DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix > Struct Template Reference

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

Collaboration diagram for DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >:

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::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::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.

See also

IntegralInvariantCovarianceEstimator

Definition at line 573 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::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::Argument

Definition at line 582 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 580 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 581 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 583 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 579 of file IIGeometricFunctors.h.

Self

template<typename TSpace , typename TMatrix = SimpleMatrix< typename TSpace::RealVector::Component, TSpace::dimension, TSpace::dimension>>

typedef IIGaussianCurvature3DFunctor<TSpace> DGtal::functors::IIGaussianCurvature3DFunctor< TSpace, TMatrix >::Self

Definition at line 577 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 578 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 584 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::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 619 of file IIGeometricFunctors.h.

      {
        double r3 = r * r * r;
        double r6 = r3 * r3;
        d6_PIr6 = 6.0 / ( M_PI * r6 );
        d8_5r = 8.0 / ( 5.0 * r );
        double h2 = h * h;
        dh5 = h2 * h2 * h;
      }

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 597 of file IIGeometricFunctors.h.

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

      {
        Argument cp_arg = arg;
        cp_arg *= dh5;
        EigenDecomposition<Space::dimension, Component, Matrix>
          ::getEigenDecomposition( cp_arg, eigenVectors, eigenValues );

        ASSERT ( !std::isnan(eigenValues[0]) ); // NaN
        ASSERT ( (std::abs(eigenValues[0]) <= std::abs(eigenValues[1])) 
              && (std::abs(eigenValues[1]) <= std::abs(eigenValues[2])) );

        Value k1 = d6_PIr6 * ( eigenValues[2] - ( 3.0 * eigenValues[1] )) + d8_5r;
        Value k2 = d6_PIr6 * ( eigenValues[1] - ( 3.0 * eigenValues[2] )) + d8_5r;
        return k1 * k2;
      }

Field Documentation

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 631 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 632 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 630 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 637 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 635 of file IIGeometricFunctors.h.

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

• IIGeometricFunctors.h