albaMatrix3x3 Class Reference

#include <albaMatrix3x3.h>

Inheritance diagram for albaMatrix3x3:

Collaboration diagram for albaMatrix3x3:

Public Member Functions
	albaTypeMacro (albaMatrix3x3, albaObject)
virtual void	Print (std::ostream &os, const int indent=0) const
	albaMatrix3x3 ()
virtual	~albaMatrix3x3 ()
albaMatrix3x3 &	operator= (const albaMatrix3x3 &mat)
	albaMatrix3x3 (albaMatrix3x3 &mat)
void	DeepCopy (albaMatrix3x3 *mat)
void	MultiplyVector (const double in[3], double out[3])
albaMatrix3x3Elements	GetElements () const
void	SetElement (int i, int j, double value)
double	GetElement (int i, int j) const
void	GetVersor (int axis, double versor[3])
void	Zero ()
void	Identity ()
void	Transpose ()
void	Invert ()
void	Orthogonalize ()
double	Determinant ()
void	QuaternionToMatrix (const double quat[4])
void	MatrixToQuaternion (double quat[4])
void	SingularValueDecomposition (double U[3][3], double w[3], double VT[3][3])
void	LUFactor (int index[3])
void	LUSolve (const int index[3], double x[3])
double *	operator[] (const unsigned int i)
const double *	operator[] (unsigned int i) const
Public Member Functions inherited from albaObject
	albaObject ()
virtual	~albaObject ()
virtual void	Delete ()
virtual const char *	GetTypeName () const
virtual bool	IsA (const char *type_name) const
virtual bool	IsA (const albaTypeID &type_id) const
virtual albaObject *	NewObjectInstance () const =0
virtual const albaTypeID &	GetTypeId () const
virtual void	Print (std::ostream &os, const int indent=0) const
	albaObject (const albaObject &c)
Public Member Functions inherited from albaTimeStamped
virtual void	Modified ()
virtual unsigned long	GetMTime ()

Static Public Member Functions
static void	MultiplyVector (const float A[3][3], const float in[3], float out[3])
static void	MultiplyVector (const double A[3][3], const double in[3], double out[3])
static void	Multiply (const double A[3][3], const double B[3][3], double C[3][3])
static void	Multiply (const albaMatrix3x3 &A, albaMatrix3x3 &B, albaMatrix3x3 &C)
static void	GetVersor (int axis, const albaMatrix3x3 &matrix, double versor[3])
static void	Zero (double elements[9])
static void	Identity (double A[3][3])
static void	Transpose (const double A[3][3], double AT[3][3])
static void	Invert (const double A[3][3], double AI[3][3])
static void	Orthogonalize (const double A[3][3], double B[3][3])
static void	Diagonalize (const double A[3][3], double w[3], double V[3][3])
static double	Determinant (double A[3][3])
static double	Determinant (const double c1[3], const double c2[3], const double c3[3])
static double	Determinant (double a1, double a2, double a3, double b1, double b2, double b3, double c1, double c2, double c3)
static void	QuaternionToMatrix (const double quat[4], double A[3][3])
static void	MatrixToQuaternion (const double A[3][3], double quat[4])
static void	SingularValueDecomposition (const double A[3][3], double U[3][3], double w[3], double VT[3][3])
static int	Jacobi (const double A[3][3], double w[3], double v[3][3])
static int	JacobiN (double **a, int n, double *w, double **v)
static void	LUFactor (double A[3][3], int index[3])
static void	LUSolve (const double A[3][3], const int index[3], double x[3])
static double	DegreesToRadians ()
static double	Pi ()
static double	RadiansToDegrees ()
static double	Determinant2x2 (double a, double b, double c, double d)
static double	Determinant2x2 (const double c1[2], const double c2[2])
static double	Norm (const double x[3])
static void	Cross (const double x[3], const double y[3], double z[3])
static double	Normalize (double x[3])
Static Public Member Functions inherited from albaObject
static const char *	GetStaticTypeName ()
static bool	IsStaticType (const char *type_name)
static bool	IsStaticType (const albaTypeID &type_id)
static const albaTypeID &	GetStaticTypeId ()
static albaObject *	SafeDownCast (albaObject *o)

Protected Attributes
double	m_Elements [3][3]
Protected Attributes inherited from albaObject
bool	m_HeapFlag
Protected Attributes inherited from albaTimeStamped
albaMTime	m_MTime

Detailed Description

albaMatrix3x3 - Simple 3x3 Matrix.

This class defines a simple 3x3 Matrix class, and some operators over it. This is typically used for internal algorithms, use albaMatrix for complex usage.

