Aim: Utility class to compute curvatures measures induced by (1) the normal cycle induced by a SurfaceMesh, (2) the standard Lipschitz-Killing invariant forms of area and curvatures. More...

#include <DGtal/geometry/meshes/NormalCycleComputer.h>

Public Types
typedef TRealPoint	RealPoint

typedef TRealVector	RealVector

typedef NormalCycleComputer< RealPoint, RealVector >	Self

typedef DGtal::SurfaceMesh< RealPoint, RealVector >	SurfaceMesh

typedef RealVector::Component	Scalar

typedef SimpleMatrix< Scalar, dimension, dimension >	RealTensor

typedef NormalCycleFormula< RealPoint, RealVector >	Formula

typedef SurfaceMeshMeasure< RealPoint, RealVector, Scalar >	ScalarMeasure

typedef SurfaceMeshMeasure< RealPoint, RealVector, RealTensor >	TensorMeasure

typedef std::vector< Scalar >	Scalars

typedef std::vector< RealPoint >	RealPoints

typedef std::vector< RealVector >	RealVectors

typedef std::vector< RealTensor >	RealTensors

typedef SurfaceMesh::Size	Size

typedef SurfaceMesh::Index	Index

typedef SurfaceMesh::Vertex	Vertex

typedef SurfaceMesh::Face	Face

Public Member Functions
	BOOST_STATIC_ASSERT ((dimension==3))

	NormalCycleComputer (ConstAlias< SurfaceMesh > aMesh)

ScalarMeasure	computeMu0 () const

ScalarMeasure	computeMu1 () const

ScalarMeasure	computeMu2 () const

TensorMeasure	computeMuXY () const

TensorMeasure	computeMuXYs () const

Static Public Member Functions
Formulas for estimating curvatures from measures
static Scalar	meanCurvature (Scalar mu0, Scalar mu1)

static Scalar	GaussianCurvature (Scalar mu0, Scalar mu2)

static std::tuple< Scalar, Scalar, RealVector, RealVector >	principalCurvatures (Scalar mu0, RealTensor muXY, const RealVector &N)

Static Public Attributes
static const Dimension	dimension = RealPoint::dimension

Protected Attributes
const SurfaceMesh &	myMesh
	A reference to the mesh over which computations are done. More...

Detailed Description

template<typename TRealPoint, typename TRealVector>
struct DGtal::NormalCycleComputer< TRealPoint, TRealVector >

Aim: Utility class to compute curvatures measures induced by (1) the normal cycle induced by a SurfaceMesh, (2) the standard Lipschitz-Killing invariant forms of area and curvatures.

Description of template class 'NormalCycleComputer'

Warning: Most curvature measures induces by the normal cycle have meaning only for surfaces with planar faces.

Template Parameters

TRealPoint	an arbitrary model of RealPoint.
TRealVector	an arbitrary model of RealVector.

Examples: geometry/meshes/curvature-measures-nc-3d.cpp, and geometry/meshes/curvature-measures-nc-XY-3d.cpp.

Definition at line 67 of file NormalCycleComputer.h.

Member Typedef Documentation

◆ Face

template<typename TRealPoint , typename TRealVector >

typedef SurfaceMesh::Face DGtal::NormalCycleComputer< TRealPoint, TRealVector >::Face

Definition at line 87 of file NormalCycleComputer.h.

◆ Formula

template<typename TRealPoint , typename TRealVector >

typedef NormalCycleFormula< RealPoint, RealVector > DGtal::NormalCycleComputer< TRealPoint, TRealVector >::Formula

Definition at line 77 of file NormalCycleComputer.h.

◆ Index

template<typename TRealPoint , typename TRealVector >

typedef SurfaceMesh::Index DGtal::NormalCycleComputer< TRealPoint, TRealVector >::Index

Definition at line 85 of file NormalCycleComputer.h.

◆ RealPoint

template<typename TRealPoint , typename TRealVector >

typedef TRealPoint DGtal::NormalCycleComputer< TRealPoint, TRealVector >::RealPoint

Definition at line 69 of file NormalCycleComputer.h.

◆ RealPoints

template<typename TRealPoint , typename TRealVector >

typedef std::vector< RealPoint > DGtal::NormalCycleComputer< TRealPoint, TRealVector >::RealPoints

Definition at line 81 of file NormalCycleComputer.h.

◆ RealTensor

template<typename TRealPoint , typename TRealVector >

typedef SimpleMatrix< Scalar, dimension, dimension > DGtal::NormalCycleComputer< TRealPoint, TRealVector >::RealTensor

Definition at line 76 of file NormalCycleComputer.h.

