rkMatrix ) const

Matrix3& G3D::Matrix3::operator-= ( const Matrix3 & rkMatrix )

Matrix3& G3D::Matrix3::operator= ( const Matrix3 & rkMatrix ) [inline]

bool G3D::Matrix3::operator== ( const Matrix3 & rkMatrix ) const

const float* G3D::Matrix3::operator[] ( int iRow ) const [inline]

float* G3D::Matrix3::operator[] ( int iRow ) [inline]

member access, allows use of construct mat[r][c]

void G3D::Matrix3::orthonormalize ( )

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

void G3D::Matrix3::qDUDecomposition ( Matrix3 & rkQ,

Vector3 & rkD,

Vector3 & rkU

) const

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

bool G3D::Matrix3::qLAlgorithm ( float afDiag[3],

float afSubDiag[3]

) [protected]

void G3D::Matrix3::serialize ( class BinaryOutput & b ) const

void G3D::Matrix3::set ( float fEntry00,

float fEntry01,

float fEntry02,

float fEntry10,

float fEntry11,

float fEntry12,

float fEntry20,

float fEntry21,

float fEntry22

)

Sets all elements.

void G3D::Matrix3::setColumn ( int iCol,

const Vector3 & vector

)

void G3D::Matrix3::setRow ( int iRow,

const Vector3 & vector

)

void G3D::Matrix3::singularValueComposition ( const Matrix3 & rkL,

const Vector3 & rkS,

const Matrix3 & rkR

)

singular value decomposition

void G3D::Matrix3::singularValueDecomposition ( Matrix3 & rkL,

Vector3 & rkS,

Matrix3 & rkR

) const

singular value decomposition

float G3D::Matrix3::spectralNorm ( ) const

static void G3D::Matrix3::tensorProduct ( const Vector3 & rkU,

const Vector3 & rkV,

Matrix3 & rkProduct

) [static]

void G3D::Matrix3::toAxisAngle ( Vector3 & rkAxis,

float & rfRadians

) const

matrix must be orthonormal

bool G3D::Matrix3::toEulerAnglesXYZ ( float & rfYAngle,

float & rfPAngle,

float & 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 G3D::Matrix3::toEulerAnglesXZY ( float & rfYAngle,

float & rfPAngle,

float & rfRAngle

) const

bool G3D::Matrix3::toEulerAnglesYXZ ( float & rfYAngle,

float & rfPAngle,

float & rfRAngle

) const

bool G3D::Matrix3::toEulerAnglesYZX ( float & rfYAngle,

float & rfPAngle,

float & rfRAngle

) const

bool G3D::Matrix3::toEulerAnglesZXY ( float & rfYAngle,

float & rfPAngle,

float & rfRAngle

) const

bool G3D::Matrix3::toEulerAnglesZYX ( float & rfYAngle,

float & rfPAngle,

float & rfRAngle

) const

std::string G3D::Matrix3::toString ( ) const

Matrix3 G3D::Matrix3::transpose ( ) const

static void G3D::Matrix3::transpose ( const Matrix3 & A,

Matrix3 & out

) [inline, static]

Optimized implementation of out = A.transpose(). It is safe (but slow) to call with A and out possibly pointer equal to one another.
Note that A.transpose() * v can be computed more efficiently as v * A.