DGtal  1.3.beta
Public Types | Public Member Functions | Private Attributes
DGtal::functors::IISecondPrincipalCurvature3DFunctor< TSpace, TMatrix > Struct Template Reference

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

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

Public Types

typedef IISecondPrincipalCurvature3DFunctor< 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::IISecondPrincipalCurvature3DFunctor< TSpace, TMatrix >

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

Description of template class 'IISecondPrincipalCurvature3DFunctor'

Template Parameters
TSpacea model of CSpace, for instance SpaceND.
TMatrixa model of CMatrix, for instance SimpleMatrix.
See also
IntegralInvariantCovarianceEstimator

Definition at line 831 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::IISecondPrincipalCurvature3DFunctor< TSpace, TMatrix >::Argument

Definition at line 840 of file IIGeometricFunctors.h.

◆ Component

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
typedef RealVector::Component DGtal::functors::IISecondPrincipalCurvature3DFunctor< TSpace, TMatrix >::Component

Definition at line 838 of file IIGeometricFunctors.h.

◆ Matrix

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
typedef TMatrix DGtal::functors::IISecondPrincipalCurvature3DFunctor< TSpace, TMatrix >::Matrix

Definition at line 839 of file IIGeometricFunctors.h.

◆ Quantity

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
typedef Component DGtal::functors::IISecondPrincipalCurvature3DFunctor< TSpace, TMatrix >::Quantity

Definition at line 841 of file IIGeometricFunctors.h.

◆ RealVector

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
typedef Space::RealVector DGtal::functors::IISecondPrincipalCurvature3DFunctor< TSpace, TMatrix >::RealVector

Definition at line 837 of file IIGeometricFunctors.h.

◆ Self

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
typedef IISecondPrincipalCurvature3DFunctor<TSpace> DGtal::functors::IISecondPrincipalCurvature3DFunctor< TSpace, TMatrix >::Self

Definition at line 835 of file IIGeometricFunctors.h.

◆ Space

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
typedef TSpace DGtal::functors::IISecondPrincipalCurvature3DFunctor< TSpace, TMatrix >::Space

Definition at line 836 of file IIGeometricFunctors.h.

◆ Value

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
typedef Quantity DGtal::functors::IISecondPrincipalCurvature3DFunctor< TSpace, TMatrix >::Value

Definition at line 842 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::IISecondPrincipalCurvature3DFunctor< 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::IISecondPrincipalCurvature3DFunctor< 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::IISecondPrincipalCurvature3DFunctor< 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::IISecondPrincipalCurvature3DFunctor< TSpace, TMatrix >::init ( Component  h,
Component  r 
)
inline

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

Parameters
hthe gridstep
rthe ball radius

Definition at line 875 of file IIGeometricFunctors.h.

876  {
877  double r3 = r * r * r;
878  double r6 = r3 * r3;
879  d6_PIr6 = 6.0 / ( M_PI * r6 );
880  d8_5r = 8.0 / ( 5.0 * r );
881  double h2 = h * h;
882  dh5 = h2 * h2 * h;
883  }

References DGtal::functors::IISecondPrincipalCurvature3DFunctor< TSpace, TMatrix >::d6_PIr6, DGtal::functors::IISecondPrincipalCurvature3DFunctor< TSpace, TMatrix >::d8_5r, and DGtal::functors::IISecondPrincipalCurvature3DFunctor< TSpace, TMatrix >::dh5.

◆ operator()()

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
Value DGtal::functors::IISecondPrincipalCurvature3DFunctor< TSpace, TMatrix >::operator() ( const Argument arg) const
inline

Apply operator.

Parameters
argany symmetric positive matrix (covariance matrix
Returns
the second principal curvature value for the II covariance matrix, which is the second highest eigenvalue.

Definition at line 855 of file IIGeometricFunctors.h.

856  {
857  Argument cp_arg = arg;
858  cp_arg *= dh5;
861 
862  ASSERT ( !std::isnan(eigenValues[0]) ); // NaN
863  ASSERT ( (std::abs(eigenValues[0]) <= std::abs(eigenValues[1]))
864  && (std::abs(eigenValues[1]) <= std::abs(eigenValues[2])) );
865 
866  return d6_PIr6 * ( eigenValues[1] - ( 3.0 * eigenValues[2] )) + d8_5r;
867  }

References DGtal::functors::IISecondPrincipalCurvature3DFunctor< TSpace, TMatrix >::d6_PIr6, DGtal::functors::IISecondPrincipalCurvature3DFunctor< TSpace, TMatrix >::d8_5r, DGtal::functors::IISecondPrincipalCurvature3DFunctor< TSpace, TMatrix >::dh5, DGtal::functors::IISecondPrincipalCurvature3DFunctor< TSpace, TMatrix >::eigenValues, DGtal::functors::IISecondPrincipalCurvature3DFunctor< TSpace, TMatrix >::eigenVectors, and DGtal::EigenDecomposition< TN, TComponent, TMatrix >::getEigenDecomposition().

Field Documentation

◆ d6_PIr6

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
Quantity DGtal::functors::IISecondPrincipalCurvature3DFunctor< TSpace, TMatrix >::d6_PIr6
private

◆ d8_5r

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
Quantity DGtal::functors::IISecondPrincipalCurvature3DFunctor< TSpace, TMatrix >::d8_5r
private

◆ dh5

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
Quantity DGtal::functors::IISecondPrincipalCurvature3DFunctor< TSpace, TMatrix >::dh5
private

◆ eigenValues

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
RealVector DGtal::functors::IISecondPrincipalCurvature3DFunctor< TSpace, TMatrix >::eigenValues
mutableprivate

A data member only used for temporary calculations.

Definition at line 893 of file IIGeometricFunctors.h.

Referenced by DGtal::functors::IISecondPrincipalCurvature3DFunctor< TSpace, TMatrix >::operator()().

◆ eigenVectors

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
Matrix DGtal::functors::IISecondPrincipalCurvature3DFunctor< TSpace, TMatrix >::eigenVectors
mutableprivate

A data member only used for temporary calculations.

Definition at line 891 of file IIGeometricFunctors.h.

Referenced by DGtal::functors::IISecondPrincipalCurvature3DFunctor< TSpace, TMatrix >::operator()().


The documentation for this struct 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::functors::IISecondPrincipalCurvature3DFunctor::eigenValues
RealVector eigenValues
A data member only used for temporary calculations.
Definition: IIGeometricFunctors.h:893
DGtal::functors::IISecondPrincipalCurvature3DFunctor::eigenVectors
Matrix eigenVectors
A data member only used for temporary calculations.
Definition: IIGeometricFunctors.h:891
DGtal::functors::IISecondPrincipalCurvature3DFunctor::d6_PIr6
Quantity d6_PIr6
Definition: IIGeometricFunctors.h:887
DGtal::functors::IISecondPrincipalCurvature3DFunctor::d8_5r
Quantity d8_5r
Definition: IIGeometricFunctors.h:888
DGtal::functors::IISecondPrincipalCurvature3DFunctor::Argument
Matrix Argument
Definition: IIGeometricFunctors.h:840
DGtal::functors::IISecondPrincipalCurvature3DFunctor::dh5
Quantity dh5
Definition: IIGeometricFunctors.h:886