Aim: A functor Matrix -> Real that returns the Gaussian curvature by diagonalizing the given covariance matrix. This functor is valid starting from 3D space. Note that the Gaussian curvature is computed by multiplying the two gretest curvature values in absolute value. More...

#include <DGtal/geometry/surfaces/estimation/IIGeometricFunctors.h>

Public Types
typedef IIGaussianCurvature3DFunctor< TSpace >	Self

typedef TSpace	Space

typedef Space::RealVector	RealVector

typedef RealVector::Component	Component

typedef TMatrix	Matrix

typedef Matrix	Argument

typedef Component	Quantity

typedef Quantity	Value

Public Member Functions
	BOOST_CONCEPT_ASSERT ((concepts::CMatrix< Matrix >))

	BOOST_CONCEPT_ASSERT ((concepts::CSpace< TSpace >))

	BOOST_STATIC_ASSERT ((Space::dimension==3))

Value	operator() (const Argument &arg) const

void	init (Component h, Component r)

Private Attributes
Quantity	dh5

Quantity	d6_PIr6

Quantity	d8_5r

Matrix	eigenVectors
	A data member only used for temporary calculations. More...

RealVector	eigenValues
	A data member only used for temporary calculations. More...

Detailed Description

template<typename TSpace, typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
struct DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >

Aim: A functor Matrix -> Real that returns the Gaussian curvature by diagonalizing the given covariance matrix. This functor is valid starting from 3D space. Note that the Gaussian curvature is computed by multiplying the two gretest curvature values in absolute value.

Description of template class 'IIGaussianCurvature3DFunctor'

Template Parameters

TSpace	a model of CSpace, for instance SpaceND.
TMatrix	a model of CMatrix, for instance SimpleMatrix.

See also: IntegralInvariantCovarianceEstimator

Definition at line 666 of file IIGeometricFunctors.h.

Member Typedef Documentation

◆ Argument

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>

typedef Matrix DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::Argument

Definition at line 675 of file IIGeometricFunctors.h.

◆ Component

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>

typedef RealVector::Component DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::Component

Definition at line 673 of file IIGeometricFunctors.h.

◆ Matrix

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>

typedef TMatrix DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::Matrix

Definition at line 674 of file IIGeometricFunctors.h.

◆ Quantity

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>

typedef Component DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::Quantity

Definition at line 676 of file IIGeometricFunctors.h.

◆ RealVector

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>

typedef Space::RealVector DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::RealVector

Definition at line 672 of file IIGeometricFunctors.h.

◆ Self

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>

typedef IIGaussianCurvature3DFunctor<TSpace> DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::Self

Definition at line 670 of file IIGeometricFunctors.h.

◆ Space

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>

typedef TSpace DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::Space

Definition at line 671 of file IIGeometricFunctors.h.

◆ Value

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>

typedef Quantity DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::Value

Definition at line 677 of file IIGeometricFunctors.h.

Member Function Documentation

◆ BOOST_CONCEPT_ASSERT() [1/2]

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>

DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::BOOST_CONCEPT_ASSERT ( (concepts::CMatrix< Matrix >) )

◆ BOOST_CONCEPT_ASSERT() [2/2]

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>

DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::BOOST_CONCEPT_ASSERT ( (concepts::CSpace< TSpace >) )

◆ BOOST_STATIC_ASSERT()

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>

DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::BOOST_STATIC_ASSERT ( (Space::dimension==3) )

◆ init()

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>

void DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::init	(	Component	h,
		Component	r
	)

inline

Initializes the functor with the gridstep and the ball Euclidean radius.

Parameters

h	the gridstep
r	the ball radius

Definition at line 712 of file IIGeometricFunctors.h.

      {
        double r3 = r * r * r;
        double r6 = r3 * r3;
        d6_PIr6 = 6.0 / ( M_PI * r6 );
        d8_5r = 8.0 / ( 5.0 * r );
        double h2 = h * h;
        dh5 = h2 * h2 * h;
      }

References DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::d6_PIr6, DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::d8_5r, and DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::dh5.

◆ operator()()

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>

Value DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::operator() ( const Argument & arg ) const

inline

Apply operator.

Parameters

arg	any symmetric positive matrix (covariance matrix

Returns: the Gaussian curvature value for the II covariance matrix, which is the second highest eigenvalue * second highest eigenvalue.

Definition at line 690 of file IIGeometricFunctors.h.

      {
        Argument cp_arg = arg;
        cp_arg *= dh5;
        EigenDecomposition<Space::dimension, Component, Matrix>
          ::getEigenDecomposition( cp_arg, eigenVectors, eigenValues );
 
        ASSERT ( !std::isnan(eigenValues[0]) ); // NaN
        ASSERT ( (std::abs(eigenValues[0]) <= std::abs(eigenValues[1]))
              && (std::abs(eigenValues[1]) <= std::abs(eigenValues[2])) );
 
        Value k1 = d6_PIr6 * ( eigenValues[2] - ( 3.0 * eigenValues[1] )) + d8_5r;
        Value k2 = d6_PIr6 * ( eigenValues[1] - ( 3.0 * eigenValues[2] )) + d8_5r;
        return k1 * k2;
      }