DGtal  1.5.beta
DGtal::functors::IIPrincipalCurvaturesAndDirectionsFunctor< TSpace, TMatrix > Class Template Reference

Aim: A functor Matrix -> std::pair<RealVector,RealVector> that returns the first and the second principal curvature directions by diagonalizing the given covariance matrix. This functor is valid only for 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 IIPrincipalCurvaturesAndDirectionsFunctor< TSpace > Self

typedef TSpace Space

typedef Space::RealVector RealVector

typedef RealVector::Component Component

typedef TMatrix Matrix

typedef Matrix Argument

typedef std::tuple< double, double, RealVector, RealVectorQuantity

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>> class DGtal::functors::IIPrincipalCurvaturesAndDirectionsFunctor< TSpace, TMatrix >

Aim: A functor Matrix -> std::pair<RealVector,RealVector> that returns the first and the second principal curvature directions by diagonalizing the given covariance matrix. This functor is valid only for 3D space. Note that by second we mean the direction with second greatest curvature in absolute value.

Description of template class 'IIPrincipalCurvaturesAndDirectionsFunctor'

Template Parameters
 TSpace a model of CSpace, for instance SpaceND. TMatrix a model of CMatrix, for instance SimpleMatrix.
IntegralInvariantCovarianceEstimator

Definition at line 460 of file IIGeometricFunctors.h.

## ◆ Argument

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

Definition at line 469 of file IIGeometricFunctors.h.

## ◆ Component

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

Definition at line 467 of file IIGeometricFunctors.h.

## ◆ Matrix

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

Definition at line 468 of file IIGeometricFunctors.h.

## ◆ Quantity

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

Definition at line 470 of file IIGeometricFunctors.h.

## ◆ RealVector

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

Definition at line 466 of file IIGeometricFunctors.h.

## ◆ Self

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

Definition at line 464 of file IIGeometricFunctors.h.

## ◆ Space

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

Definition at line 465 of file IIGeometricFunctors.h.

## ◆ Value

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

Definition at line 471 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::IIPrincipalCurvaturesAndDirectionsFunctor< 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::IIPrincipalCurvaturesAndDirectionsFunctor< 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::IIPrincipalCurvaturesAndDirectionsFunctor< 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::IIPrincipalCurvaturesAndDirectionsFunctor< TSpace, TMatrix >::init ( Component h, Component r )
inline

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

Definition at line 506 of file IIGeometricFunctors.h.

507  {
508  double r3 = r * r * r;
509  double r6 = r3 * r3;
510  d6_PIr6 = 6.0 / ( M_PI * r6 );
511  d8_5r = 8.0 / ( 5.0 * r );
512  double h2 = h * h;
513  dh5 = h2 * h2 * h;
514  }

## ◆ operator()()

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

Apply operator.

Parameters
 arg any symmetric positive matrix (covariance matrix
Returns
the principal curvature values and directions in a std::tuple.

Definition at line 484 of file IIGeometricFunctors.h.

485  {
486  Argument cp_arg = arg;
487  cp_arg *= dh5;
490
491  ASSERT ( !std::isnan(eigenValues[0]) ); // NaN
492  ASSERT ( (std::abs(eigenValues[0]) <= std::abs(eigenValues[1]))
493  && (std::abs(eigenValues[1]) <= std::abs(eigenValues[2])) );
494
495  Quantity res(d6_PIr6 * ( eigenValues[2] - ( 3.0 * eigenValues[1] )) + d8_5r,
496  d6_PIr6 * ( eigenValues[1] - ( 3.0 * eigenValues[2] )) + d8_5r,
497  eigenVectors.column( 1 ),
498  eigenVectors.column( 2 ));
499  return res;
500  }
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.
std::tuple< double, double, RealVector, RealVector > Quantity
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::IIPrincipalCurvaturesAndDirectionsFunctor< TSpace, TMatrix >::d6_PIr6
private

Definition at line 518 of file IIGeometricFunctors.h.

## ◆ d8_5r

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

Definition at line 519 of file IIGeometricFunctors.h.

## ◆ dh5

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

Definition at line 517 of file IIGeometricFunctors.h.

## ◆ eigenValues

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

A data member only used for temporary calculations.

Definition at line 523 of file IIGeometricFunctors.h.

## ◆ eigenVectors

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

A data member only used for temporary calculations.

Definition at line 521 of file IIGeometricFunctors.h.

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