DGtal  1.0.0
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>

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

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::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 824 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 833 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 831 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 832 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 834 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 830 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 828 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 829 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 835 of file IIGeometricFunctors.h.

Member Function Documentation

◆ BOOST_CONCEPT_ASSERT()

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 872 of file IIGeometricFunctors.h.

873  {
874  double r3 = r * r * r;
875  double r6 = r3 * r3;
876  d6_PIr6 = 6.0 / ( M_PI * r6 );
877  d8_5r = 8.0 / ( 5.0 * r );
878  double h2 = h * h;
879  dh5 = h2 * h2 * h;
880  }

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 849 of file IIGeometricFunctors.h.

850  {
851  Argument cp_arg = arg;
852  cp_arg *= dh5;
855 
856  ASSERT ( !std::isnan(eigenValues[0]) ); // NaN
857  ASSERT ( (std::abs(eigenValues[0]) <= std::abs(eigenValues[1]))
858  && (std::abs(eigenValues[1]) <= std::abs(eigenValues[2])) );
859 
860  return Value(
861  d6_PIr6 * ( eigenValues[2] - ( 3.0 * eigenValues[1] )) + d8_5r,
862  d6_PIr6 * ( eigenValues[1] - ( 3.0 * eigenValues[2] )) + d8_5r
863  );
864  }
Matrix eigenVectors
A data member only used for temporary calculations.
static void getEigenDecomposition(const Matrix &matrix, Matrix &eigenVectors, Vector &eigenValues)
Compute both eigen vectors and eigen values from an input matrix.
RealVector eigenValues
A data member only used for temporary calculations.

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 890 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 888 of file IIGeometricFunctors.h.

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


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