Class for Legendre 2D polynomials computation. More...

#include <gcg.h>

Inheritance diagram for gcgLEGENDREBASIS2D< NUMTYPE >:

Public Member Functions
bool	setBasisDegree (unsigned int degree)
	Sets the maximum degree of the polynomials of the basis. The number of polynomials = (degree + 1)*(degree+2)/2. More...

bool	setNumberOfSamples (unsigned int nsamplesX, unsigned int nsamplesY)
	Sets the number of samples in X and Y directions for the discretization of polynomial functions. Call it (or call synchBasisWithFile()) BEFORE using getDiscreteValue(), projectSignal(), reconstructSignal() or basisInformation(). This method computes all polynomial basis vectors which might be slow if current degree is big. More...

unsigned int	getNumberOfCoefficients ()
	Returns the number of coefficients used in 2D polynomial projection/reconstruction. More...

bool	synchBasisWithFile (const char *filename, unsigned int nsamplesX, unsigned int nsamplesY)
	Loads the basis functions of current degree, discretized with nsamplesX * nsamplesY elements, stored in the given file. All missing polynomials of the file are discretized and saved for further use. This function sychronizes file and memory polynomial functions and can considerably save time. Use this function instead of setNumberOfSamples() to avoid the computation of all basis functions that might be stored in the file. More...

NUMTYPE	getPointValue (unsigned int i, unsigned int j, NUMTYPE x, NUMTYPE y)
	Computes the value Pi,j(x,y), where i+j <= degree, are the polynomial degrees in X and Y axe, and x, y in [-1, 1] * [-1, 1] are the coordinates of the point to be evaluated. More...

NUMTYPE	getIntegralValue (unsigned int i, unsigned int j, NUMTYPE xmin, NUMTYPE xmax, NUMTYPE ymin, NUMTYPE ymax)
	Computes the integral of the polynomial Pi,j in the region [xmin, xmax] * [ymin, ymax]. More...

NUMTYPE	getDiscreteValue (unsigned int i, unsigned int j, unsigned int ix, unsigned int iy)
	Compute normalized value Pi,j(ix, iy), where i+j <= degree, are the polynomial degrees in x and y, and ix in [0, nsamplesX-1], and iy in [0, nsamplesY-1] are the coordinates of the sample of a uniform discretization of the domain [-1, 1] * [-1, 1] with nsamplesX * nsamplesY samples. Call setNumberOfSamples() or synchBasisWithFile() to set the number of samples to be used. More...

bool	projectSignal (int atX, int atY, gcgDISCRETE2D< float > vector, gcgDISCRETE1D< NUMTYPE > outputcoef)
	Computes the ((degree-2) * (degree-1)) / 2) coefficients of the projection of the 2D vector (as 2D signal) on a discretized polynomial basis. Only nsamplesX * nsamplesY elements starting at (atX, atY) are used. The coefficients are stored in the array outputcoef (as 1D signal) that is adjusted to have (degree+2)* (degre+1)/2 elements. Call setNumberOfSamples() to set the number of samples to be used. More...

bool	reconstructSignal (int atX, int atY, gcgDISCRETE1D< NUMTYPE > inputcoef, gcgDISCRETE2D< float > outputvector)
	Computes the nsamplesX * nsamplesY components of a 2D vector, using the (degree+1)(degree+2)/2 coefficients given in array inputcoef* (as 1D signal). The components are stored in the 2D array outputvector (as 2D signal) starting at position (atX, atY). Call setNumberOfSamples() or synchBasisWithFile() to set the number of samples to be used. More...

bool	basisInformation (const char *filename, bool checkorthogonality, bool savefunctionsasimages)
	Output basis information with current degree for numerical analysis. Saves information of the orthogonality of the basis with nsamplesX * nsamplesY elements. More...

Public Member Functions inherited from gcgCLASS
void *	operator new (size_t size)
	Defines a new operator to be used by instatiations of GCGlib classes instead the global one. More...

void *	operator new (size_t size, const std::nothrow_t &) throw ()
	Defines a new operator to be used by instantiations of GCGlib classes instead the global one. Returns a NULL pointer instead of throwing an exception if an error occurs. More...

void *	operator new[] (size_t size)
	Defines a new operator to be used by GCGlib array allocations instead the global one. More...

void *	operator new[] (size_t size, const std::nothrow_t &) throw ()
	Defines a new operator to be used by vector allocations instead the global one. More...

void	operator delete (void *p)
	Defines a delete operator to free instances of GCGlib classes instead the global one. It is designed to match the new operator. More...

void	operator delete (void *p, const std::nothrow_t &) throw ()
	Defines a delete operator to free instances of GCGlib classes instead the global one. It is designed to match the new operator. More...

void	operator delete[] (void *p)
	Defines a delete operator to free instances of arrays for GCGlib classes instead the global one. It is designed to match the new[] operator. More...

void	operator delete[] (void *p, const std::nothrow_t &) throw ()
	Defines a delete operator to free instances of arrays for GCGlib classes instead the global one. It is designed to match the new[] operator. More...

