DGtal  1.2.0
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
 TSpace a model of CSpace, for instance SpaceND. TMatrix a model of CMatrix, for instance SimpleMatrix.
IntegralInvariantCovarianceEstimator

Definition at line 912 of file IIGeometricFunctors.h.

## ◆ 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 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 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.

## ◆ 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
 h the gridstep r the 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  }

## ◆ 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
 arg any 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  }
static void getEigenDecomposition(const Matrix &matrix, Matrix &eigenVectors, Vector &eigenValues)
Compute both eigen vectors and eigen values from an input matrix.
Matrix eigenVectors
A data member only used for temporary calculations.
RealVector eigenValues
A data member only used for temporary calculations.

## ◆ 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

Definition at line 972 of file IIGeometricFunctors.h.

## ◆ 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

Definition at line 973 of file IIGeometricFunctors.h.

## ◆ dh5

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

Definition at line 971 of file IIGeometricFunctors.h.

## ◆ 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.

## ◆ 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.

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