◆ RealTensors

template<typename TRealPoint , typename TRealVector >

typedef std::vector< RealTensor > DGtal::NormalCycleComputer< TRealPoint, TRealVector >::RealTensors

Definition at line 83 of file NormalCycleComputer.h.

◆ RealVector

template<typename TRealPoint , typename TRealVector >

typedef TRealVector DGtal::NormalCycleComputer< TRealPoint, TRealVector >::RealVector

Definition at line 70 of file NormalCycleComputer.h.

◆ RealVectors

template<typename TRealPoint , typename TRealVector >

typedef std::vector< RealVector > DGtal::NormalCycleComputer< TRealPoint, TRealVector >::RealVectors

Definition at line 82 of file NormalCycleComputer.h.

◆ Scalar

template<typename TRealPoint , typename TRealVector >

typedef RealVector::Component DGtal::NormalCycleComputer< TRealPoint, TRealVector >::Scalar

Definition at line 75 of file NormalCycleComputer.h.

◆ ScalarMeasure

template<typename TRealPoint , typename TRealVector >

typedef SurfaceMeshMeasure< RealPoint, RealVector, Scalar > DGtal::NormalCycleComputer< TRealPoint, TRealVector >::ScalarMeasure

Definition at line 78 of file NormalCycleComputer.h.

◆ Scalars

template<typename TRealPoint , typename TRealVector >

typedef std::vector< Scalar > DGtal::NormalCycleComputer< TRealPoint, TRealVector >::Scalars

Definition at line 80 of file NormalCycleComputer.h.

◆ Self

template<typename TRealPoint , typename TRealVector >

typedef NormalCycleComputer< RealPoint, RealVector > DGtal::NormalCycleComputer< TRealPoint, TRealVector >::Self

Definition at line 71 of file NormalCycleComputer.h.

◆ Size

template<typename TRealPoint , typename TRealVector >

typedef SurfaceMesh::Size DGtal::NormalCycleComputer< TRealPoint, TRealVector >::Size

Definition at line 84 of file NormalCycleComputer.h.

◆ SurfaceMesh

template<typename TRealPoint , typename TRealVector >

typedef DGtal::SurfaceMesh< RealPoint, RealVector > DGtal::NormalCycleComputer< TRealPoint, TRealVector >::SurfaceMesh

Definition at line 74 of file NormalCycleComputer.h.

◆ TensorMeasure

template<typename TRealPoint , typename TRealVector >

typedef SurfaceMeshMeasure< RealPoint, RealVector, RealTensor > DGtal::NormalCycleComputer< TRealPoint, TRealVector >::TensorMeasure

Definition at line 79 of file NormalCycleComputer.h.

◆ Vertex

template<typename TRealPoint , typename TRealVector >

typedef SurfaceMesh::Vertex DGtal::NormalCycleComputer< TRealPoint, TRealVector >::Vertex

Definition at line 86 of file NormalCycleComputer.h.

Constructor & Destructor Documentation

◆ NormalCycleComputer()

template<typename TRealPoint , typename TRealVector >

DGtal::NormalCycleComputer< TRealPoint, TRealVector >::NormalCycleComputer ( ConstAlias< SurfaceMesh > aMesh )

Constructor from mesh.

Parameters

aMesh any simplified mesh that is referenced in this object.

Member Function Documentation

◆ BOOST_STATIC_ASSERT()

template<typename TRealPoint , typename TRealVector >

DGtal::NormalCycleComputer< TRealPoint, TRealVector >::BOOST_STATIC_ASSERT ( (dimension==3) )

◆ computeMu0()

template<typename TRealPoint , typename TRealVector >

ScalarMeasure DGtal::NormalCycleComputer< TRealPoint, TRealVector >::computeMu0 ( ) const

Returns: the \( \mu_0 \) normal cycle measure, i.e. the area measure.

◆ computeMu1()

template<typename TRealPoint , typename TRealVector >

ScalarMeasure DGtal::NormalCycleComputer< TRealPoint, TRealVector >::computeMu1 ( ) const

Returns: the \( \mu_1 \) normal cycle measure, i.e. twice the mean curvature measure.

◆ computeMu2()

template<typename TRealPoint , typename TRealVector >

ScalarMeasure DGtal::NormalCycleComputer< TRealPoint, TRealVector >::computeMu2 ( ) const

Returns: the \( \mu_2 \) normal cycle measure, i.e. the Gaussian curvature measure.

◆ computeMuXY()

template<typename TRealPoint , typename TRealVector >

TensorMeasure DGtal::NormalCycleComputer< TRealPoint, TRealVector >::computeMuXY ( ) const

Returns: the \( \mu^{X,Y} \) normal cycle measure, i.e. the anisotropic tensor curvature measure.

