Detailed Description

template<class T>
class gismo::gsFitting< T >

Class for performing a fit of a parametrized point cloud with a gsGeometry.

Inheritance diagram for gsFitting< T >:

Collaboration diagram for gsFitting< T >:

Public Types
enum	tdm_method
	choose the method for computing the coefficients: TDM, PDM, HDM with different blending weights

Public Member Functions
void	applySmoothing (T lambda, gsSparseMatrix< T > &A_mat)
	Adds to the matrix A_mat terms for minimization of second derivative, weighted with parameter lambda.

void	assembleSystem (const gsMatrix< T > &points_int, const gsMatrix< T > &params_int, const gsMatrix< T > &points_bdy, const gsMatrix< T > &params_bdy, const index_t &num_basis, const gsSparseMatrix< T > &NNT, gsSparseMatrix< T > &A_tilde, gsMatrix< T > &rhs)
	assembleSystem: assembles the linear system for the Hybrid Distance Minimization method

void	assembleSystem (gsSparseMatrix< T > &A_mat, gsMatrix< T > &B)
	Assembles system for the least square fit.

void	blending_weights (const gsSparseMatrix< T > &N_int, const index_t &num_int, const T &mu, const T &sigma, const gsMatrix< T > &params_int, tdm_method method, gsSparseMatrix< T > &NNT)
	blending_weights: computes the blending weights mu and sigma for the balance mu * PDM + sigma * TDM in the HDM method

void	compute (T lambda=0)
	compute: Computes the coefficients of the spline geometry via penalized least squares

void	compute_normals (const index_t &num_int, const gsMatrix< T > &params_int, gsSparseMatrix< T > &N_int)
	compute_normals: Computes the normals of the fitted geometry at the input parameter values params_int

void	compute_tdm (T lambda, T mu, T sigma, const std::vector< index_t > &interpIdx, tdm_method method=hybrid_curvature_pdm_tdm_boundary_pdm)
	compute_hdm: computes the coefficients of the spline geometry via Hybrid Distance Minimization (HDM)

void	computeApproxError (T &error, int type=0) const

void	computeErrors ()

std::vector< T >	computeErrors (const gsMatrix<> &param_values, const gsMatrix<> &points)

void	computeMaxNormErrors ()

gsMatrix< T >	fill_pointWiseErrors (const index_t &num_int, T &max_err_int)
	vector of length num_int containing all the point-wise errors; store also the max err value in max_err_int

void	get_Error (std::vector< T > &errors, int type=0) const

const gsBasis< T > &	getBasis () const
	Returns the basis of the approximation.

	gsFitting ()
	default constructor

	gsFitting (gsMatrix< T > const &param_values, gsMatrix< T > const &points, gsBasis< T > &basis)
	gsFitting: Main constructor of the fitting class

	gsFitting (gsMatrix< T > const &param_values, gsMatrix< T > const &points, gsVector< index_t > offset, gsMappedBasis< 2, T > &mbasis)
	gsFitting: Main constructor of the fitting class for multi-patch

void	initializeGeometry (const gsMatrix< T > &coefficients, const gsMatrix< T > &parameters)
	initializeGeometry: Initializes the fitted geometry with given coefficients and parameters

void	initParametricDomain ()
	Initialize the parametric domain of the point cloud.

gsMatrix< T >	inverse_principal_curvatures (const index_t &num_int, const gsMatrix< T > &params_int)
	vector of length num_int containing rho = 1/max(c1, c2), where c1, c2 are the principal curvature values computed at every parametric point params_int

bool	is_corner (gsMatrix< T > &parametric_domain, gsVector< T > &parameter)
	check if the given parameter parameter is a corner of the domain parametric_domain

bool	is_point_inside_support (const gsMatrix< T > &parameter, const gsMatrix< T > &support)

bool	is_point_inside_support (const T x, const T y, const gsMatrix< T > &support)
	check if the given parameter x, y is inside the support support; same as is_point_inside_support, but different input format

bool	is_point_within_cell (const gsMatrix< T > &parameter, const gsMatrix< T > &element)
	check if the given parameter parameter is within the cell element

bool	is_point_within_cell (const T x, const T y, const gsMatrix< T > &element)
	check if the given parameter x, y is within the cell element; same as is_point_within_cell, but different input format

void	iterativeCompute (T const &tolerance, unsigned const &num_iters=10)
	Computes the least squares fit for a gsBasis.

