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

#include <fitting_surface_pdm.h>

Inheritance diagram for pcl::on_nurbs::FittingSurface:

Classes
class	myvec
struct	Parameter
	Parameters for fitting. More...
Public Member Functions
virtual void	assemble (Parameter param=Parameter())
	Assemble the system of equations for fitting.
	FittingSurface (NurbsDataSurface *data, const ON_NurbsSurface &ns)
	Constructor initializing with the B-Spline surface given in argument 2.
	FittingSurface (int order, NurbsDataSurface *data, Eigen::Vector3d z=Eigen::Vector3d(0.0, 0.0, 1.0))
	Constructor initializing B-Spline surface using initNurbsPCA(...).
void	refine (int dim)
	Refines surface by inserting a knot in the middle of each element.
void	setInvMapParams (unsigned in_max_steps, double in_accuracy)
	Set parameters for inverse mapping.
void	setQuiet (bool val)
	Enable/Disable debug outputs in console.
virtual 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.
virtual 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 B-Spline surface.
static ON_NurbsSurface	initNurbs4Corners (int order, ON_3dPoint ll, ON_3dPoint lr, ON_3dPoint ur, ON_3dPoint ul)
	Initializing a B-Spline surface using 4 corners.
static ON_NurbsSurface	initNurbsPCA (int order, NurbsDataSurface *data, Eigen::Vector3d z=Eigen::Vector3d(0.0, 0.0, 1.0))
	Initializing a B-Spline surface using principal-component-analysis and eigen values.
static ON_NurbsSurface	initNurbsPCABoundingBox (int order, NurbsDataSurface *data, Eigen::Vector3d z=Eigen::Vector3d(0.0, 0.0, 1.0))
	Initializing a B-Spline surface using principal-component-analysis and bounding box of points.
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).
static Eigen::Vector2d	inverseMapping (const ON_NurbsSurface &nurbs, const Eigen::Vector3d &pt, const Eigen::Vector2d &hint, Eigen::Vector3d &p, int maxSteps, double accuracy, bool quiet)
static Eigen::Vector2d	inverseMappingBoundary (const ON_NurbsSurface &nurbs, const Eigen::Vector3d &pt, 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 boundary of the B-Spline surface using Newtons method and point-distance (L2-, Euclidean norm).
static Eigen::Vector2d	inverseMappingBoundary (const ON_NurbsSurface &nurbs, const Eigen::Vector3d &pt, int side, double 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 one side of the boundary of the B-Spline surface using Newtons method and point-distance (L2-, Euclidean norm).
static void	refine (ON_NurbsSurface &nurbs, int dim)
Public Attributes
NurbsDataSurface *	m_data
ON_NurbsSurface	m_nurbs
Protected Member Functions
virtual void	addBoundaryRegularisation (int order, int resU, int resV, double weight, unsigned &row)
	Add minimization constraint: boundary smoothness by derivatives regularisation.
virtual void	addCageBoundaryRegularisation (double weight, int side, unsigned &row)
	Add minimization constraint: boundary smoothness by control point regularisation.
virtual void	addCageCornerRegularisation (double weight, unsigned &row)
	Add minimization constraint: corner smoothness by control point regularisation.
virtual void	addCageInteriorRegularisation (double weight, unsigned &row)
	Add minimization constraint: interior smoothness by control point regularisation.
virtual void	addInteriorRegularisation (int order, int resU, int resV, double weight, unsigned &row)
	Add minimization constraint: interior smoothness by derivatives regularisation.
virtual void	addPointConstraint (const Eigen::Vector2d &params, const Eigen::Vector3d &point, double weight, unsigned &row)
	Add minimization constraint: point-to-surface distance (point-distance-minimization).
virtual void	assembleBoundary (double wBnd, unsigned &row)
	Assemble point-to-surface constraints for boundary points.
virtual void	assembleInterior (double wInt, unsigned &row)
	Assemble point-to-surface constraints for interior points.
int	gl2gc (int A)
int	gl2gr (int A)
int	grc2gl (int I, int J)
void	init ()
	Initialisation of member variables.
int	lrc2gl (int E, int F, int i, int j)
Protected Attributes
double	in_accuracy
int	in_max_steps
std::vector< double >	m_elementsU
std::vector< double >	m_elementsV
double	m_maxU
double	m_maxV
double	m_minU
double	m_minV
bool	m_quiet
NurbsSolve	m_solver

Detailed Description

Fitting a 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_surface_pdm.h.

Constructor & Destructor Documentation

FittingSurface::FittingSurface	(	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 73 of file fitting_surface_pdm.cpp.

FittingSurface::FittingSurface	(	int	order,
		NurbsDataSurface *	data,
		Eigen::Vector3d	z = `Eigen::Vector3d (0.0, 0.0, 1.0)`
	)

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

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 60 of file fitting_surface_pdm.cpp.

