Fitting a 2D B-Spline curve to 2D point-clouds using asymmetric point-distance-minimization Based on paper: TODO. More...

#include <fitting_curve_2d_apdm.h>

Inheritance diagram for pcl::on_nurbs::FittingCurve2dAPDM:

[legend]

List of all members.

Classes
struct	FitParameter
struct	Parameter
	Parameters for fitting. More...
Public Member Functions
void	addCPsOnClosestPointViolation (double max_error)
	Adds control points in the middle and of elements, if the ends or the middle of the element is farther than max_error to the closest data point.
virtual void	assemble (const Parameter &parameter)
	Assemble the system of equations for fitting.
void	fitting (FitParameter &param)
	Fitting with iterative refinement and adaptive knot insertion.
	FittingCurve2dAPDM (int order, NurbsDataCurve2d *data)
	Constructor initializing B-Spline curve using initNurbsCurve2D(...).
	FittingCurve2dAPDM (NurbsDataCurve2d *data, const ON_NurbsCurve &nc)
	Constructor initializing with the B-Spline curve given in argument 2.
void	refine ()
	Refines curve by inserting a knot in the middle of each element.
void	refine (double xi)
	Refines curve by inserting a knot in the middle of the element belonging to xi.
void	setInverseParams (int max_steps=200, double accuracy=1e-6)
	Set parameters for inverse mapping.
void	setQuiet (bool val)
	Enable/Disable debug outputs in console.
virtual double	solve (double damp=1.0)
	Solve system of equations using Eigen or UmfPack (can be defined in on_nurbs.cmake), and updates B-Spline curve if a solution can be obtained.
virtual double	updateCurve (double damp)
	Update curve according to the current system of equations.
Static Public Member Functions
static double	findClosestElementMidPoint (const ON_NurbsCurve &nurbs, const Eigen::Vector2d &pt)
	Given a point pt, the function finds the closest midpoint of the elements of the curve.
static double	findClosestElementMidPoint (const ON_NurbsCurve &nurbs, const Eigen::Vector2d &pt, double hint)
static int	findElement (double xi, const std::vector< double > &elements)
	Find the element in which the parameter xi lies.
static std::vector< double >	getElementVector (const ON_NurbsCurve &nurbs)
	Get the elements of a B-Spline curve.
static ON_NurbsCurve	initCPsNurbsCurve2D (int order, const vector_vec2d &cps)
	Initialize a closed B-Spline curve given a list of control points.
static ON_NurbsCurve	initNurbsCurve2D (int order, const vector_vec2d &data, int ncps=0, double radiusF=1.0)
	Initialize a closed B-Spline curve using the bounding circle of the point-cloud.
static double	inverseMapping (const ON_NurbsCurve &nurbs, const Eigen::Vector2d &pt, const double &hint, double &error, Eigen::Vector2d &p, Eigen::Vector2d &t, double rScale, int maxSteps=100, double accuracy=1e-6, bool quiet=true)
	Inverse mapping / point inversion: Given a point pt, this function finds the closest point on the B-Spline curve using Newtons method and point-distance (L2-, Euclidean norm).
static double	inverseMappingO2 (const ON_NurbsCurve &nurbs, const Eigen::Vector2d &pt, double &error, Eigen::Vector2d &p, Eigen::Vector2d &t)
static ON_NurbsCurve	removeCPsOnLine (const ON_NurbsCurve &nurbs, double min_curve_th=-0.9)
	Removes control points when it is collinear with its neighboring control points.
Public Attributes
NurbsDataCurve2d *	m_data
ON_NurbsCurve	m_nurbs
ON_TextLog	m_out
Protected Member Functions
virtual void	addCageRegularisation (double weight, unsigned &row, const std::vector< double > &elements, double wConcav=0.0)
	Add minimization constraint: smoothness by control point regularisation.
virtual void	addPointConstraint (const double &param, const Eigen::Vector2d &point, double weight, unsigned &row)
	Add minimization constraint: point-to-curve distance (point-distance-minimization).
virtual void	assembleClosestPoints (const std::vector< double > &elements, double weight, double sigma2, unsigned samples_per_element, unsigned &row)
	Assemble closest points constraints. At each midpoint of the curve elements the closest data points are computed and point-to-curve constraints are added.
virtual void	assembleInterior (double wInt, double sigma2, double rScale, unsigned &row)
	Assemble point-to-curve constraints.
Protected Attributes
double	in_accuracy
int	in_max_steps
bool	m_quiet
NurbsSolve	m_solver

Detailed Description

Fitting a 2D B-Spline curve to 2D point-clouds using asymmetric point-distance-minimization Based on paper: TODO.

