Fitting a 3D B-Spline curve to point-clouds using point-distance-minimization and optionally asymmetric-distance-minimization Based on paper: TODO. More...

#include <fitting_curve_pdm.h>

Classes
struct	Parameter
Public Member Functions
void	assemble (const Parameter &parameter)
	Assemble the system of equations for fitting.
	FittingCurve (int order, NurbsDataCurve *data)
	Constructor initializing B-Spline curve using initNurbsCurve2D(...).
	FittingCurve (NurbsDataCurve *data, const ON_NurbsCurve &ns)
	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	setQuiet (bool val)
	Enable/Disable debug outputs in console.
void	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.
void	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::Vector3d &pt)
	Given a point pt, the function finds the closest midpoint of the elements of the curve.
static int	findElement (double xi, const std::vector< double > &elements)
	Find the element in which the parameter xi lies.
static ON_NurbsCurve	initNurbsCurve2D (int order, const vector_vec2d &data)
	Initialize a closed B-Spline curve using the bounding circle of the point-cloud.
static ON_NurbsCurve	initNurbsCurvePCA (int order, const vector_vec3d &data, int ncps=0, double rf=1.0)
	Initialize a closed B-Spline curve using the eigenvalues as elliptic parameters (z=0).
static double	inverseMapping (const ON_NurbsCurve &nurbs, const Eigen::Vector3d &pt, const double &hint, double &error, Eigen::Vector3d &p, Eigen::Vector3d &t, 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).
Public Attributes
NurbsDataCurve *	m_data
ON_NurbsCurve	m_nurbs
ON_TextLog	m_out
Private Member Functions
void	addCageRegularisation (double weight, unsigned &row)
	Add minimization constraint: smoothness by control point regularisation.
void	addPointConstraint (const double &param, const Eigen::Vector3d &point, double weight, unsigned &row)
	Add minimization constraint: point-to-surface distance (point-distance-minimization).
void	assembleInterior (double wInt, unsigned &row)
	Assemble point-to-surface constraints.
Static Private Member Functions
static std::vector< double >	getElementVector (const ON_NurbsCurve &nurbs)
	Get the elements of a B-Spline curve.
Private Attributes
double	in_accuracy
int	in_max_steps
bool	m_quiet
NurbsSolve	m_solver

Detailed Description

Fitting a 3D B-Spline curve to point-clouds using point-distance-minimization and optionally asymmetric-distance-minimization Based on paper: TODO.

Author:: Thomas Mörwald

Definition at line 57 of file fitting_curve_pdm.h.

Constructor & Destructor Documentation

FittingCurve::FittingCurve	(	int	order,
		NurbsDataCurve *	data
	)

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

Parameters:

[in]	order	the polynomial order of the B-Spline curve.
[in]	data	pointer to the 3D point-cloud data to be fit

Definition at line 44 of file fitting_curve_pdm.cpp.

FittingCurve::FittingCurve	(	NurbsDataCurve *	data,
		const ON_NurbsCurve &	ns
	)

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

Parameters:

[in]	data	pointer to the 3D point-cloud data to be fit.
[in]	nc	B-Spline curve used for fitting.

Definition at line 59 of file fitting_curve_pdm.cpp.

Member Function Documentation

void FittingCurve::addCageRegularisation	(	double	weight,
		unsigned &	row
	)		`[private]`

Add minimization constraint: smoothness by control point regularisation.

Definition at line 186 of file fitting_curve_pdm.cpp.

void FittingCurve::addPointConstraint	(	const double &	param,
		const Eigen::Vector3d &	point,
		double	weight,
		unsigned &	row
	)		`[private]`

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

Definition at line 163 of file fitting_curve_pdm.cpp.

void FittingCurve::assemble ( const Parameter & parameter )

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 105 of file fitting_curve_pdm.cpp.

void FittingCurve::assembleInterior	(	double	wInt,
		unsigned &	row
	)		`[private]`

Assemble point-to-surface constraints.

Definition at line 311 of file fitting_curve_pdm.cpp.

double FittingCurve::findClosestElementMidPoint	(	const ON_NurbsCurve &	nurbs,
		const Eigen::Vector3d &	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 415 of file fitting_curve_pdm.cpp.

int FittingCurve::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_pdm.cpp.

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

Get the elements of a B-Spline curve.

Definition at line 282 of file fitting_curve_pdm.cpp.

ON_NurbsCurve FittingCurve::initNurbsCurve2D	(	int	order,
		const vector_vec2d &	data
	)		`[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	3D point-cloud

Returns:: B-Spline curve.

Definition at line 207 of file fitting_curve_pdm.cpp.

ON_NurbsCurve FittingCurve::initNurbsCurvePCA	(	int	order,
		const vector_vec3d &	data,
		int	ncps = `0`,
		double	rf = `1.0`
	)		`[static]`

Initialize a closed B-Spline curve using the eigenvalues as elliptic parameters (z=0).

Parameters:

[in]	order	polynomial order of the curve.
[in]	data	3D point-cloud

Returns:: B-Spline curve.

Definition at line 244 of file fitting_curve_pdm.cpp.

double FittingCurve::inverseMapping	(	const ON_NurbsCurve &	nurbs,
		const Eigen::Vector3d &	pt,
		const double &	hint,
		double &	error,
		Eigen::Vector3d &	p,
		Eigen::Vector3d &	t,
		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