◆ computeMuXYs()

template<typename TRealPoint , typename TRealVector >

TensorMeasure DGtal::NormalCycleComputer< TRealPoint, TRealVector >::computeMuXYs ( ) const

Returns: the \( \tilde{\mu}^{X,Y} \) normal cycle measure, i.e. the anisotropic tensor curvature measure with swapped eigenvectors.

◆ GaussianCurvature()

template<typename TRealPoint , typename TRealVector >

static Scalar DGtal::NormalCycleComputer< TRealPoint, TRealVector >::GaussianCurvature	(	Scalar	mu0,
		Scalar	mu2
	)

inlinestatic

Parameters

mu0	the mu0 measure (i.e. area) of some set
mu2	the mu2 measure (i.e. the Gaussian curvature measue) of the same set

Returns: the estimated Gaussian curvature on this set.

Definition at line 127 of file NormalCycleComputer.h.

    {
      return ( mu0 != 0.0 ) ? mu2 / mu0 : 0.0;
    }

◆ meanCurvature()

template<typename TRealPoint , typename TRealVector >

static Scalar DGtal::NormalCycleComputer< TRealPoint, TRealVector >::meanCurvature	(	Scalar	mu0,
		Scalar	mu1
	)

inlinestatic

Parameters

mu0	the mu0 measure (i.e. area) of some set
mu1	the mu1 measure (i.e. twice the mean curvature measue) of the same set

Returns: the estimated mean curvature on this set.

Definition at line 118 of file NormalCycleComputer.h.

    {
      return ( mu0 != 0.0 ) ? mu1 / ( 2.0 * mu0 ) : 0.0;
    }

◆ principalCurvatures()

template<typename TRealPoint , typename TRealVector >

static std::tuple< Scalar, Scalar, RealVector, RealVector > DGtal::NormalCycleComputer< TRealPoint, TRealVector >::principalCurvatures	(	Scalar	mu0,
		RealTensor	muXY,
		const RealVector &	N
	)

inlinestatic

Parameters

mu0	the mu0 measure (i.e. area) of some set
muXY	the anisotropic muXY measure (i.e. the second fundamental form measue) of the same set
N	the normal vector at the location of the set

Returns: a tuple (K1,K2,D1,D2) where K1 and K2 are two principal curvatures (K1<=K2) and D1 and D2 are their associated principal directions.

Definition at line 141 of file NormalCycleComputer.h.

    {
      muXY += muXY.transpose();
      muXY *= 0.5;
      const double   coef_N = 1000.0 * mu0;
      // Trick to force orthogonality to normal vector.
      for ( int j = 0; j < 3; j++ )
        for ( int k = 0; k < 3; k++ )
          muXY( j, k ) += coef_N * N[ j ] * N[ k ];
      RealTensor V;
      RealVector L;
      EigenDecomposition< 3, double>::getEigenDecomposition( muXY, V, L );
      return std::make_tuple( ( mu0 != 0.0 ) ? -L[ 1 ] / mu0 : 0.0,
                              ( mu0 != 0.0 ) ? -L[ 0 ] / mu0 : 0.0,
                              V.column( 1 ),
                              V.column( 0 ) );
    }    

References DGtal::SimpleMatrix< TComponent, TM, TN >::column(), DGtal::EigenDecomposition< TN, TComponent, TMatrix >::getEigenDecomposition(), and DGtal::SimpleMatrix< TComponent, TM, TN >::transpose().

Field Documentation

◆ dimension

template<typename TRealPoint , typename TRealVector >

const Dimension DGtal::NormalCycleComputer< TRealPoint, TRealVector >::dimension = RealPoint::dimension

static

Definition at line 72 of file NormalCycleComputer.h.

◆ myMesh

template<typename TRealPoint , typename TRealVector >

const SurfaceMesh& DGtal::NormalCycleComputer< TRealPoint, TRealVector >::myMesh

protected

A reference to the mesh over which computations are done.

Definition at line 164 of file NormalCycleComputer.h.

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

NormalCycleComputer.h

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ Face

◆ Formula

◆ Index

◆ RealPoint

◆ RealPoints

◆ RealTensor

◆ RealTensors

◆ RealVector

◆ RealVectors

◆ Scalar

◆ ScalarMeasure

◆ Scalars

◆ Self

◆ Size

◆ SurfaceMesh

◆ TensorMeasure

◆ Vertex

Constructor & Destructor Documentation

◆ NormalCycleComputer()

Member Function Documentation

◆ BOOST_STATIC_ASSERT()

◆ computeMu0()

◆ computeMu1()

◆ computeMu2()

◆ computeMuXY()

◆ computeMuXYs()

◆ GaussianCurvature()

◆ meanCurvature()

◆ principalCurvatures()

Field Documentation

◆ dimension

◆ myMesh