gsHFitting< d, T > Class Template Reference

Detailed Description

template<short_t d, class T>
class gismo::gsHFitting< d, T >

This class applies hierarchical fitting of parametrized point clouds.

Template Parameters

T	coefficient type

Inheritance diagram for gsHFitting< d, T >:

Collaboration diagram for gsHFitting< d, T >:

Public Member Functions
void	applySmoothing (T lambda, gsSparseMatrix< T > &A_mat)
void	assembleSystem (gsSparseMatrix< T > &A_mat, gsMatrix< T > &B)
	Assembles system for the least square fit.
void	compute (T lambda=0)
	Computes the least squares fit for a gsBasis.
void	computeApproxError (T &error, int type=0) const
	Computes the approximation error of the fitted curve to the original point cloud.
void	computeErrors ()
	Computes the euclidean error for each point.
void	computeMaxNormErrors ()
	Computes the maximum norm error for each point.
void	get_Error (std::vector< T > &errors, int type=0) const
	return the errors for each point
const std::vector< unsigned > &	get_extension () const
	Returns the chosen cell extension.
const gsBasis< T > &	getBasis () const
	Returns the basis of the approximation.
std::vector< index_t >	getBoxes (const std::vector< T > &errors, const T threshold)
	Returns boxes which define refinment area.
T	getRefPercentage () const
	Return the refinement percentage.
gsMatrix< T > &	getreturnParamValues ()
	returns the parameter values
	gsHFitting ()
	Default constructor.
	gsHFitting (gsMatrix< T > const &param_values, gsMatrix< T > const &points, gsHTensorBasis< d, T > &basis, T refin, const std::vector< unsigned > &extension, T lambda=0)
	Main constructor of the fitting class. More...
void	iterativeCompute (T const &tolerance, unsigned const &num_iters=10)
	Computes the least squares fit for a gsBasis.
void	iterativeRefine (int iterations, T tolerance, T err_threshold=-1)
	iterative_refine iteratively refine the basis More...
T	maxPointError () const
	Returns the maximum point-wise error from the pount cloud (or zero if not fitted)
T	minPointError () const
	Returns the minimum point-wise error from the pount cloud (or zero if not fitted)
const gsMappedSpline< 2, T > &	mresult () const
	gives back the computed approximation for multipatch geometry
bool	nextIteration (T tolerance, T err_threshold, index_t maxPcIter=0)
	nextIteration One step of the refinement of iterative_refine(...); More...
bool	nextIteration (T tolerance, T err_threshold, const std::vector< boxSide > &fixedSides, index_t maxPcIter=0)
	Like nextIteration without fixedSides but keeping the values on these sides unchanged throughout the fit.
size_t	numPointsBelow (T threshold) const
	Computes the number of points below the error threshold (or zero if not fitted)
const std::vector< T > &	pointWiseErrors () const
	Return the errors for each point.
gsGeometry< T > *	result () const
	gives back the computed approximation
gsMatrix< T >	returnPoints () const
	returns the points
void	setConstraints (const gsSparseMatrix< T > &lhs, const gsMatrix< T > &rhs)
void	setConstraints (const std::vector< index_t > &indices, const std::vector< gsMatrix< T > > &coefs)
void	setConstraints (const std::vector< boxSide > &fixedSides)
void	setConstraints (const std::vector< boxSide > &fixedSides, const std::vector< gsBSpline< T > > &fixedCurves)
void	setExtension (std::vector< unsigned > const &extension)
	Sets the cell extension.
void	setRefPercentage (double refPercent)
	Sets the refinement percentage.

Protected Member Functions
virtual void	appendBox (std::vector< index_t > &boxes, std::vector< index_t > &cells, const gsVector< T > &parameter)
T	setRefineThreshold (const std::vector< T > &errors)
	Identifies the threshold from where we should refine.

Static Protected Member Functions
static void	append (std::vector< index_t > &boxes, const gsVector< index_t > &box)
	Appends a box to the end of boxes (This function also works for cells)
static bool	isCellAlreadyInserted (const gsVector< index_t, d > &a_cell, const std::vector< index_t > &cells)
	Checks if a_cell is already inserted in container of cells.

