DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix > Struct Template Reference

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

Collaboration diagram for DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >:

Public Types
typedef IIPrincipalCurvatures3DFunctor< TSpace >	Self
typedef TSpace	Space
typedef Space::RealVector	RealVector
typedef RealVector::Component	Component
typedef TMatrix	Matrix
typedef Matrix	Argument
typedef std::pair< Component, Component >	Quantity
typedef Quantity	Value

Public Member Functions
	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
double	dh5
double	d6_PIr6
double	d8_5r
Matrix	eigenVectors
RealVector	eigenValues

Detailed Description

template<typename TSpace, typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
struct DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >

Aim: A functor Matrix -> std::pair<Real,Real> that returns the first and the second principal curvature value by diagonalizing the given covariance matrix. This functor is valid starting from 3D space. Note that by first we mean the value with first greatest curvature in absolute value.

Description of template class 'IIPrincipalCurvatures3DFunctor'

Template Parameters

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

See also

IntegralInvariantCovarianceEstimator

Definition at line 819 of file IIGeometricFunctors.h.

Member Typedef Documentation

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

typedef Matrix DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::Argument

Definition at line 828 of file IIGeometricFunctors.h.

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

typedef RealVector::Component DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::Component

Definition at line 826 of file IIGeometricFunctors.h.

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

typedef TMatrix DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::Matrix

Definition at line 827 of file IIGeometricFunctors.h.

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

typedef std::pair<Component, Component> DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::Quantity

Definition at line 829 of file IIGeometricFunctors.h.

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

typedef Space::RealVector DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::RealVector

Definition at line 825 of file IIGeometricFunctors.h.

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

typedef IIPrincipalCurvatures3DFunctor<TSpace> DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::Self

Definition at line 823 of file IIGeometricFunctors.h.

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

typedef TSpace DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::Space

Definition at line 824 of file IIGeometricFunctors.h.

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

typedef Quantity DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::Value

Definition at line 830 of file IIGeometricFunctors.h.

Member Function Documentation

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

DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::BOOST_CONCEPT_ASSERT

(

(concepts::CSpace< TSpace >)

)

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

DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::BOOST_STATIC_ASSERT

(

(Space::dimension==3)

)

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

void DGtal::functors::IIPrincipalCurvatures3DFunctor< 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 867 of file IIGeometricFunctors.h.

References DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::d6_PIr6, DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::d8_5r, and DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::dh5.

      {
        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;
      }

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

Value DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::operator() ( const Argument &  arg ) const

inline

Apply operator.

Parameters

arg	any symmetric positive matrix (covariance matrix

Returns

the first and the second principal curvature value in a std::pair for the II covariance matrix, which are the first and the second highest eigenvalue.

Definition at line 844 of file IIGeometricFunctors.h.

References DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::d6_PIr6, DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::d8_5r, DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::dh5, DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::eigenValues, and DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::eigenVectors.

      {
        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])) );

        return Value( 
                d6_PIr6 * ( eigenValues[2] - ( 3.0 * eigenValues[1] )) + d8_5r,
                d6_PIr6 * ( eigenValues[1] - ( 3.0 * eigenValues[2] )) + d8_5r
               );
      }

Field Documentation

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

double DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::d6_PIr6

private

Definition at line 879 of file IIGeometricFunctors.h.

Referenced by DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::init(), and DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::operator()().

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

double DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::d8_5r

private

Definition at line 880 of file IIGeometricFunctors.h.

Referenced by DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::init(), and DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::operator()().

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

double DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::dh5

private

Definition at line 878 of file IIGeometricFunctors.h.

Referenced by DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::init(), and DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::operator()().

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

RealVector DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::eigenValues

mutableprivate

A data member only used for temporary calculations.

Definition at line 885 of file IIGeometricFunctors.h.

Referenced by DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::operator()().

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

Matrix DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::eigenVectors

mutableprivate

A data member only used for temporary calculations.

Definition at line 883 of file IIGeometricFunctors.h.

Referenced by DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::operator()().

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

• IIGeometricFunctors.h