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, RealVector >	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
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.

See also: IntegralInvariantCovarianceEstimator

Definition at line 460 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::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<double, double, RealVector, RealVector> 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<TSpace> 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.

Member Function Documentation

◆ 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.

       {
         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;
        }

References DGtal::functors::IIPrincipalCurvaturesAndDirectionsFunctor< TSpace, TMatrix >::d6_PIr6, DGtal::functors::IIPrincipalCurvaturesAndDirectionsFunctor< TSpace, TMatrix >::d8_5r, and DGtal::functors::IIPrincipalCurvaturesAndDirectionsFunctor< TSpace, TMatrix >::dh5.

◆ 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.

       {
         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])) );
  
         Quantity res(d6_PIr6 * ( eigenValues[2] - ( 3.0 * eigenValues[1] )) + d8_5r,
                      d6_PIr6 * ( eigenValues[1] - ( 3.0 * eigenValues[2] )) + d8_5r,
                      eigenVectors.column( 1 ),
                      eigenVectors.column( 2 ));
         return res;
       }