Public Attributes
unsigned int	degree
	Degree of the polynomials. Read-only. See setBasisDegree().

unsigned int	nsamplesX
	Current samples in X direction. Read-only. See setNumberOfSamples().

unsigned int	nsamplesY
	Current samples in Y direction. Read-only. See setNumberOfSamples().

Detailed Description

template<>
class gcgLEGENDREBASIS2D< NUMTYPE >

Class for Legendre 2D polynomials computation.

Template Parameters

NUMTYPE Type of the samples representing the signal. Supported types: float or double.

Use gcgLEGENDREBASIS2D<float> for single precision and gcgLEGENDREBASIS2D<double> for double precision. Methods for projection and reconstruction are avalaible. The performance of the numeric methods can be verified by using the basisInformation() method.

Since: 0.01.6

Member Function Documentation

◆ basisInformation()

bool gcgLEGENDREBASIS2D< NUMTYPE >::basisInformation	(	const char *	filename,
		bool	checkorthogonality,
		bool	savefunctionsasimages
	)

Output basis information with current degree for numerical analysis. Saves information of the orthogonality of the basis with nsamplesX * nsamplesY elements.

Parameters

[in]	filename	name of output text file. Call setNumberOfSamples() or synchBasisWithFile() to set the number of samples to be used.
[in]	checkorthogonality	if true, computes the internal product of all functions of the basis. This can be time consuming.
[in]	savefunctionsasimages	if true, saves the function basis as gray scale images to be visually checked.

Returns: true if file creation was successful.

◆ getDiscreteValue()

NUMTYPE gcgLEGENDREBASIS2D< NUMTYPE >::getDiscreteValue	(	unsigned int	i,
		unsigned int	j,
		unsigned int	ix,
		unsigned int	iy
	)

Compute normalized value Pi,j(ix, iy), where i+j <= degree, are the polynomial degrees in x and y, and ix in [0, nsamplesX-1], and iy in [0, nsamplesY-1] are the coordinates of the sample of a uniform discretization of the domain [-1, 1] * [-1, 1] with nsamplesX * nsamplesY samples. Call setNumberOfSamples() or synchBasisWithFile() to set the number of samples to be used.

Parameters

[in]	i	degree of the polynomial function in X direction.
[in]	j	degree of the polynomial function in Y direction.
[in]	ix	index of the sample in X. Must be in the interval [0 nsamplesX - 1].
[in]	iy	index of the sample in Y. Must be in the interval [0 nsamplesY - 1].

Returns: the normalized value of the sample of function Pi,j at position (ix,iy).

See also: setNumberOfSamples(); synchBasisWithFile(); setBasisDegree(); getSampleValue(); getPointValue()

◆ getIntegralValue()

NUMTYPE gcgLEGENDREBASIS2D< NUMTYPE >::getIntegralValue	(	unsigned int	i,
		unsigned int	j,
		NUMTYPE	xmin,
		NUMTYPE	xmax,
		NUMTYPE	ymin,
		NUMTYPE	ymax
	)

Computes the integral of the polynomial Pi,j in the region [xmin, xmax] * [ymin, ymax].

Parameters

[in]	i	degree of the polynomial function in X direction.
[in]	j	degree of the polynomial function in Y direction.
[in]	xmin	inferior limit of the interval in X.
[in]	xmax	superior limit of the interval in X.
[in]	ymin	inferior limit of the interval in Y.
[in]	ymax	superior limit of the interval in Y.

Returns: the value of the integral of polynomial Pi,j in the interval [xmin, xmax] * [ymin, ymax].

◆ getNumberOfCoefficients()

unsigned int gcgLEGENDREBASIS2D< NUMTYPE >::getNumberOfCoefficients ( )

virtual

Returns the number of coefficients used in 2D polynomial projection/reconstruction.

Returns: the number of polynomials of the basis = degree + 1.

Implements gcgBASIS2D< NUMTYPE >.

◆ getPointValue()

NUMTYPE gcgLEGENDREBASIS2D< NUMTYPE >::getPointValue	(	unsigned int	i,
		unsigned int	j,
		NUMTYPE	x,
		NUMTYPE	y
	)

Computes the value Pi,j(x,y), where i+j <= degree, are the polynomial degrees in X and Y axe, and x, y in [-1, 1] * [-1, 1] are the coordinates of the point to be evaluated.

Parameters

[in]	i	degree of the polynomial function in X direction.
[in]	j	degree of the polynomial function in Y direction.
[in]	x	abcissa coordinate of the point to be evaluated. Must be in the interval [-1, 1]
[in]	y	coordinate of the point to be evaluated. Must be in the interval [-1, 1]

Returns: the value of the polynomial Pi,j at point (x, y).