Author:: Thomas Mörwald

Definition at line 55 of file fitting_curve_2d_apdm.h.

Constructor & Destructor Documentation

FittingCurve2dAPDM::FittingCurve2dAPDM	(	int	order,
		NurbsDataCurve2d *	data
	)

Constructor initializing B-Spline curve using initNurbsCurve2D(...).

Parameters:

[in]	order	the polynomial order of the B-Spline curve.
[in]	data	pointer to the 2D point-cloud data to be fit.

Definition at line 44 of file fitting_curve_2d_apdm.cpp.

FittingCurve2dAPDM::FittingCurve2dAPDM	(	NurbsDataCurve2d *	data,
		const ON_NurbsCurve &	nc
	)

Constructor initializing with the B-Spline curve given in argument 2.

Parameters:

[in]	data	pointer to the 2D point-cloud data to be fit.
[in]	nc	B-Spline curve used for fitting.

Definition at line 59 of file fitting_curve_2d_apdm.cpp.

Member Function Documentation

void FittingCurve2dAPDM::addCageRegularisation	(	double	weight,
		unsigned &	row,
		const std::vector< double > &	elements,
		double	wConcav = `0.0`
	)		`[protected, virtual]`

Add minimization constraint: smoothness by control point regularisation.

Reimplemented in pcl::on_nurbs::FittingCurve2dASDM, and pcl::on_nurbs::FittingCurve2dATDM.

Definition at line 410 of file fitting_curve_2d_apdm.cpp.

void FittingCurve2dAPDM::addCPsOnClosestPointViolation ( double max_error )

Adds control points in the middle and of elements, if the ends or the middle of the element is farther than max_error to the closest data point.

Parameters:

[in] max_error defining the max allowed distance between data points and curve.

Definition at line 237 of file fitting_curve_2d_apdm.cpp.

void FittingCurve2dAPDM::addPointConstraint	(	const double &	param,
		const Eigen::Vector2d &	point,
		double	weight,
		unsigned &	row
	)		`[protected, virtual]`

Add minimization constraint: point-to-curve distance (point-distance-minimization).

Definition at line 388 of file fitting_curve_2d_apdm.cpp.

void FittingCurve2dAPDM::assemble ( const Parameter & parameter ) [virtual]

Assemble the system of equations for fitting.

for large point-clouds this is time consuming.
should be done once before refinement to initialize the starting points for point inversion.

Reimplemented in pcl::on_nurbs::FittingCurve2dASDM, and pcl::on_nurbs::FittingCurve2dATDM.

Definition at line 142 of file fitting_curve_2d_apdm.cpp.

void FittingCurve2dAPDM::assembleClosestPoints	(	const std::vector< double > &	elements,
		double	weight,
		double	sigma2,
		unsigned	samples_per_element,
		unsigned &	row
	)		`[protected, virtual]`

Assemble closest points constraints. At each midpoint of the curve elements the closest data points are computed and point-to-curve constraints are added.

Definition at line 736 of file fitting_curve_2d_apdm.cpp.

void FittingCurve2dAPDM::assembleInterior	(	double	wInt,
		double	sigma2,
		double	rScale,
		unsigned &	row
	)		`[protected, virtual]`

Assemble point-to-curve constraints.

Reimplemented in pcl::on_nurbs::FittingCurve2dASDM, and pcl::on_nurbs::FittingCurve2dATDM.

