DGtal  1.3.beta
Public Types | Public Member Functions | Private Attributes
DGtal::functors::IISecondPrincipalDirectionFunctor< TSpace, TMatrix > Class Template Reference

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. More...
 
 IISecondPrincipalDirectionFunctor (const Self &)
 Copy constructor. Nothing to do. More...
 
Selfoperator= (const Self &)
 
Value operator() (const Argument &arg) const
 
void init (Component, Component)
 

Private Attributes

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>>
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
TSpacea model of CSpace, for instance SpaceND.
TMatrixa 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
argany 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.

331  {
334 
335  ASSERT ( !std::isnan(eigenValues[0]) ); // NaN
336 #ifdef DEBUG
337  for( Dimension i_dim = 1; i_dim < Space::dimension; ++i_dim )
338  {
339  ASSERT ( std::abs(eigenValues[i_dim - 1]) <= std::abs(eigenValues[i_dim]) );
340  }
341 #endif
342 
343  return eigenVectors.column( Space::dimension - 2 ); // second principal curvature direction is associated to greatest eigenvalue.
344  }

References DGtal::SpaceND< dim, TInteger >::dimension, DGtal::functors::IISecondPrincipalDirectionFunctor< TSpace, TMatrix >::eigenValues, DGtal::functors::IISecondPrincipalDirectionFunctor< TSpace, TMatrix >::eigenVectors, and DGtal::EigenDecomposition< TN, TComponent, TMatrix >::getEigenDecomposition().

◆ 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:
DGtal::EigenDecomposition::getEigenDecomposition
static void getEigenDecomposition(const Matrix &matrix, Matrix &eigenVectors, Vector &eigenValues)
Compute both eigen vectors and eigen values from an input matrix.
DGtal::Dimension
DGtal::uint32_t Dimension
Definition: Common.h:137
DGtal::functors::IISecondPrincipalDirectionFunctor::eigenVectors
Matrix eigenVectors
A data member only used for temporary calculations.
Definition: IIGeometricFunctors.h:354
DGtal::SpaceND::dimension
static const Dimension dimension
static constants to store the dimension.
Definition: SpaceND.h:132
DGtal::functors::IISecondPrincipalDirectionFunctor::eigenValues
RealVector eigenValues
A data member only used for temporary calculations.
Definition: IIGeometricFunctors.h:356