See also

albaMatrix

Definition at line 32 of file albaMatrix3x3.h.

Constructor & Destructor Documentation

albaMatrix3x3() [1/2]

albaMatrix3x3::albaMatrix3x3

(

)

~albaMatrix3x3()

virtual albaMatrix3x3::~albaMatrix3x3 ( )

virtual

albaMatrix3x3() [2/2]

albaMatrix3x3::albaMatrix3x3

(

albaMatrix3x3 &

mat

)

Member Function Documentation

albaTypeMacro()

albaMatrix3x3::albaTypeMacro	(	albaMatrix3x3	,
		albaObject
	)

Print()

virtual void albaMatrix3x3::Print ( std::ostream &  os, const int  indent = 0  ) const

virtual

print debug information for this object

Reimplemented from albaObject.

operator=()

albaMatrix3x3 & albaMatrix3x3::operator=

(

const albaMatrix3x3 &

mat

)

DeepCopy()

void albaMatrix3x3::DeepCopy

(

albaMatrix3x3 *

mat

)

copy the given matrix content

MultiplyVector() [1/3]

static void albaMatrix3x3::MultiplyVector ( const float  A[3][3], const float  in[3], float  out[3]  )

static

Multiply a vector by a 3x3 matrix.

The result is placed in out.

MultiplyVector() [2/3]

static void albaMatrix3x3::MultiplyVector ( const double  A[3][3], const double  in[3], double  out[3]  )

static

Multiply a vector by a 3x3 matrix.

The result is placed in out.

MultiplyVector() [3/3]

void albaMatrix3x3::MultiplyVector ( const double  in[3], double  out[3]  )

inline

Multiply a vector by this matrix.

The result is placed in out.

Definition at line 55 of file albaMatrix3x3.h.

References MultiplyVector().

Referenced by MultiplyVector().

Here is the call graph for this function:

Multiply() [1/2]

static void albaMatrix3x3::Multiply ( const double  A[3][3], const double  B[3][3], double  C[3][3]  )

static

Multiply one 3x3 matrix by another according to C = AB.

Multiply() [2/2]

static void albaMatrix3x3::Multiply ( const albaMatrix3x3 &  A, albaMatrix3x3 &  B, albaMatrix3x3 &  C  )

inlinestatic

Multiply this matrix by another according to C = AB.

Definition at line 62 of file albaMatrix3x3.h.

GetElements()

albaMatrix3x3Elements albaMatrix3x3::GetElements ( ) const

inline

Definition at line 65 of file albaMatrix3x3.h.

SetElement()

void albaMatrix3x3::SetElement ( int  i, int  j, double  value  )

inline

Sets the element i,j in the matrix.

Remember to call explicitly Modified when using this function.

Definition at line 70 of file albaMatrix3x3.h.

GetElement()

double albaMatrix3x3::GetElement ( int  i, int  j  ) const

inline

Returns the element i,j from the matrix.

Definition at line 73 of file albaMatrix3x3.h.

GetVersor() [1/2]

static void albaMatrix3x3::GetVersor ( int  axis, const albaMatrix3x3 &  matrix, double  versor[3]  )

static

Get the given matrix versor.

Static version.

GetVersor() [2/2]

void albaMatrix3x3::GetVersor ( int  axis, double  versor[3]  )

inline

Get the given matrix versor.

Definition at line 78 of file albaMatrix3x3.h.

References GetVersor().

Referenced by GetVersor().

Here is the call graph for this function:

Zero() [1/2]

void albaMatrix3x3::Zero ( )

inline

Set all of the elements to zero.

Static version.

Definition at line 81 of file albaMatrix3x3.h.

References albaTimeStamped::Modified(), and Zero().

Referenced by Zero().

Here is the call graph for this function:

Zero() [2/2]

static void albaMatrix3x3::Zero ( double  elements[9] )

static

Set all of the elements to zero.

Identity() [1/2]

void albaMatrix3x3::Identity ( )

inline

Set equal to Identity matrix.

Definition at line 86 of file albaMatrix3x3.h.

References Identity(), and albaTimeStamped::Modified().

Referenced by Identity().

Here is the call graph for this function:

Identity() [2/2]

static void albaMatrix3x3::Identity ( double  A[3][3] )

static

Transpose() [1/2]

static void albaMatrix3x3::Transpose ( const double  A[3][3], double  AT[3][3]  )

static

Transpose the 3x3 matrix.

Transpose() [2/2]

void albaMatrix3x3::Transpose ( )

inline

Definition at line 91 of file albaMatrix3x3.h.

