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

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) )

References DGtal::SpaceND< 3, Integer >::dimension.

◆ 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 d6_PIr6, d8_5r, and 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;
      }

References d6_PIr6, d8_5r, dh5, eigenValues, and eigenVectors.

Field Documentation

◆ d6_PIr6

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

Quantity DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::d6_PIr6

private

Definition at line 724 of file IIGeometricFunctors.h.

Referenced by init(), and operator()().

◆ d8_5r

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

Quantity DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::d8_5r

private

Definition at line 725 of file IIGeometricFunctors.h.

Referenced by init(), and operator()().

◆ dh5

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

Quantity DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::dh5

private

Definition at line 723 of file IIGeometricFunctors.h.

Referenced by init(), and operator()().

◆ eigenValues

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

RealVector DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::eigenValues

mutableprivate

A data member only used for temporary calculations.

Definition at line 730 of file IIGeometricFunctors.h.

Referenced by operator()().

◆ eigenVectors

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

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

mutableprivate

A data member only used for temporary calculations.

Definition at line 728 of file IIGeometricFunctors.h.

Referenced by operator()().

The documentation for this struct was generated from the following file:

IIGeometricFunctors.h

Public Types

Public Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

◆ Argument

◆ Component

◆ Matrix

◆ Quantity

◆ RealVector

◆ Self

◆ Space

◆ Value

Member Function Documentation

◆ BOOST_CONCEPT_ASSERT() [1/2]

◆ BOOST_CONCEPT_ASSERT() [2/2]

◆ BOOST_STATIC_ASSERT()

◆ init()

◆ operator()()

Field Documentation

◆ d6_PIr6

◆ d8_5r

◆ dh5

◆ eigenValues

◆ eigenVectors