Definition at line 641 of file fitting_curve_2d_apdm.cpp.

double FittingCurve2dAPDM::findClosestElementMidPoint	(	const ON_NurbsCurve &	nurbs,
		const Eigen::Vector2d &	pt
	)		`[static]`

Given a point pt, the function finds the closest midpoint of the elements of the curve.

Parameters:

[in]	nurbs	the B-Spline curve.
[in]	pt	the point to which the closest midpoint of the elements will be computed. return closest midpoint in parametric domain.

Definition at line 1084 of file fitting_curve_2d_apdm.cpp.

double FittingCurve2dAPDM::findClosestElementMidPoint	(	const ON_NurbsCurve &	nurbs,
		const Eigen::Vector2d &	pt,
		double	hint
	)		`[static]`

Definition at line 1035 of file fitting_curve_2d_apdm.cpp.

int FittingCurve2dAPDM::findElement	(	double	xi,
		const std::vector< double > &	elements
	)		`[static]`

Find the element in which the parameter xi lies.

Parameters:

[in]	xi	value in parameter domain of the B-Spline curve.
[in]	elements	the vector of elements of the curve.

Returns:: index of the element with respect to elements.

Definition at line 72 of file fitting_curve_2d_apdm.cpp.

void FittingCurve2dAPDM::fitting ( FitParameter & param )

Fitting with iterative refinement and adaptive knot insertion.

Parameters:

[in] param The parameters for fitting

Definition at line 117 of file fitting_curve_2d_apdm.cpp.

std::vector< double > FittingCurve2dAPDM::getElementVector ( const ON_NurbsCurve & nurbs ) [static]

Get the elements of a B-Spline curve.

Definition at line 612 of file fitting_curve_2d_apdm.cpp.

ON_NurbsCurve FittingCurve2dAPDM::initCPsNurbsCurve2D	(	int	order,
		const vector_vec2d &	cps
	)		`[static]`

Initialize a closed B-Spline curve given a list of control points.

Parameters:

[in]	order	polynomial order of the curve.
[in]	cps	sequence of control points.

Returns:: B-Spline curve.

Definition at line 504 of file fitting_curve_2d_apdm.cpp.

ON_NurbsCurve FittingCurve2dAPDM::initNurbsCurve2D	(	int	order,
		const vector_vec2d &	data,
		int	ncps = `0`,
		double	radiusF = `1.0`
	)		`[static]`

Initialize a closed B-Spline curve using the bounding circle of the point-cloud.

Parameters:

[in]	order	polynomial order of the curve.
[in]	data	2D point-cloud
[in]	ncps	number of control points
[in]	radiusF	radius factor multiplied to the radius of the bounding circle.

Returns:: B-Spline curve.

Definition at line 539 of file fitting_curve_2d_apdm.cpp.

double FittingCurve2dAPDM::inverseMapping	(	const ON_NurbsCurve &	nurbs,
		const Eigen::Vector2d &	pt,
		const double &	hint,
		double &	error,
		Eigen::Vector2d &	p,
		Eigen::Vector2d &	t,
		double	rScale,
		int	maxSteps = `100`,
		double	accuracy = `1e-6`,
		bool	quiet = `true`
	)		`[static]`

Inverse mapping / point inversion: Given a point pt, this function finds the closest point on the B-Spline curve using Newtons method and point-distance (L2-, Euclidean norm).

Parameters:

[in]	nurbs	the B-Spline curve.
[in]	pt	the point to which the closest point on the curve will be computed.
[in]	hint	the starting point in parametric domain (warning: may lead to convergence at local minima).
[in]	error	the distance between the point pt and p after convergence.
[in]	p	closest point on curve.
[in]	t	the tangent vector at point p.
[in]	maxSteps	maximum number of iterations.
[in]	accuracy	convergence criteria: if error is lower than accuracy the function returns

Returns:: closest point on curve in parametric domain.

Definition at line 802 of file fitting_curve_2d_apdm.cpp.

double FittingCurve2dAPDM::inverseMappingO2	(	const ON_NurbsCurve &	nurbs,
		const Eigen::Vector2d &	pt,
		double &	error,
		Eigen::Vector2d &	p,
		Eigen::Vector2d &	t
	)		`[static]`