DGtal 1.3.0
Searching...
No Matches
DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix > Struct Template Reference

Aim: A functor Matrix -> Real that returns the Gaussian curvature by diagonalizing the given covariance matrix. This functor is valid starting from 3D space. Note that the Gaussian curvature is computed by multiplying the two gretest curvature values in absolute value. More...

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

## Public Types

typedef IIGaussianCurvature3DFunctor< 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::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

Quantity dh5

Quantity d6_PIr6

Quantity 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::IIGaussianCurvature3DFunctor< TSpace, TMatrix >

Aim: A functor Matrix -> Real that returns the Gaussian curvature by diagonalizing the given covariance matrix. This functor is valid starting from 3D space. Note that the Gaussian curvature is computed by multiplying the two gretest curvature values in absolute value.

Description of template class 'IIGaussianCurvature3DFunctor'

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

Definition at line 666 of file IIGeometricFunctors.h.

## ◆ Argument

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
 typedef Matrix DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::Argument

Definition at line 675 of file IIGeometricFunctors.h.

## ◆ Component

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
 typedef RealVector::Component DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::Component

Definition at line 673 of file IIGeometricFunctors.h.

## ◆ Matrix

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
 typedef TMatrix DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::Matrix

Definition at line 674 of file IIGeometricFunctors.h.

## ◆ Quantity

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
 typedef Component DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::Quantity

Definition at line 676 of file IIGeometricFunctors.h.

## ◆ RealVector

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
 typedef Space::RealVector DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::RealVector

Definition at line 672 of file IIGeometricFunctors.h.

## ◆ Self

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
 typedef IIGaussianCurvature3DFunctor DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::Self

Definition at line 670 of file IIGeometricFunctors.h.

## ◆ Space

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
 typedef TSpace DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::Space

Definition at line 671 of file IIGeometricFunctors.h.

## ◆ Value

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
 typedef Quantity DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::Value

Definition at line 677 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::IIGaussianCurvature3DFunctor< 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::IIGaussianCurvature3DFunctor< 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::IIGaussianCurvature3DFunctor< 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::IIGaussianCurvature3DFunctor< 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 712 of file IIGeometricFunctors.h.

713 {
714 double r3 = r * r * r;
715 double r6 = r3 * r3;
716 d6_PIr6 = 6.0 / ( M_PI * r6 );
717 d8_5r = 8.0 / ( 5.0 * r );
718 double h2 = h * h;
719 dh5 = h2 * h2 * h;
720 }

## ◆ operator()()

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
 Value DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::operator() ( const Argument & arg ) const
inline

Apply operator.

Parameters
 arg any symmetric positive matrix (covariance matrix
Returns
the Gaussian curvature value for the II covariance matrix, which is the second highest eigenvalue * second highest eigenvalue.

Definition at line 690 of file IIGeometricFunctors.h.

691 {
692 Argument cp_arg = arg;
693 cp_arg *= dh5;
694 EigenDecomposition<Space::dimension, Component, Matrix>
695 ::getEigenDecomposition( cp_arg, eigenVectors, eigenValues );
696
697 ASSERT ( !std::isnan(eigenValues[0]) ); // NaN
698 ASSERT ( (std::abs(eigenValues[0]) <= std::abs(eigenValues[1]))
699 && (std::abs(eigenValues[1]) <= std::abs(eigenValues[2])) );
700
701 Value k1 = d6_PIr6 * ( eigenValues[2] - ( 3.0 * eigenValues[1] )) + d8_5r;
702 Value k2 = d6_PIr6 * ( eigenValues[1] - ( 3.0 * eigenValues[2] )) + d8_5r;
703 return k1 * k2;
704 }
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>>
 Quantity DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::d6_PIr6
private

Definition at line 724 of file IIGeometricFunctors.h.

## ◆ d8_5r

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
 Quantity DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::d8_5r
private

Definition at line 725 of file IIGeometricFunctors.h.

## ◆ dh5

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
 Quantity DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::dh5
private

Definition at line 723 of file IIGeometricFunctors.h.

## ◆ eigenValues

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
 RealVector DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::eigenValues
mutableprivate

A data member only used for temporary calculations.

Definition at line 730 of file IIGeometricFunctors.h.

## ◆ eigenVectors

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>
 Matrix DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::eigenVectors
mutableprivate

A data member only used for temporary calculations.

Definition at line 728 of file IIGeometricFunctors.h.

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