Member Function Documentation

void FittingSurface::addBoundaryRegularisation	(	int	order,
		int	resU,
		int	resV,
		double	weight,
		unsigned &	row
	)		`[protected, virtual]`

Add minimization constraint: boundary smoothness by derivatives regularisation.

Reimplemented in pcl::on_nurbs::FittingSurfaceTDM.

Definition at line 797 of file fitting_surface_pdm.cpp.

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

Add minimization constraint: boundary smoothness by control point regularisation.

Reimplemented in pcl::on_nurbs::FittingSurfaceTDM.

Definition at line 632 of file fitting_surface_pdm.cpp.

void FittingSurface::addCageCornerRegularisation	(	double	weight,
		unsigned &	row
	)		`[protected, virtual]`

Add minimization constraint: corner smoothness by control point regularisation.

Reimplemented in pcl::on_nurbs::FittingSurfaceTDM.

Definition at line 678 of file fitting_surface_pdm.cpp.

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

Add minimization constraint: interior smoothness by control point regularisation.

Reimplemented in pcl::on_nurbs::FittingSurfaceTDM.

Definition at line 609 of file fitting_surface_pdm.cpp.

void FittingSurface::addInteriorRegularisation	(	int	order,
		int	resU,
		int	resV,
		double	weight,
		unsigned &	row
	)		`[protected, virtual]`

Add minimization constraint: interior smoothness by derivatives regularisation.

Reimplemented in pcl::on_nurbs::FittingSurfaceTDM.

Definition at line 743 of file fitting_surface_pdm.cpp.

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

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

Definition at line 529 of file fitting_surface_pdm.cpp.

void FittingSurface::assemble ( Parameter param = 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_surface_pdm.cpp.

void FittingSurface::assembleBoundary	(	double	wBnd,
		unsigned &	row
	)		`[protected, virtual]`

Assemble point-to-surface constraints for boundary points.

Definition at line 317 of file fitting_surface_pdm.cpp.

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

Assemble point-to-surface constraints for interior points.

Definition at line 273 of file fitting_surface_pdm.cpp.

Vector2d FittingSurface::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 1115 of file fitting_surface_pdm.cpp.

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

Get the elements of a B-Spline surface.

Definition at line 244 of file fitting_surface_pdm.cpp.

int pcl::on_nurbs::FittingSurface::gl2gc ( int A ) [inline, protected]

Definition at line 307 of file fitting_surface_pdm.h.

int pcl::on_nurbs::FittingSurface::gl2gr ( int A ) [inline, protected]

Definition at line 302 of file fitting_surface_pdm.h.

int pcl::on_nurbs::FittingSurface::grc2gl	(	int	I,
		int	J
	)		`[inline, protected]`

Definition at line 292 of file fitting_surface_pdm.h.

void FittingSurface::init ( ) [protected]

Initialisation of member variables.

Definition at line 189 of file fitting_surface_pdm.cpp.

ON_NurbsSurface FittingSurface::initNurbs4Corners	(	int	order,
		ON_3dPoint	ll,
		ON_3dPoint	lr,
		ON_3dPoint	ur,
		ON_3dPoint	ul
	)		`[static]`

Initializing a B-Spline surface using 4 corners.

Definition at line 358 of file fitting_surface_pdm.cpp.

ON_NurbsSurface FittingSurface::initNurbsPCA	(	int	order,
		NurbsDataSurface *	data,
		Eigen::Vector3d	z = `Eigen::Vector3d (0.0, 0.0, 1.0)`
	)		`[static]`

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

Definition at line 398 of file fitting_surface_pdm.cpp.

ON_NurbsSurface FittingSurface::initNurbsPCABoundingBox	(	int	order,
		NurbsDataSurface *	data,
		Eigen::Vector3d	z = `Eigen::Vector3d (0.0, 0.0, 1.0)`
	)		`[static]`

Initializing a B-Spline surface using principal-component-analysis and bounding box of points.

Definition at line 446 of file fitting_surface_pdm.cpp.

static Eigen::Vector2d pcl::on_nurbs::FittingSurface::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 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

Returns:: closest point on surface in parametric domain.

static Eigen::Vector2d pcl::on_nurbs::FittingSurface::inverseMapping	(	const ON_NurbsSurface &	nurbs,
		const Eigen::Vector3d &	pt,
		const Eigen::Vector2d &	hint,
		Eigen::Vector3d &	p,
		int	maxSteps,
		double	accuracy,
		bool	quiet
	)		`[static]`

static Eigen::Vector2d pcl::on_nurbs::FittingSurface::inverseMappingBoundary	(	const ON_NurbsSurface &	nurbs,
		const Eigen::Vector3d &	pt,
		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 boundary of 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]	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

Returns:: closest point on surface in parametric domain.

static Eigen::Vector2d pcl::on_nurbs::FittingSurface::inverseMappingBoundary	(	const ON_NurbsSurface &	nurbs,
		const Eigen::Vector3d &	pt,
		int	side,
		double	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 one side of the boundary of 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]	side	the side of the boundary (NORTH, SOUTH, EAST, WEST)
[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