DGtal  1.3.beta
Public Types | Public Member Functions | Private Attributes
DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix > Struct Template Reference

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. More...

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

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, ComponentQuantity
 
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

double dh5
 
double d6_PIr6
 
double 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::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
TSpacea model of CSpace, for instance SpaceND.
TMatrixa model of CMatrix, for instance SimpleMatrix.
See also
IntegralInvariantCovarianceEstimator

Definition at line 912 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::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::Argument

Definition at line 921 of file IIGeometricFunctors.h.

◆ Component

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 919 of file IIGeometricFunctors.h.

◆ Matrix

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 920 of file IIGeometricFunctors.h.

◆ Quantity

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 922 of file IIGeometricFunctors.h.

◆ RealVector

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 918 of file IIGeometricFunctors.h.

◆ Self

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 916 of file IIGeometricFunctors.h.

◆ Space

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 917 of file IIGeometricFunctors.h.

◆ Value

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 923 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::IIPrincipalCurvatures3DFunctor< 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::IIPrincipalCurvatures3DFunctor< 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::IIPrincipalCurvatures3DFunctor< 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::IIPrincipalCurvatures3DFunctor< 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 960 of file IIGeometricFunctors.h.

961  {
962  double r3 = r * r * r;
963  double r6 = r3 * r3;
964  d6_PIr6 = 6.0 / ( M_PI * r6 );
965  d8_5r = 8.0 / ( 5.0 * r );
966  double h2 = h * h;
967  dh5 = h2 * h2 * h;
968  }

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

◆ operator()()

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
argany 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 937 of file IIGeometricFunctors.h.

938  {
939  Argument cp_arg = arg;
940  cp_arg *= dh5;
943 
944  ASSERT ( !std::isnan(eigenValues[0]) ); // NaN
945  ASSERT ( (std::abs(eigenValues[0]) <= std::abs(eigenValues[1]))
946  && (std::abs(eigenValues[1]) <= std::abs(eigenValues[2])) );
947 
948  return Value(
949  d6_PIr6 * ( eigenValues[2] - ( 3.0 * eigenValues[1] )) + d8_5r,
950  d6_PIr6 * ( eigenValues[1] - ( 3.0 * eigenValues[2] )) + d8_5r
951  );
952  }

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

◆ d8_5r

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
double DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::d8_5r
private

◆ dh5

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
double DGtal::functors::IIPrincipalCurvatures3DFunctor< TSpace, TMatrix >::dh5
private

◆ eigenValues

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 978 of file IIGeometricFunctors.h.

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

◆ eigenVectors

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 976 of file IIGeometricFunctors.h.

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


The documentation for this struct was generated from the following file:
DGtal::functors::IIPrincipalCurvatures3DFunctor::Value
Quantity Value
Definition: IIGeometricFunctors.h:923
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::IIPrincipalCurvatures3DFunctor::d8_5r
double d8_5r
Definition: IIGeometricFunctors.h:973
DGtal::functors::IIPrincipalCurvatures3DFunctor::eigenVectors
Matrix eigenVectors
A data member only used for temporary calculations.
Definition: IIGeometricFunctors.h:976
DGtal::functors::IIPrincipalCurvatures3DFunctor::eigenValues
RealVector eigenValues
A data member only used for temporary calculations.
Definition: IIGeometricFunctors.h:978
DGtal::functors::IIPrincipalCurvatures3DFunctor::Argument
Matrix Argument
Definition: IIGeometricFunctors.h:921
DGtal::functors::IIPrincipalCurvatures3DFunctor::d6_PIr6
double d6_PIr6
Definition: IIGeometricFunctors.h:972
DGtal::functors::IIPrincipalCurvatures3DFunctor::dh5
double dh5
Definition: IIGeometricFunctors.h:971