T	lambda () const
	Returns the smoothing weight used in the last fitting.

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

size_t	numPointsBelow (T threshold) const
	Computes the number of points below the error threshold (or zero if not fitted)

void	parameterCorrection (T accuracy=1e-8, index_t maxIter=10, T tolOrth=1e-6)
	parameterCorrection: globally apply maxIter steps of parameter correction to the least squares fitted geometry

void	parameterCorrectionSepBoundary_pdm (T accuracy, index_t maxIter, const std::vector< index_t > &sepIndex)
	parameterCorrectionSepBoundary_pdm: apply maxIter steps of parameter correction for PDM method, separating interior and boundary points

void	parameterCorrectionSepBoundary_tdm (T accuracy, index_t maxIter, T mu, T sigma, const std::vector< index_t > &sepIndex, tdm_method method=hybrid_curvature_pdm_tdm_boundary_pdm)
	parameterCorrectionSepBoundary_tdm: apply maxIter steps of parameter correction for HDM method, separating interior and boundary points

void	parameterProjectionSepBoundary (T accuracy, const std::vector< index_t > &interpIdx)
	parameterProjectionSepBoundary: project the points onto the fitted geometry, separating interior and boundary points

const std::vector< T > &	pointWiseErrors () const
	Return the errors for each point.

gsMatrix< T >	pointWiseErrors (const gsMatrix<> &parameters, const gsMatrix<> &points)

gsMatrix< T >	principal_curvatures (const gsMatrix< T > &params)
	compute the principal curvatures (c1, c2) at the given parameters params

gsGeometry< T > *	result () const
	gives back the computed approximation

gsMatrix< T > &	returnParamValues ()
	returns the parameter values

gsMatrix< T >	returnPoints () const
	returns the points

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

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

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

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

void	updateGeometry (gsMatrix< T > coefficients, gsMatrix< T > parameters)
	updateGeometry: Updates the fitted geometry with new coefficients and parameters

virtual	~gsFitting ()
	Destructor.

Protected Member Functions
void	assembleBlockB (const gsMatrix< T > &points, const gsMatrix< T > &params, index_t num_basis, gsSparseMatrix< T > &result) const
	Assembles 3xblock collocation matrix.

void	assembleBlockX (const gsMatrix< T > &points, gsMatrix< T > &result) const
	Assembles the right hand side vectors for PDM/TDM.

Protected Attributes
gsFunctionSet< T > *	m_basis
	Pointer keeping the basis.

gsSparseMatrix< T >	m_constraintsLHS

gsMatrix< T >	m_constraintsRHS

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

gsGeometry< T > *	m_result
	Pointer keeping the resulting geometry.

Private Member Functions
void	extendSystem (gsSparseMatrix< T > &A_mat, gsMatrix< T > &m_B)
	Extends the system of equations by taking constraints into account.

Constructor & Destructor Documentation

◆ gsFitting()

template<class T >

gsFitting	(	gsMatrix< T > const &	param_values,
		gsMatrix< T > const &	points,
		gsBasis< T > &	basis
	)

gsFitting: Main constructor of the fitting class

Parameters

param_values	a matrix containing the parameter values that parametrize the points
points	matrix containing the points to be fitted
basis	basis to use for fitting

Member Function Documentation

◆ assembleSystem()

template<class T >

void assembleSystem	(	const gsMatrix< T > &	points_int,
		const gsMatrix< T > &	params_int,
		const gsMatrix< T > &	points_bdy,
		const gsMatrix< T > &	params_bdy,
		const index_t &	num_basis,
		const gsSparseMatrix< T > &	NNT,
		gsSparseMatrix< T > &	A_tilde,
		gsMatrix< T > &	rhs
	)

assembleSystem: assembles the linear system for the Hybrid Distance Minimization method

