Fitting a cylindric (dim 0 clamped, dim 1 periodic) B-Spline surface to 3D point-clouds using point-distance-minimization Based on paper: TODO. More...

#include <fitting_sphere_pdm.h>

Public Member Functions
void	assemble (double smoothness=0.000001f)
	Assemble the system of equations for fitting.
	FittingSphere (int order, NurbsDataSurface *data)
	Constructor initializing B-Spline surface using initNurbsPCACylinder(...).
	FittingSphere (NurbsDataSurface *data, const ON_NurbsSurface &ns)
	Constructor initializing with the B-Spline surface given in argument 2.
void	setInvMapParams (int in_max_steps, double invMapInt_accuracy)
	Set parameters for inverse mapping.
void	setQuiet (bool val)
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 surface if a solution can be obtained.
void	updateSurf (double damp)
	Update surface according to the current system of equations.
Static Public Member Functions
static Eigen::Vector2d	findClosestElementMidPoint (const ON_NurbsSurface &nurbs, const Eigen::Vector3d &pt)
	Given a point pt, the function finds the closest midpoint of the elements of the surface.
static std::vector< double >	getElementVector (const ON_NurbsSurface &nurbs, int dim)
	Get the elements of a cylindric B-Spline surface.
static ON_NurbsSurface	initNurbsSphere (int order, NurbsDataSurface *data, Eigen::Vector3d pole_axis=Eigen::Vector3d(0.0, 0.0, 1.0))
	Initializing a cylindric B-Spline surface using principal-component-analysis and eigen values.
static Eigen::Vector2d	inverseMapping (const ON_NurbsSurface &nurbs, const Eigen::Vector3d &pt, const Eigen::Vector2d &hint, double &error, Eigen::Vector3d &p, Eigen::Vector3d &tu, Eigen::Vector3d &tv, 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 surface using Newtons method and point-distance (L2-, Euclidean norm).
Public Attributes
NurbsDataSurface *	m_data
ON_NurbsSurface	m_nurbs
ON_TextLog	m_out
Protected Member Functions
void	addCageBoundaryRegularisation (double weight, int side, unsigned &row)
	Add minimization constraint: corner smoothness by control point regularisation.
void	addCageInteriorRegularisation (double weight, unsigned &row)
	Add minimization constraint: interior smoothness by control point regularisation.
void	addPointConstraint (const Eigen::Vector2d &params, 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 for interior points.
void	init ()
	Initialisation of member variables.
Private Member Functions
int	gl2gc (int A)
int	gl2gr (int A)
int	grc2gl (int I, int J)
int	lrc2gl (int E, int F, int i, int j)
Private Attributes
double	in_accuracy
int	in_max_steps
bool	m_quiet
NurbsSolve	m_solver

Detailed Description

Fitting a cylindric (dim 0 clamped, dim 1 periodic) B-Spline surface to 3D point-clouds using point-distance-minimization Based on paper: TODO.

Author:: Thomas Mörwald

Definition at line 55 of file fitting_sphere_pdm.h.

Constructor & Destructor Documentation

FittingSphere::FittingSphere	(	int	order,
		NurbsDataSurface *	data
	)

Constructor initializing B-Spline surface using initNurbsPCACylinder(...).

Parameters:

[in]	order	the polynomial order of the B-Spline surface.
[in]	data	pointer to the 2D point-cloud data to be fit.
[in]	z	vector defining front face of surface.

Definition at line 45 of file fitting_sphere_pdm.cpp.

FittingSphere::FittingSphere	(	NurbsDataSurface *	data,
		const ON_NurbsSurface &	ns
	)

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

Parameters:

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

Definition at line 58 of file fitting_sphere_pdm.cpp.

Member Function Documentation

void FittingSphere::addCageBoundaryRegularisation	(	double	weight,
		int	side,
		unsigned &	row
	)		`[protected]`

Add minimization constraint: corner smoothness by control point regularisation.

Definition at line 401 of file fitting_sphere_pdm.cpp.

void FittingSphere::addCageInteriorRegularisation	(	double	weight,
		unsigned &	row
	)		`[protected]`

Add minimization constraint: interior smoothness by control point regularisation.

Definition at line 376 of file fitting_sphere_pdm.cpp.

void FittingSphere::addPointConstraint	(	const Eigen::Vector2d &	params,
		const Eigen::Vector3d &	point,
		double	weight,
		unsigned &	row
	)		`[protected]`

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

Definition at line 341 of file fitting_sphere_pdm.cpp.

void FittingSphere::assemble ( double smoothness = 0.000001f )

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 78 of file fitting_sphere_pdm.cpp.

void FittingSphere::assembleInterior	(	double	wInt,
		unsigned &	row
	)		`[protected]`

Assemble point-to-surface constraints for interior points.

Definition at line 300 of file fitting_sphere_pdm.cpp.

Vector2d FittingSphere::findClosestElementMidPoint	(	const ON_NurbsSurface &	nurbs,
		const Eigen::Vector3d &	pt
	)		`[static]`

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

Parameters:

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

Definition at line 509 of file fitting_sphere_pdm.cpp.

std::vector< double > FittingSphere::getElementVector	(	const ON_NurbsSurface &	nurbs,
		int	dim
	)		`[static]`

Get the elements of a cylindric B-Spline surface.

Definition at line 242 of file fitting_sphere_pdm.cpp.

int pcl::on_nurbs::FittingSphere::gl2gc ( int A ) [inline, private]

Definition at line 184 of file fitting_sphere_pdm.h.

int pcl::on_nurbs::FittingSphere::gl2gr ( int A ) [inline, private]

Definition at line 179 of file fitting_sphere_pdm.h.

int pcl::on_nurbs::FittingSphere::grc2gl	(	int	I,
		int	J
	)		`[inline, private]`

Definition at line 167 of file fitting_sphere_pdm.h.

void FittingSphere::init ( ) [protected]

Initialisation of member variables.

Definition at line 69 of file fitting_sphere_pdm.cpp.

ON_NurbsSurface FittingSphere::initNurbsSphere	(	int	order,
		NurbsDataSurface *	data,
		Eigen::Vector3d	pole_axis = `Eigen::Vector3d (0.0, 0.0, 1.0)`
	)		`[static]`

Initializing a cylindric B-Spline surface using principal-component-analysis and eigen values.

Definition at line 164 of file fitting_sphere_pdm.cpp.

Vector2d FittingSphere::inverseMapping	(	const ON_NurbsSurface &	nurbs,
		const Eigen::Vector3d &	pt,
		const Eigen::Vector2d &	hint,
		double &	error,
		Eigen::Vector3d &	p,
		Eigen::Vector3d &	tu,
		Eigen::Vector3d &	tv,
		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 surface using Newtons method and point-distance (L2-, Euclidean norm).

Parameters:

[in]	nurbs	the B-Spline surface.
[in]	pt	the point to which the closest point on the surface 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 boundary point on surface.
[in]	tu	the tangent vector at point p in u-direction.
[in]	tv	the tangent vector at point p in v-direction.
[in]	maxSteps	maximum number of iterations.
[in]	accuracy	convergence criteria: if error is lower than accuracy the function returns