See also: getSampleValue(); getDiscreteValue()

◆ projectSignal()

bool gcgLEGENDREBASIS2D< NUMTYPE >::projectSignal	(	int	atX,
		int	atY,
		gcgDISCRETE2D< float > *	vector,
		gcgDISCRETE1D< NUMTYPE > *	outputcoef
	)

virtual

Computes the ((degree-2) * (degree-1)) / 2) coefficients of the projection of the 2D vector (as 2D signal) on a discretized polynomial basis. Only nsamplesX * nsamplesY elements starting at (atX, atY) are used. The coefficients are stored in the array outputcoef (as 1D signal) that is adjusted to have (degree+2)* (degre+1)/2 elements. Call setNumberOfSamples() to set the number of samples to be used.

Parameters

[in]	atX	origin X coordinate of the signal for this projection (relative to vector).
[in]	atY	origin Y coordinate of the signal for this projection (relative to vector).
[in]	vector	array (as 2D signal) containing components of the 2D vector to be projected onto the basis.
[out]	outputcoef	array (as 1D signal) that receives the computed coefficients. It is adjusted to have (degree+2)*(degre+1)/2 elements.

Returns: true if projection is successful.

See also: setBasisDegree(); setNumberOfSamples(); synchBasisWithFile(); reconstructSignal()

Implements gcgBASIS2D< NUMTYPE >.

◆ reconstructSignal()

bool gcgLEGENDREBASIS2D< NUMTYPE >::reconstructSignal	(	int	atX,
		int	atY,
		gcgDISCRETE1D< NUMTYPE > *	inputcoef,
		gcgDISCRETE2D< float > *	outputvector
	)

virtual

Computes the nsamplesX * nsamplesY components of a 2D vector, using the (degree+1)*(degree+2)/2 coefficients given in array inputcoef (as 1D signal). The components are stored in the 2D array outputvector (as 2D signal) starting at position (atX, atY). Call setNumberOfSamples() or synchBasisWithFile() to set the number of samples to be used.

Parameters

[in]	atX	origin X coordinate of the signal for this projection (relative to outputvector).
[in]	atY	origin Y coordinate of the signal for this projection (relative to outputvector).
[in]	inputcoef	array (as 1D signal) of (degree+1)*(degree+2)/2 coefficients representing the vector to be reconstructed.
[out]	outputvector	2D array (as 2D signal) that receives the reconstructed vector. Must have room for nsamplesX * nsamplesY elements.

Returns: true if reconstruction is successful.

See also: setBasisDegree(); setNumberOfSamples(); synchBasisWithFile(); projectSignal()

Implements gcgBASIS2D< NUMTYPE >.

◆ setBasisDegree()

bool gcgLEGENDREBASIS2D< NUMTYPE >::setBasisDegree ( unsigned int degree )

Sets the maximum degree of the polynomials of the basis. The number of polynomials = (degree + 1)*(degree+2)/2.

Parameters

[in] degree maximum degree of the polynomial basis.

Returns: true if setup succeded

◆ setNumberOfSamples()

bool gcgLEGENDREBASIS2D< NUMTYPE >::setNumberOfSamples	(	unsigned int	nsamplesX,
		unsigned int	nsamplesY
	)

Sets the number of samples in X and Y directions for the discretization of polynomial functions. Call it (or call synchBasisWithFile()) BEFORE using getDiscreteValue(), projectSignal(), reconstructSignal() or basisInformation(). This method computes all polynomial basis vectors which might be slow if current degree is big.

Parameters

[in]	nsamplesX	number of points in X.
[in]	nsamplesY	number of points in Y.

Returns: true if discretized basis creation is successful.

See also: synchBasisWithFile(); getDiscreteValue(); projectSignal(); reconstructSignal(); basisInformation()

◆ synchBasisWithFile()

bool gcgLEGENDREBASIS2D< NUMTYPE >::synchBasisWithFile	(	const char *	filename,
		unsigned int	nsamplesX,
		unsigned int	nsamplesY
	)

Loads the basis functions of current degree, discretized with nsamplesX * nsamplesY elements, stored in the given file. All missing polynomials of the file are discretized and saved for further use. This function sychronizes file and memory polynomial functions and can considerably save time. Use this function instead of setNumberOfSamples() to avoid the computation of all basis functions that might be stored in the file.

Parameters

[in]	filename	name of the file containing discretized polynomial basis.
[in]	nsamplesX	number of points in X.
[in]	nsamplesY	number of points in Y.

Returns: true if synchronization succeded.

See also: setNumberOfSamples()

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

M:/Documentos/Projetos/Projetos/GCGlib/src/gcg.h

Public Member Functions

Public Attributes

Detailed Description

template<> class gcgLEGENDREBASIS2D< NUMTYPE >

Member Function Documentation

◆ basisInformation()

◆ getDiscreteValue()

◆ getIntegralValue()

◆ getNumberOfCoefficients()

◆ getPointValue()

◆ projectSignal()

◆ reconstructSignal()

◆ setBasisDegree()

◆ setNumberOfSamples()

◆ synchBasisWithFile()

template<>
class gcgLEGENDREBASIS2D< NUMTYPE >