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

#include <fitting_curve_2d.h>

Classes
struct	FitParameter
struct	Parameter
	Parameters for fitting. More...
Public Member Functions
virtual void	addControlPointConstraint (int i, const Eigen::Vector2d &f, double weight)
virtual void	assemble (const Parameter &parameter)
	Assemble the system of equations for fitting.
	FittingCurve2d (int order, NurbsDataCurve2d *data)
	Constructor initializing B-Spline curve using initNurbsCurve2D(...).
	FittingCurve2d (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	initNurbsCPS (int order, const vector_vec2d &cps)
	Initialize a closed B-Spline curve given a list of control points.
static ON_NurbsCurve	initNurbsPCA (int order, NurbsDataCurve2d *data, int ncps=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 void	reverse (ON_NurbsCurve &curve)
	Reverse direction of rotation of a closed B-spline curve.
Public Attributes
NurbsDataCurve2d *	m_data
ON_NurbsCurve	m_nurbs
ON_TextLog	m_out
Protected Member Functions
virtual void	addCageRegularisation (double weight, unsigned &row)
	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	assembleInterior (double wInt, 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 point-distance-minimization Based on paper: TODO.

Author:: Thomas Mörwald

Definition at line 56 of file fitting_curve_2d.h.

Constructor & Destructor Documentation

FittingCurve2d::FittingCurve2d	(	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.cpp.

FittingCurve2d::FittingCurve2d	(	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.cpp.

Member Function Documentation

void FittingCurve2d::addCageRegularisation	(	double	weight,
		unsigned &	row
	)		`[protected, virtual]`

Add minimization constraint: smoothness by control point regularisation.

Definition at line 228 of file fitting_curve_2d.cpp.

void FittingCurve2d::addControlPointConstraint	(	int	i,
		const Eigen::Vector2d &	f,
		double	weight
	)		`[virtual]`

Definition at line 147 of file fitting_curve_2d.cpp.

void FittingCurve2d::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 208 of file fitting_curve_2d.cpp.

void FittingCurve2d::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.

Definition at line 117 of file fitting_curve_2d.cpp.

void FittingCurve2d::assembleInterior	(	double	wInt,
		double	rScale,
		unsigned &	row
	)		`[protected, virtual]`

Assemble point-to-curve constraints.

Definition at line 396 of file fitting_curve_2d.cpp.

double FittingCurve2d::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 710 of file fitting_curve_2d.cpp.

double FittingCurve2d::findClosestElementMidPoint	(	const ON_NurbsCurve &	nurbs,
		const Eigen::Vector2d &	pt,
		double	hint
	)		`[static]`

Definition at line 661 of file fitting_curve_2d.cpp.

int FittingCurve2d::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.cpp.

std::vector< double > FittingCurve2d::getElementVector ( const ON_NurbsCurve & nurbs ) [static]

Get the elements of a B-Spline curve.

Definition at line 367 of file fitting_curve_2d.cpp.

ON_NurbsCurve FittingCurve2d::initNurbsCPS	(	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 246 of file fitting_curve_2d.cpp.

ON_NurbsCurve FittingCurve2d::initNurbsPCA	(	int	order,
		NurbsDataCurve2d *	data,
		int	ncps = `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 (if 0, minimum number of control points required are used)

Returns:: B-Spline curve.

Definition at line 282 of file fitting_curve_2d.cpp.

double FittingCurve2d::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 438 of file fitting_curve_2d.cpp.

double FittingCurve2d::inverseMappingO2	(	const ON_NurbsCurve &	nurbs,
		const Eigen::Vector2d &	pt,
		double &	error,
		Eigen::Vector2d &	p,
		Eigen::Vector2d &	t
	)		`[static]`

Definition at line 505 of file fitting_curve_2d.cpp.

void FittingCurve2d::refine ( )

Refines curve by inserting a knot in the middle of each element.

Definition at line 91 of file fitting_curve_2d.cpp.

void FittingCurve2d::refine ( double xi )

Refines curve by inserting a knot in the middle of the element belonging to xi.

Parameters:

[in] xi parameter defining the element to be refined.

Definition at line 105 of file fitting_curve_2d.cpp.

void FittingCurve2d::reverse ( ON_NurbsCurve & curve ) [static]

Reverse direction of rotation of a closed B-spline curve.

Parameters:

[in] curve the curve to be reversed

Definition at line 352 of file fitting_curve_2d.cpp.

void pcl::on_nurbs::FittingCurve2d::setInverseParams	(	int	max_steps = `200`,
		double	accuracy = `1e-6`
	)		`[inline]`

Set parameters for inverse mapping.

Definition at line 205 of file fitting_curve_2d.h.

void pcl::on_nurbs::FittingCurve2d::setQuiet ( bool val ) [inline]

Enable/Disable debug outputs in console.

Definition at line 197 of file fitting_curve_2d.h.

double FittingCurve2d::solve ( double damp = 1.0 ) [virtual]

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.

Definition at line 169 of file fitting_curve_2d.cpp.

double FittingCurve2d::updateCurve ( double damp ) [virtual]

Update curve according to the current system of equations.

Parameters:

[in] damp damping factor from one iteration to the other.

Definition at line 180 of file fitting_curve_2d.cpp.

Member Data Documentation

double pcl::on_nurbs::FittingCurve2d::in_accuracy [protected]

Definition at line 227 of file fitting_curve_2d.h.

int pcl::on_nurbs::FittingCurve2d::in_max_steps [protected]

Definition at line 226 of file fitting_curve_2d.h.

NurbsDataCurve2d* pcl::on_nurbs::FittingCurve2d::m_data

Definition at line 83 of file fitting_curve_2d.h.

ON_NurbsCurve pcl::on_nurbs::FittingCurve2d::m_nurbs

Definition at line 82 of file fitting_curve_2d.h.

ON_TextLog pcl::on_nurbs::FittingCurve2d::m_out

Definition at line 81 of file fitting_curve_2d.h.

bool pcl::on_nurbs::FittingCurve2d::m_quiet [protected]

Definition at line 225 of file fitting_curve_2d.h.

NurbsSolve pcl::on_nurbs::FittingCurve2d::m_solver [protected]

Definition at line 224 of file fitting_curve_2d.h.

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

Classes

Public Member Functions

Static Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation