Aim: A functor Matrix -> RealVector that returns the second principal curvature direction by diagonalizing the given covariance matrix. This functor is valid starting from 3D space. Note that by second we mean the direction with second greatest curvature in absolute value. More...

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

Public Types
typedef IISecondPrincipalDirectionFunctor< TSpace >	Self

typedef TSpace	Space

typedef Space::RealVector	RealVector

typedef RealVector::Component	Component

typedef TMatrix	Matrix

typedef Matrix	Argument

typedef RealVector	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))

	IISecondPrincipalDirectionFunctor ()
	Default constructor.

	IISecondPrincipalDirectionFunctor (const Self &)
	Copy constructor. Nothing to do.

Self &	operator= (const Self &)

Value	operator() (const Argument &arg) const

void	init (Component, Component)

Private Attributes
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>>
class DGtal::functors::IISecondPrincipalDirectionFunctor< TSpace, TMatrix >

Aim: A functor Matrix -> RealVector that returns the second principal curvature direction by diagonalizing the given covariance matrix. This functor is valid starting from 3D space. Note that by second we mean the direction with second greatest curvature in absolute value.

Description of template class 'IISecondPrincipalDirectionFunctor'

Template Parameters

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

See also: IntegralInvariantCovarianceEstimator

Definition at line 298 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::IISecondPrincipalDirectionFunctor< TSpace, TMatrix >::Argument

Definition at line 307 of file IIGeometricFunctors.h.

◆ Component

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

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

Definition at line 305 of file IIGeometricFunctors.h.

◆ Matrix

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

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

Definition at line 306 of file IIGeometricFunctors.h.

◆ Quantity

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

typedef RealVector DGtal::functors::IISecondPrincipalDirectionFunctor< TSpace, TMatrix >::Quantity

Definition at line 308 of file IIGeometricFunctors.h.

◆ RealVector

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

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

Definition at line 304 of file IIGeometricFunctors.h.

◆ Self

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

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

Definition at line 302 of file IIGeometricFunctors.h.

◆ Space

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

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

Definition at line 303 of file IIGeometricFunctors.h.

◆ Value

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

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

Definition at line 309 of file IIGeometricFunctors.h.

Constructor & Destructor Documentation

◆ IISecondPrincipalDirectionFunctor() [1/2]

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

DGtal::functors::IISecondPrincipalDirectionFunctor< TSpace, TMatrix >::IISecondPrincipalDirectionFunctor ( )

inline

Default constructor.

Definition at line 316 of file IIGeometricFunctors.h.

316{}

◆ IISecondPrincipalDirectionFunctor() [2/2]

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

DGtal::functors::IISecondPrincipalDirectionFunctor< TSpace, TMatrix >::IISecondPrincipalDirectionFunctor ( const Self & )

inline

Copy constructor. Nothing to do.

Definition at line 318 of file IIGeometricFunctors.h.

318{}

Member Function Documentation

◆ BOOST_CONCEPT_ASSERT() [1/2]

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

DGtal::functors::IISecondPrincipalDirectionFunctor< 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::IISecondPrincipalDirectionFunctor< 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::IISecondPrincipalDirectionFunctor< 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::IISecondPrincipalDirectionFunctor< TSpace, TMatrix >::init	(	Component	,
		Component	)

inline

Initializes the functor with the gridstep and the ball Euclidean radius. Not used for this estimator.

Definition at line 350 of file IIGeometricFunctors.h.

350{}

◆ operator()()

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

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

inline

Apply operator.

Parameters

arg	any symmetric positive matrix (covariance matrix

Returns: the second principal curvature direction for the II covariance matrix, which is the eigenvector associated with the highest eigenvalue.

Definition at line 330 of file IIGeometricFunctors.h.

      {
        EigenDecomposition<Space::dimension, Component, Matrix>
          ::getEigenDecomposition( arg, eigenVectors, eigenValues );
 
        ASSERT ( !std::isnan(eigenValues[0]) ); // NaN
#ifdef DEBUG
        for( Dimension i_dim = 1; i_dim < Space::dimension; ++i_dim )
        {
          ASSERT ( std::abs(eigenValues[i_dim - 1]) <= std::abs(eigenValues[i_dim]) );
        }
#endif
 
        return eigenVectors.column( Space::dimension - 2 ); // second principal curvature direction is associated to greatest eigenvalue.
      }

References DGtal::SpaceND< dim, TInteger >::dimension, DGtal::functors::IISecondPrincipalDirectionFunctor< TSpace, TMatrix >::eigenValues, and DGtal::functors::IISecondPrincipalDirectionFunctor< TSpace, TMatrix >::eigenVectors.

◆ operator=()

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

Self & DGtal::functors::IISecondPrincipalDirectionFunctor< TSpace, TMatrix >::operator= ( const Self & )

inline

Assignment. Nothing to do.

Returns: itself

Definition at line 321 of file IIGeometricFunctors.h.

321{ return *this; }

Field Documentation

◆ eigenValues

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

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

mutableprivate

A data member only used for temporary calculations.

Definition at line 356 of file IIGeometricFunctors.h.

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

◆ eigenVectors

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

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

mutableprivate

A data member only used for temporary calculations.

Definition at line 354 of file IIGeometricFunctors.h.

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

The documentation for this class 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

Constructor & Destructor Documentation

◆ IISecondPrincipalDirectionFunctor() [1/2]

◆ IISecondPrincipalDirectionFunctor() [2/2]

Member Function Documentation

◆ BOOST_CONCEPT_ASSERT() [1/2]

◆ BOOST_CONCEPT_ASSERT() [2/2]

◆ BOOST_STATIC_ASSERT()

◆ init()

◆ operator()()

◆ operator=()

Field Documentation

◆ eigenValues

◆ eigenVectors