References albaTimeStamped::Modified(), and Transpose().

Referenced by Transpose().

Here is the call graph for this function:

Invert() [1/2]

static void albaMatrix3x3::Invert ( const double  A[3][3], double  AI[3][3]  )

static

Invert the 3x3 matrix.

Invert() [2/2]

void albaMatrix3x3::Invert ( )

inline

Definition at line 95 of file albaMatrix3x3.h.

References Invert(), and albaTimeStamped::Modified().

Referenced by Invert().

Here is the call graph for this function:

Orthogonalize() [1/2]

static void albaMatrix3x3::Orthogonalize ( const double  A[3][3], double  B[3][3]  )

static

Orthogonalize a 3x3 matrix and put the result in B.

If matrix A has a negative determinant, then B will be a rotation plus a flip i.e. it will have a determinant of -1.

Orthogonalize() [2/2]

void albaMatrix3x3::Orthogonalize ( )

inline

Orthogonalize this matrix in place.

If this matrix has a negative determinant, then the result will be a rotation plus a flip i.e. it will have a determinant of -1.

Definition at line 107 of file albaMatrix3x3.h.

References albaTimeStamped::Modified(), and Orthogonalize().

Referenced by Orthogonalize().

Here is the call graph for this function:

Diagonalize()

static void albaMatrix3x3::Diagonalize ( const double  A[3][3], double  w[3], double  V[3][3]  )

static

Diagonalize a symmetric 3x3 matrix and return the eigenvalues in w and the eigenvectors in the columns of V.

The matrix V will have a positive determinant, and the three eigenvectors will be aligned as closely as possible with the x, y, and z axes.

Determinant() [1/4]

double albaMatrix3x3::Determinant ( double  A[3][3] )

inlinestatic

Return the determinant of a 3x3 matrix.

Definition at line 235 of file albaMatrix3x3.h.

Determinant() [2/4]

double albaMatrix3x3::Determinant ( )

inline

Compute the determinant of the matrix and return it.

Definition at line 120 of file albaMatrix3x3.h.

References Determinant().

Referenced by Determinant().

Here is the call graph for this function:

Determinant() [3/4]

double albaMatrix3x3::Determinant ( const double  c1[3], const double  c2[3], const double  c3[3]  )

inlinestatic

Definition at line 243 of file albaMatrix3x3.h.

Determinant() [4/4]

double albaMatrix3x3::Determinant ( double  a1, double  a2, double  a3, double  b1, double  b2, double  b3, double  c1, double  c2, double  c3  )

inlinestatic

Definition at line 252 of file albaMatrix3x3.h.

References Determinant2x2().

Here is the call graph for this function:

QuaternionToMatrix() [1/2]

static void albaMatrix3x3::QuaternionToMatrix ( const double  quat[4], double  A[3][3]  )

static

Convert a quaternion to a 3x3 rotation matrix.

The quaternion does not have to be normalized beforehand.

QuaternionToMatrix() [2/2]

void albaMatrix3x3::QuaternionToMatrix ( const double  quat[4] )

inline

Convert a quaternion to a 3x3 rotation matrix.

The quaternion does not have to be normalized beforehand.

Definition at line 138 of file albaMatrix3x3.h.

References QuaternionToMatrix().

Referenced by QuaternionToMatrix().

Here is the call graph for this function:

MatrixToQuaternion() [1/2]

static void albaMatrix3x3::MatrixToQuaternion ( const double  A[3][3], double  quat[4]  )

static

Convert a 3x3 matrix into a quaternion.

This will provide the best possible answer even if the matrix is not a pure rotation matrix. The method used is that of B.K.P. Horn.

MatrixToQuaternion() [2/2]

void albaMatrix3x3::MatrixToQuaternion ( double  quat[4] )

inline

Convert a 3x3 matrix into a quaternion.

This will provide the best possible answer even if the matrix is not a pure rotation matrix. The method used is that of B.K.P. Horn.

Definition at line 150 of file albaMatrix3x3.h.

References MatrixToQuaternion().

Referenced by MatrixToQuaternion().

Here is the call graph for this function:

SingularValueDecomposition() [1/2]

static void albaMatrix3x3::SingularValueDecomposition ( const double  A[3][3], double  U[3][3], double  w[3], double  VT[3][3]  )

static

Perform singular value decomposition on a 3x3 matrix.

This is not done using a conventional SVD algorithm, instead it is done using Orthogonalize3x3 and Diagonalize3x3. Both output matrices U and VT will have positive determinants, and the w values will be arranged such that the three rows of VT are aligned as closely as possible with the x, y, and z axes respectively. If the determinant of A is negative, then the three w values will be negative.