Parameters

points_int	interior points
params_int	interior parameters
points_bdy	boundary points
params_bdy	boundary parameters
num_basis	dimension of the basis
NNT	matrix containing the normals and the blending weights
A_tilde	output system matrix
rhs	output right-hand side vector

◆ blending_weights()

template<class T >

void blending_weights	(	const gsSparseMatrix< T > &	N_int,
		const index_t &	num_int,
		const T &	mu,
		const T &	sigma,
		const gsMatrix< T > &	params_int,
		tdm_method	method,
		gsSparseMatrix< T > &	NNT
	)

blending_weights: computes the blending weights mu and sigma for the balance mu * PDM + sigma * TDM in the HDM method

Parameters

N_int	matrix containing the nomals at the parameters params_int
num_int	indeces of the interior parameters
mu	weight for PDM
sigma	weight for TDM
params_int	input parameter values
method	method for computing the blending weights: constant, based on point-wise error, based on curvature
NNT	output matrix containing the normals and the blending weights

◆ compute()

template<class T >

void compute ( T lambda = 0 )

compute: Computes the coefficients of the spline geometry via penalized least squares

Parameters

lambda smoothing weight

◆ compute_normals()

template<class T >

void compute_normals	(	const index_t &	num_int,
		const gsMatrix< T > &	params_int,
		gsSparseMatrix< T > &	N_int
	)

compute_normals: Computes the normals of the fitted geometry at the input parameter values params_int

Parameters

num_int	index of the input parameter values
params_int	input parameter values
N_int	matrix containing the normals

◆ compute_tdm()

template<class T >

void compute_tdm	(	T	lambda,
		T	mu,
		T	sigma,
		const std::vector< index_t > &	interpIdx,
		tdm_method	method = `hybrid_curvature_pdm_tdm_boundary_pdm`
	)

compute_hdm: computes the coefficients of the spline geometry via Hybrid Distance Minimization (HDM)

Parameters

lambda	smoothing weight
mu	weight for the PDM
sigma	weight for the TDM
interpIdx	vector containing the number of interior points and the indices of the boundary points
method	method for computing the blending weights

◆ computeApproxError()

template<class T >

void computeApproxError	(	T &	error,
		int	type = `0`
	)		const

Computes the approximation error error of the fitted geometry to the original point cloud type = 0: sum of squares, type = 1: sum of absolute values (l_1 norm)

◆ computeErrors() [1/2]

template<class T >

void computeErrors ( )

Computes the point-wise errors in euclidean norm as well as the max and min errors, and updates the member variables m_pointErrors, m_max_error, m_min_error; different from computeMaxNormErrors(), where the error is computed in inifinity/maximum norm

◆ computeErrors() [2/2]

template<class T >

std::vector< T > computeErrors	(	const gsMatrix<> &	param_values,
		const gsMatrix<> &	points
	)

Computes min, max and mse errors in euclidean norms between the fitted geometry at the parameters param_values and the input point cloud points it does not update the member variables

◆ computeMaxNormErrors()

template<class T >

void computeMaxNormErrors ( )

Computes the point-wise errors in infinity/maximum norm as well as the max and min errors, and updates the member variables m_pointErrors, m_max_error, m_min_error; different from computeErrors(), where the error is computed in euclidean norm

◆ get_Error()

template<class T >

void get_Error	(	std::vector< T > &	errors,
		int	type = `0`
	)		const

Compute the point-wise errors for each point type = 0: point-wise infinity/maximum norm

◆ initializeGeometry()

template<class T >

void initializeGeometry	(	const gsMatrix< T > &	coefficients,
		const gsMatrix< T > &	parameters
	)

initializeGeometry: Initializes the fitted geometry with given coefficients and parameters

Parameters

coefficients	the input coefficients
parameters	the input parameters

◆ is_point_inside_support()

template<class T >

bool is_point_inside_support	(	const gsMatrix< T > &	parameter,
		const gsMatrix< T > &	support
	)

check if the given parameter parameter is inside the support support difference with is_point_inside_cell in the inclusion of the left and right interval extremes.