Protected Attributes
gsFunctionSet< T > *	m_basis
	Pointer keeping the basis.
gsSparseMatrix< T >	m_constraintsLHS
gsMatrix< T >	m_constraintsRHS
std::vector< unsigned >	m_ext
	Size of the extension.
T	m_lambda
	Smoothing parameter.
T	m_max_error
	Maximum point-wise error.
T	m_min_error
	Minimum point-wise error.
gsMappedSpline< 2, T >	m_mresult
	Pointer keeping the resulting multipatch geometry.
gsMatrix< T >	m_param_values
	the parameter values of the point cloud
gsMatrix< T >	m_points
	the points of the point cloud
T	m_ref
	How many % to refine - 0-1 interval.
gsGeometry< T > *	m_result
	Pointer keeping the resulting geometry.

Constructor & Destructor Documentation

gsHFitting ( gsMatrix< T > const &  param_values, gsMatrix< T > const &  points, gsHTensorBasis< d, T > &  basis, T  refin, const std::vector< unsigned > &  extension, T  lambda = 0  )

inline

Main constructor of the fitting class.

Parameters

param_values	a matrix containing the parameter values that parametrize the points
points	The points to be fitted
basis	Hiearchical basis to use for fitting
refin	Percentage of errors to refine (if this strategy is chosen)
extension	Extension to apply to marked cells
lambda	Smoothing parameter

Member Function Documentation

void appendBox ( std::vector< index_t > &  boxes, std::vector< index_t > &  cells, const gsVector< T > &  parameter  )

protectedvirtual

Appends a box around parameter to the boxes only if the box is not already in boxes

void applySmoothing ( T  lambda, gsSparseMatrix< T > &  A_mat  )

inherited

Adds to the matrix A_mat terms for minimization of second derivative, weighted with parameter lambda.

void iterativeRefine	(	int	iterations,
		T	tolerance,
		T	err_threshold = -1
	)

iterative_refine iteratively refine the basis

Parameters

iterations	maximum number of iterations
tolerance	(>=0) if the max error is below the tolerance the refinement stops
err_threshold	if non negative all cells with errors bigger than the threshold are refined / If it is equal to -1 the m_ref percentage is used 0 = global refinement

bool nextIteration	(	T	tolerance,
		T	err_threshold,
		index_t	maxPcIter = 0
	)

nextIteration One step of the refinement of iterative_refine(...);

Parameters

tolerance	(>=0) if the maximum error is below the tolerance the refinement stops;
err_threshold	the same as in iterative_refine(...).

void setConstraints ( const gsSparseMatrix< T > &  lhs, const gsMatrix< T > &  rhs  )

inlineinherited

Sets constraints that the coefficients of the resulting geometry have to conform to. More precisely, denoting the coefficient vector by x, it enforces lhs * x = rhs.

void setConstraints ( const std::vector< index_t > &  indices, const std::vector< gsMatrix< T > > &  coefs  )

inherited

Sets constraints on that the coefficients of the resulting geometry have to conform to.

Parameters

indices	indices (in the coefficient vector) of the prescribed coefficients.
coefs	prescribed coefficients.

void setConstraints ( const std::vector< boxSide > &  fixedSides )

inherited

Sets constraints in such a way that the previous values at fixedSides of the geometry remain intact.

void setConstraints ( const std::vector< boxSide > &  fixedSides, const std::vector< gsBSpline< T > > &  fixedCurves  )

inherited

Set constraints in such a way that the resulting geometry on each of fixedSides will coincide with the corresponding curve in fixedCurves.

Member Data Documentation

gsSparseMatrix<T> m_constraintsLHS

protectedinherited

Left hand-side of the constraints that the coefficients of the resulting geometry have to conform to. This corresponds to matrix D in Prautzch, Boehm, Paluszny: Bezier and B-spline techniques, Section 4.7.

gsMatrix<T> m_constraintsRHS

protectedinherited

Right hand-side of the constraints that the coefficients of the resulting geometry have to conform to. This corresponds to vector q in Prautzch, Boehm, Paluszny: Bezier and B-spline techniques, Section 4.7.