SingularValueDecomposition() [2/2]

void albaMatrix3x3::SingularValueDecomposition ( double  U[3][3], double  w[3], double  VT[3][3]  )

inline

Perform singular value decomposition on a 3x3 matrix.

See the static version.

Definition at line 165 of file albaMatrix3x3.h.

Jacobi()

static int albaMatrix3x3::Jacobi ( const double  A[3][3], double  w[3], double  v[3][3]  )

static

JacobiN()

static int albaMatrix3x3::JacobiN ( double **  a, int  n, double *  w, double **  v  )

static

Jacobi iteration for the solution of eigenvectors/eigenvalues of this 3x3 real symmetric matrix.

Output eigenvalues in w; and output eigenvectors in v. Resulting eigenvalues/vectors are sorted in decreasing order; eigenvectors are normalized. JacobiN iteration for the solution of eigenvectors/eigenvalues of a nxn real symmetric matrix. Square nxn matrix a; size of matrix in n; output eigenvalues in w; and output eigenvectors in v. Resulting eigenvalues/vectors are sorted in decreasing order; eigenvectors are normalized. w and v need to be allocated previously

LUFactor() [1/2]

static void albaMatrix3x3::LUFactor ( double  A[3][3], int  index[3]  )

static

LU Factorization of a 3x3 matrix.

The diagonal elements are the multiplicative inverse of those in the standard LU factorization.

LUFactor() [2/2]

void albaMatrix3x3::LUFactor ( int  index[3] )

inline

Definition at line 194 of file albaMatrix3x3.h.

References LUFactor().

Referenced by LUFactor().

Here is the call graph for this function:

LUSolve() [1/2]

static void albaMatrix3x3::LUSolve ( const double  A[3][3], const int  index[3], double  x[3]  )

static

LU back substitution for a 3x3 matrix.

The diagonal elements are the multiplicative inverse of those in the standard LU factorization.

LUSolve() [2/2]

void albaMatrix3x3::LUSolve ( const int  index[3], double  x[3]  )

inline

Definition at line 200 of file albaMatrix3x3.h.

DegreesToRadians()

static double albaMatrix3x3::DegreesToRadians ( )

inlinestatic

Useful constants.

(double-precision version)

Definition at line 205 of file albaMatrix3x3.h.

Pi()

static double albaMatrix3x3::Pi ( )

inlinestatic

Definition at line 206 of file albaMatrix3x3.h.

RadiansToDegrees()

static double albaMatrix3x3::RadiansToDegrees ( )

inlinestatic

Definition at line 207 of file albaMatrix3x3.h.

operator[]() [1/2]

double * albaMatrix3x3::operator[] ( const unsigned int  i )

inline

bracket operator to access & write single elements

Definition at line 210 of file albaMatrix3x3.h.

operator[]() [2/2]

const double * albaMatrix3x3::operator[] ( unsigned int  i ) const

inline

bracket operator to access single elements

Definition at line 213 of file albaMatrix3x3.h.

Determinant2x2() [1/2]

static double albaMatrix3x3::Determinant2x2 ( double  a, double  b, double  c, double  d  )

inlinestatic

Calculate the determinant of a 2x2 matrix: | a b | | c d |.

Definition at line 216 of file albaMatrix3x3.h.

Referenced by Determinant().

Determinant2x2() [2/2]

static double albaMatrix3x3::Determinant2x2 ( const double  c1[2], const double  c2[2]  )

inlinestatic

Calculate the determinant of a 2x2 matrix with columns c1 and c2.

Definition at line 219 of file albaMatrix3x3.h.

Norm()

static double albaMatrix3x3::Norm ( const double  x[3] )

inlinestatic

Compute the norm of 3-vector (double-precision version).

Definition at line 223 of file albaMatrix3x3.h.

Referenced by Normalize().

Cross()

void albaMatrix3x3::Cross ( const double  x[3], const double  y[3], double  z[3]  )

inlinestatic

Definition at line 263 of file albaMatrix3x3.h.

Normalize()

double albaMatrix3x3::Normalize ( double  x[3] )

inlinestatic

Definition at line 272 of file albaMatrix3x3.h.

References Norm().

Here is the call graph for this function:

Member Data Documentation

m_Elements

double albaMatrix3x3::m_Elements[3][3]

protected

internal representation

Definition at line 231 of file albaMatrix3x3.h.

---

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

• albaMatrix3x3.h