Aim: Estimates Mean curvature using CGAL Jet Fitting and Monge Form. More...

#include <DGtal/geometry/surfaces/estimation/estimationFunctors/MongeJetFittingMeanCurvatureEstimator.h>

Public Types
typedef TSurfel	Surfel

typedef TEmbedder	SCellEmbedder

typedef double	Quantity

typedef SCellEmbedder::RealPoint	RealPoint

typedef CGAL::Cartesian< double >	CGALKernel

typedef CGALKernel::Point_3	CGALPoint

typedef CGAL::Monge_via_jet_fitting< CGALKernel >	CGALMongeViaJet

typedef CGALMongeViaJet::Monge_form	CGALMongeForm

Public Member Functions
	MongeJetFittingMeanCurvatureEstimator (ConstAlias< SCellEmbedder > anEmbedder, const double h, unsigned int d=4)

void	pushSurfel (const Surfel &aSurf, const double aDistance)

Quantity	eval ()

void	reset ()

Private Attributes
const SCellEmbedder *	myEmbedder
	Alias of the geometrical embedder.

std::vector< CGALPoint >	myPoints
	Array of CGAL points.

double	myH
	Grid step.

unsigned int	myD
	Degree of the polynomial surface to fit.

Detailed Description

template<typename TSurfel, typename TEmbedder>
class DGtal::functors::MongeJetFittingMeanCurvatureEstimator< TSurfel, TEmbedder >

Aim: Estimates Mean curvature using CGAL Jet Fitting and Monge Form.

Description of template class 'MongeJetFittingMeanCurvatureEstimator'

Be carefull, this functor uses a polynomial surface fitting from point set. Curvature information is given from Monge basis which could be up to the orientation of the normal vector. Hence, if the estimated normal \( n \) is such that \( n\cdot n_0>0\) with \( n_0\) being the true normal at the point set center, everything is ok. Otherwise, we have to inverse the princiapl curvature sign: \( k_1=-k_2\) and \( k_2= -k_1\).

The mean curvature estimation is thus given up to a sign.

model of concepts::CLocalEstimatorFromSurfelFunctor.

Template Parameters

TSurfel	type of surfels
TEmbedder	type of functors which embed surfel to \( \mathbb{R}^3\)

Definition at line 90 of file MongeJetFittingMeanCurvatureEstimator.h.

Member Typedef Documentation

◆ CGALKernel

template<typename TSurfel , typename TEmbedder >

typedef CGAL::Cartesian<double> DGtal::functors::MongeJetFittingMeanCurvatureEstimator< TSurfel, TEmbedder >::CGALKernel

Definition at line 99 of file MongeJetFittingMeanCurvatureEstimator.h.

◆ CGALMongeForm

template<typename TSurfel , typename TEmbedder >

typedef CGALMongeViaJet::Monge_form DGtal::functors::MongeJetFittingMeanCurvatureEstimator< TSurfel, TEmbedder >::CGALMongeForm

Definition at line 102 of file MongeJetFittingMeanCurvatureEstimator.h.

◆ CGALMongeViaJet

template<typename TSurfel , typename TEmbedder >

typedef CGAL::Monge_via_jet_fitting<CGALKernel> DGtal::functors::MongeJetFittingMeanCurvatureEstimator< TSurfel, TEmbedder >::CGALMongeViaJet

Definition at line 101 of file MongeJetFittingMeanCurvatureEstimator.h.

◆ CGALPoint

template<typename TSurfel , typename TEmbedder >

typedef CGALKernel::Point_3 DGtal::functors::MongeJetFittingMeanCurvatureEstimator< TSurfel, TEmbedder >::CGALPoint

Definition at line 100 of file MongeJetFittingMeanCurvatureEstimator.h.

◆ Quantity

template<typename TSurfel , typename TEmbedder >

typedef double DGtal::functors::MongeJetFittingMeanCurvatureEstimator< TSurfel, TEmbedder >::Quantity

Definition at line 96 of file MongeJetFittingMeanCurvatureEstimator.h.

◆ RealPoint

template<typename TSurfel , typename TEmbedder >

typedef SCellEmbedder::RealPoint DGtal::functors::MongeJetFittingMeanCurvatureEstimator< TSurfel, TEmbedder >::RealPoint

Definition at line 97 of file MongeJetFittingMeanCurvatureEstimator.h.

◆ SCellEmbedder

template<typename TSurfel , typename TEmbedder >

typedef TEmbedder DGtal::functors::MongeJetFittingMeanCurvatureEstimator< TSurfel, TEmbedder >::SCellEmbedder

Definition at line 95 of file MongeJetFittingMeanCurvatureEstimator.h.

◆ Surfel

template<typename TSurfel , typename TEmbedder >

typedef TSurfel DGtal::functors::MongeJetFittingMeanCurvatureEstimator< TSurfel, TEmbedder >::Surfel

Definition at line 94 of file MongeJetFittingMeanCurvatureEstimator.h.

Constructor & Destructor Documentation

◆ MongeJetFittingMeanCurvatureEstimator()

template<typename TSurfel , typename TEmbedder >

DGtal::functors::MongeJetFittingMeanCurvatureEstimator< TSurfel, TEmbedder >::MongeJetFittingMeanCurvatureEstimator	(	ConstAlias< SCellEmbedder >	anEmbedder,
		const double	h,
		unsigned int	d = 4 )

inline

Constructor.

Parameters

anEmbedder	embedder to map surfel to R^n.
h	gridstep.
d	degree of the polynomial surface to fit.

Definition at line 111 of file MongeJetFittingMeanCurvatureEstimator.h.

                                                                             :
      myEmbedder(&anEmbedder), myH(h), myD(d)
    {
      FATAL_ERROR_MSG(d>=2,"Polynomial surface degree must be greater than 2");
    }

Member Function Documentation

◆ eval()

template<typename TSurfel , typename TEmbedder >

Quantity DGtal::functors::MongeJetFittingMeanCurvatureEstimator< TSurfel, TEmbedder >::eval ( )

inline

Evaluate the curvature from Monge form.

Returns: the mean curvature

Definition at line 139 of file MongeJetFittingMeanCurvatureEstimator.h.

    {
      CGALMongeForm monge_form;
      CGALMongeViaJet monge_fit;
 
      monge_form = monge_fit(myPoints.begin() , myPoints.end(), myD, (2<myD)? myD : 2);
 
      double k1 = monge_form.principal_curvatures ( 0 );
      double k2 = monge_form.principal_curvatures ( 1 );
      return 0.5*(k1+k2);
    }

References DGtal::functors::MongeJetFittingMeanCurvatureEstimator< TSurfel, TEmbedder >::myD, and DGtal::functors::MongeJetFittingMeanCurvatureEstimator< TSurfel, TEmbedder >::myPoints.

◆ pushSurfel()

template<typename TSurfel , typename TEmbedder >

void DGtal::functors::MongeJetFittingMeanCurvatureEstimator< TSurfel, TEmbedder >::pushSurfel	(	const Surfel &	aSurf,
		const double	aDistance )

inline

Add the geometrical embedding of a surfel to the point list

Parameters

aSurf	a surfel to add
aDistance	of aSurf to the neighborhood boundary

Definition at line 124 of file MongeJetFittingMeanCurvatureEstimator.h.

    {
      BOOST_VERIFY(aDistance==aDistance);
 
      RealPoint p = myEmbedder->operator()(aSurf);
      CGALPoint pp(p[0]*myH,p[1]*myH,p[2]*myH);
      myPoints.push_back(pp);
    }