DGtal  0.9.3
Public Types | Public Member Functions | Private Attributes
DGtal::functors::IIFirstPrincipalCurvature3DFunctor< TSpace, TMatrix > Struct Template Reference

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

Collaboration diagram for DGtal::functors::IIFirstPrincipalCurvature3DFunctor< TSpace, TMatrix >:
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Public Types

typedef IIFirstPrincipalCurvature3DFunctor< 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::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
 
RealVector eigenValues
 

Detailed Description

template<typename TSpace, typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
struct DGtal::functors::IIFirstPrincipalCurvature3DFunctor< TSpace, TMatrix >

Aim: A functor Matrix -> Real that returns the first 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 'IIFirstPrincipalCurvature3DFunctor'

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

Definition at line 656 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::IIFirstPrincipalCurvature3DFunctor< TSpace, TMatrix >::Argument

Definition at line 665 of file IIGeometricFunctors.h.

◆ Component

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
typedef RealVector::Component DGtal::functors::IIFirstPrincipalCurvature3DFunctor< TSpace, TMatrix >::Component

Definition at line 663 of file IIGeometricFunctors.h.

◆ Matrix

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
typedef TMatrix DGtal::functors::IIFirstPrincipalCurvature3DFunctor< TSpace, TMatrix >::Matrix

Definition at line 664 of file IIGeometricFunctors.h.

◆ Quantity

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
typedef Component DGtal::functors::IIFirstPrincipalCurvature3DFunctor< TSpace, TMatrix >::Quantity

Definition at line 666 of file IIGeometricFunctors.h.

◆ RealVector

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
typedef Space::RealVector DGtal::functors::IIFirstPrincipalCurvature3DFunctor< TSpace, TMatrix >::RealVector

Definition at line 662 of file IIGeometricFunctors.h.

◆ Self

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
typedef IIFirstPrincipalCurvature3DFunctor<TSpace> DGtal::functors::IIFirstPrincipalCurvature3DFunctor< TSpace, TMatrix >::Self

Definition at line 660 of file IIGeometricFunctors.h.

◆ Space

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
typedef TSpace DGtal::functors::IIFirstPrincipalCurvature3DFunctor< TSpace, TMatrix >::Space

Definition at line 661 of file IIGeometricFunctors.h.

◆ Value

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
typedef Quantity DGtal::functors::IIFirstPrincipalCurvature3DFunctor< TSpace, TMatrix >::Value

Definition at line 667 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::IIFirstPrincipalCurvature3DFunctor< 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::IIFirstPrincipalCurvature3DFunctor< 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::IIFirstPrincipalCurvature3DFunctor< 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 701 of file IIGeometricFunctors.h.

702  {
703  double r3 = r * r * r;
704  double r6 = r3 * r3;
705  d6_PIr6 = 6.0 / ( M_PI * r6 );
706  d8_5r = 8.0 / ( 5.0 * r );
707  double h2 = h * h;
708  dh5 = h2 * h2 * h;
709  }

◆ operator()()

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
Value DGtal::functors::IIFirstPrincipalCurvature3DFunctor< TSpace, TMatrix >::operator() ( const Argument arg) const
inline

Apply operator.

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

Definition at line 680 of file IIGeometricFunctors.h.

References DGtal::functors::IINormalDirectionFunctor< TSpace, TMatrix >::eigenValues, DGtal::functors::IINormalDirectionFunctor< TSpace, TMatrix >::eigenVectors, and DGtal::EigenDecomposition< TN, TComponent, TMatrix >::getEigenDecomposition().

681  {
682  Argument cp_arg = arg;
683  cp_arg *= dh5;
686 
687  ASSERT ( !std::isnan(eigenValues[0]) ); // NaN
688  ASSERT ( (std::abs(eigenValues[0]) <= std::abs(eigenValues[1]))
689  && (std::abs(eigenValues[1]) <= std::abs(eigenValues[2])) );
690 
691 
692  return d6_PIr6 * ( eigenValues[2] - ( 3.0 * eigenValues[1] )) + d8_5r;
693  }
RealVector eigenValues
A data member only used for temporary calculations.
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.

Field Documentation

◆ d6_PIr6

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
Quantity DGtal::functors::IIFirstPrincipalCurvature3DFunctor< TSpace, TMatrix >::d6_PIr6
private

Definition at line 713 of file IIGeometricFunctors.h.

◆ d8_5r

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
Quantity DGtal::functors::IIFirstPrincipalCurvature3DFunctor< TSpace, TMatrix >::d8_5r
private

Definition at line 714 of file IIGeometricFunctors.h.

◆ dh5

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
Quantity DGtal::functors::IIFirstPrincipalCurvature3DFunctor< TSpace, TMatrix >::dh5
private

Definition at line 712 of file IIGeometricFunctors.h.

◆ eigenValues

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
RealVector DGtal::functors::IIFirstPrincipalCurvature3DFunctor< TSpace, TMatrix >::eigenValues
mutableprivate

A data member only used for temporary calculations.

Definition at line 719 of file IIGeometricFunctors.h.

◆ eigenVectors

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
Matrix DGtal::functors::IIFirstPrincipalCurvature3DFunctor< TSpace, TMatrix >::eigenVectors
mutableprivate

A data member only used for temporary calculations.

Definition at line 717 of file IIGeometricFunctors.h.


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