Util::Matrix< Dim, Dim > Class Template Reference

#include <geometry.h>

Inheritance diagram for Util::Matrix< Dim, Dim >:

Public Member Functions
	Matrix (void)
	Matrix (const Matrix< Dim+1, Dim+1 > &m)
	Matrix (const Matrix< Dim-1, Dim-1 > &m, Point< Dim-1 > p=Point< Dim-1 >())
double	subDeterminant (int r, int c) const
double	determinant (void) const
double	trace (void) const
Matrix	inverse (void) const
bool	setInverse (Matrix &m) const
Point< Dim-1 >	operator* (const Point< Dim-1 > &p) const
void	SVD (Matrix &r1, Matrix &diagonal, Matrix &r2) const
Matrix	symmetrize (void) const
Matrix	skewSymmetrize (void) const
Matrix	closestRotation (void) const
template<unsigned int Cols>
Matrix< Dim, Cols >	operator* (const Matrix< Dim, Cols > &m) const
Public Member Functions inherited from Util::_BaseMatrix< Dim, Dim, Matrix< Dim, Dim >, Matrix< Dim, Dim > >
	_BaseMatrix (void)
double &	operator() (int r, int c)
const double &	operator() (int r, int c) const
Matrix< Dim, Dim >	transpose (void) const
Point< Rows >	operator* (const Point< Cols > &p) const
Matrix< Dim, Dim >	operator* (double s) const
Matrix< Dim, Dim >	operator+ (const Matrix< Dim, Dim > &m) const
double	dot (const _BaseMatrix &p) const
Public Member Functions inherited from Util::_InnerProductSpace< Matrix< Dim, Dim > >
double	squareNorm (void) const
double	length (void) const
Matrix< Dim, Dim >	unit (void) const

Static Public Member Functions
static Matrix	Identity (void)
static Matrix	Log (const Matrix &m, double eps=0.0001)
static Matrix	SquareRoot (const Matrix &m, double eps=0.000001)
static Matrix	Exp (const Matrix &m, int terms=100)
Static Public Member Functions inherited from Util::_InnerProductSpace< Matrix< Dim, Dim > >
static double	Dot (const Matrix< Dim, Dim > &e1, const Matrix< Dim, Dim > &e2)
static double	SquareNorm (const Matrix< Dim, Dim > &e)
static double	Length (const Matrix< Dim, Dim > &e)
static double	SquareDistance (const Matrix< Dim, Dim > &e1, const Matrix< Dim, Dim > &e2)
static double	Distance (const Matrix< Dim, Dim > &e1, const Matrix< Dim, Dim > &e2)

Detailed Description

template<unsigned int Dim>
class Util::Matrix< Dim, Dim >

Specialization of the matrix class for the case when it is square.

Constructor & Destructor Documentation

Matrix() [1/3]

template<unsigned int Dim>

Util::SquareMatrix::Matrix

(

void

)

The default constructor that initializes the matrix to zero.

Matrix() [2/3]

template<unsigned int Dim>

Util::Matrix< Dim, Dim >::Matrix

(

const Matrix< Dim+1, Dim+1 > &

m

)

This constructor generates a matrix by slicing out the top left sub-matrix

Matrix() [3/3]

template<unsigned int Dim>

Util::Matrix< Dim, Dim >::Matrix	(	const Matrix< Dim-1, Dim-1 > &	m,
		Point< Dim-1 >	p = Point< Dim-1 >() )

This constructor generates matrix by projectivizing the input matrix, using m as the linear part and p as the translation.

Member Function Documentation

closestRotation()

template<unsigned int Dim>

Matrix< Dim, Dim > Util::Matrix< Dim, Dim >::closestRotation

(

void

)

const

This method returns the closest rotation matrix

determinant()

template<unsigned int Dim>

double Util::SquareMatrix::determinant

(

void

)

const

This method returns the determinant of the matrix.

Exp()

template<unsigned int Dim>

Matrix< Dim, Dim > Util::Matrix< Dim, Dim >::Exp ( const Matrix< Dim, Dim > & m, int terms = 100 )

static

This method returns the exponent of a matrix using a Taylor approximation with the specified number of terms.

Identity()

template<unsigned int Dim>

SquareMatrix< Dim > Util::SquareMatrix::Identity ( void )

static

This static method returns the identity matrix.

inverse()

template<unsigned int Dim>

SquareMatrix< Dim > Util::SquareMatrix::inverse

(

void

)

const

This method returns the inverse of a matrix. The method throws an exception if the determinant is zero.

Log()

template<unsigned int Dim>

SquareMatrix< Dim > Util::SquareMatrix::Log ( const Matrix< Dim, Dim > & m, double eps = 0.0001 )

static

This method returns the logarithm of a matrix, using the specified threshold to terminate the approxmation.

operator*() [1/2]

template<unsigned int Dim>

template<unsigned int Cols>

Matrix< Dim, Cols > Util::SquareMatrix::operator*

(

const Matrix< Dim, Cols > &

m

)

const

Multiplication of matrices

operator*() [2/2]

template<unsigned int Dim>

Point< Dim-1 > Util::SquareMatrix::operator*

(

const Point< Dim-1 > &

p

)

const

This method transforms a (Dim-1)-dimensional point by applying the projective transformation.

setInverse()

template<unsigned int Dim>

bool Util::SquareMatrix::setInverse

(

Matrix< Dim, Dim > &

m

)

const

This method tries to set the reference to the inverse of the matrix. The boolean value indicates if it succeeded (i.e. if the matrix is non-singular).

skewSymmetrize()

template<unsigned int Dim>

SquareMatrix< Dim > Util::SquareMatrix::skewSymmetrize

(

void

)

const

This method returns nearest skew-symmetric matrix

SquareRoot()

template<unsigned int Dim>

SquareMatrix< Dim > Util::SquareMatrix::SquareRoot ( const Matrix< Dim, Dim > & m, double eps = 0.000001 )

static

This method returns the square-root of a matrix, using the specified threshold to terminate the approxmation.

subDeterminant()

template<unsigned int Dim>

double Util::SquareMatrix::subDeterminant	(	int	r,
		int	c ) const

This method returns the determinant of the sub-matrix with the prescribed columns and rows removed.

SVD()

template<unsigned int Dim>

void Util::SquareMatrix::SVD	(	Matrix< Dim, Dim > &	r1,
		Matrix< Dim, Dim > &	diagonal,
		Matrix< Dim, Dim > &	r2 ) const

This method computes the SVD decomposition of the Dim x Dim matrix, such that r1 and r2 are rotations and the Dim x Dim matrix is equal to r1*diagonal*r2

symmetrize()

template<unsigned int Dim>

SquareMatrix< Dim > Util::SquareMatrix::symmetrize

(

void

)

const

This method returns nearest symmetric matrix

trace()

template<unsigned int Dim>

double Util::SquareMatrix::trace

(

void

)

const

This method returns the trace of the matrix.

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

• Assignments/Util/geometry.h
• Assignments/Util/geometry.inl
• Assignments/Util/geometry.todo.inl