◆ parameterCorrection()

template<class T >

void parameterCorrection	(	T	accuracy = `1e-8`,
		index_t	maxIter = `10`,
		T	tolOrth = `1e-6`
	)

parameterCorrection: globally apply maxIter steps of parameter correction to the least squares fitted geometry

Parameters

accuracy	accuracy of the closest point computation
maxIter	maximum number of parameter correction steps
tolOrth	orthogonality tolerance

◆ parameterCorrectionSepBoundary_pdm()

template<class T >

void parameterCorrectionSepBoundary_pdm	(	T	accuracy,
		index_t	maxIter,
		const std::vector< index_t > &	sepIndex
	)

parameterCorrectionSepBoundary_pdm: apply maxIter steps of parameter correction for PDM method, separating interior and boundary points

Parameters

accuracy	accuracy of the closest point computation
maxIter	maximum number of parameter correction steps
sepIndex	vector containing the number of interior points and the indices of the boundary points

◆ parameterCorrectionSepBoundary_tdm()

template<class T >

void parameterCorrectionSepBoundary_tdm	(	T	accuracy,
		index_t	maxIter,
		T	mu,
		T	sigma,
		const std::vector< index_t > &	sepIndex,
		tdm_method	method = `hybrid_curvature_pdm_tdm_boundary_pdm`
	)

parameterCorrectionSepBoundary_tdm: apply maxIter steps of parameter correction for HDM method, separating interior and boundary points

Parameters

accuracy	accuracy of the closest point computation
maxIter	maximum number of parameter correction steps
mu	weight for PDM
sigma	weight for TDM
sepIndex	vector containing the number of interior points and the indices of the boundary points
method	method for computing the blending weights

◆ parameterProjectionSepBoundary()

template<class T >

void parameterProjectionSepBoundary	(	T	accuracy,
		const std::vector< index_t > &	interpIdx
	)

parameterProjectionSepBoundary: project the points onto the fitted geometry, separating interior and boundary points

Parameters

accuracy	accuracy of the closest point computation, for the foot-point projection
interpIdx	vector containing the number of interior points and the indices of the boundary points

◆ pointWiseErrors()

template<class T >

gsMatrix< T > pointWiseErrors	(	const gsMatrix<> &	parameters,
		const gsMatrix<> &	points
	)

Compute point-wise error in euclidean norm between the fitted geometry at the parameters parameters and the input point cloud points similar to computeErrors(), but different input and output format; it does not update the member variables

◆ setConstraints() [1/4]

template<class T >

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

inline

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.

◆ setConstraints() [2/4]

template<class T >

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

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

◆ setConstraints() [3/4]

template<class T >

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

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

◆ setConstraints() [4/4]

template<class T >

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

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.

◆ updateGeometry()

template<class T >

void updateGeometry	(	gsMatrix< T >	coefficients,
		gsMatrix< T >	parameters
	)

updateGeometry: Updates the fitted geometry with new coefficients and parameters

Parameters

coefficients	the new coefficients
parameters	the new parameters

Member Data Documentation

◆ m_constraintsLHS

template<class T >

gsSparseMatrix<T> m_constraintsLHS

protected

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.

◆ m_constraintsRHS

template<class T >

gsMatrix<T> m_constraintsRHS

protected

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.

Detailed Description

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Constructor & Destructor Documentation

◆ gsFitting()

Member Function Documentation

◆ assembleSystem()

◆ blending_weights()

◆ compute()

◆ compute_normals()

◆ compute_tdm()

◆ computeApproxError()

◆ computeErrors() [1/2]

◆ computeErrors() [2/2]

◆ computeMaxNormErrors()

◆ get_Error()

◆ initializeGeometry()

◆ is_point_inside_support()

◆ parameterCorrection()

◆ parameterCorrectionSepBoundary_pdm()

◆ parameterCorrectionSepBoundary_tdm()

◆ parameterProjectionSepBoundary()

◆ pointWiseErrors()

◆ setConstraints() [1/4]

◆ setConstraints() [2/4]

◆ setConstraints() [3/4]

◆ setConstraints() [4/4]

◆ updateGeometry()

Member Data Documentation

◆ m_constraintsLHS

◆ m_constraintsRHS