Aim: Utility class to compute curvature measures induced by (1) a corrected normal current defined by a surface mesh with prescribed normals and (2) the standard Lipschitz-Killing invariant forms of area and curvatures. More...

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

Public Types
typedef TRealPoint	RealPoint

typedef TRealVector	RealVector

typedef CorrectedNormalCurrentComputer< RealPoint, RealVector >	Self

typedef DGtal::SurfaceMesh< RealPoint, RealVector >	SurfaceMesh

typedef RealVector::Component	Scalar

typedef SimpleMatrix< Scalar, dimension, dimension >	RealTensor

typedef CorrectedNormalCurrentFormula< 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))

	CorrectedNormalCurrentComputer (ConstAlias< SurfaceMesh > aMesh, bool unit_u=false)

ScalarMeasure	computeMu0 () const

ScalarMeasure	computeMu1 () const

ScalarMeasure	computeMu2 () const

TensorMeasure	computeMuXY () 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 Member Functions
ScalarMeasure	computeMu0ConstantU () const

ScalarMeasure	computeMu1ConstantU () const

ScalarMeasure	computeMu2ConstantU () const

TensorMeasure	computeMuXYConstantU () const

ScalarMeasure	computeMu0InterpolatedU () const

ScalarMeasure	computeMu1InterpolatedU () const

ScalarMeasure	computeMu2InterpolatedU () const

TensorMeasure	computeMuXYInterpolatedU () const

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

bool	myUnitU

Detailed Description

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

Aim: Utility class to compute curvature measures induced by (1) a corrected normal current defined by a surface mesh with prescribed normals and (2) the standard Lipschitz-Killing invariant forms of area and curvatures.

Description of template class 'CorrectedNormalCurrentComputer'

Note: By default it tries to compute interpolated corrected curvature measures, if the mesh has a normal at each vertex, otherwise it computes constant corrected curvature measures.

Template Parameters

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

Examples: geometry/meshes/curvature-comparator-ii-cnc-3d.cpp, geometry/meshes/curvature-measures-icnc-3d.cpp, geometry/meshes/curvature-measures-icnc-XY-3d.cpp, geometry/meshes/digpoly-curvature-measures-cnc-3d.cpp, geometry/meshes/digpoly-curvature-measures-cnc-XY-3d.cpp, geometry/meshes/obj-curvature-measures-icnc-3d.cpp, geometry/meshes/obj-curvature-measures-icnc-XY-3d.cpp, geometry/meshes/vol-curvature-measures-icnc-3d.cpp, and geometry/meshes/vol-curvature-measures-icnc-XY-3d.cpp.

Definition at line 69 of file CorrectedNormalCurrentComputer.h.

Member Typedef Documentation

◆ Face

template<typename TRealPoint , typename TRealVector >

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

Definition at line 89 of file CorrectedNormalCurrentComputer.h.

◆ Formula

template<typename TRealPoint , typename TRealVector >

typedef CorrectedNormalCurrentFormula< RealPoint, RealVector > DGtal::CorrectedNormalCurrentComputer< TRealPoint, TRealVector >::Formula

Definition at line 79 of file CorrectedNormalCurrentComputer.h.

◆ Index

template<typename TRealPoint , typename TRealVector >

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

Definition at line 87 of file CorrectedNormalCurrentComputer.h.

◆ RealPoint

template<typename TRealPoint , typename TRealVector >

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

Definition at line 71 of file CorrectedNormalCurrentComputer.h.

◆ RealPoints

template<typename TRealPoint , typename TRealVector >

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

Definition at line 83 of file CorrectedNormalCurrentComputer.h.

◆ RealTensor

template<typename TRealPoint , typename TRealVector >

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

Definition at line 78 of file CorrectedNormalCurrentComputer.h.

◆ RealTensors

template<typename TRealPoint , typename TRealVector >

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

Definition at line 85 of file CorrectedNormalCurrentComputer.h.

◆ RealVector

template<typename TRealPoint , typename TRealVector >

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

Definition at line 72 of file CorrectedNormalCurrentComputer.h.

◆ RealVectors

template<typename TRealPoint , typename TRealVector >

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

Definition at line 84 of file CorrectedNormalCurrentComputer.h.

◆ Scalar

template<typename TRealPoint , typename TRealVector >

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

Definition at line 77 of file CorrectedNormalCurrentComputer.h.

◆ ScalarMeasure

template<typename TRealPoint , typename TRealVector >

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

Definition at line 80 of file CorrectedNormalCurrentComputer.h.

◆ Scalars

template<typename TRealPoint , typename TRealVector >

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

Definition at line 82 of file CorrectedNormalCurrentComputer.h.

◆ Self

template<typename TRealPoint , typename TRealVector >

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

Definition at line 73 of file CorrectedNormalCurrentComputer.h.

◆ Size

template<typename TRealPoint , typename TRealVector >

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

Definition at line 86 of file CorrectedNormalCurrentComputer.h.

◆ SurfaceMesh

template<typename TRealPoint , typename TRealVector >

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

Definition at line 76 of file CorrectedNormalCurrentComputer.h.

◆ TensorMeasure

template<typename TRealPoint , typename TRealVector >

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

Definition at line 81 of file CorrectedNormalCurrentComputer.h.

◆ Vertex

template<typename TRealPoint , typename TRealVector >

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

Definition at line 88 of file CorrectedNormalCurrentComputer.h.

Constructor & Destructor Documentation

◆ CorrectedNormalCurrentComputer()

template<typename TRealPoint , typename TRealVector >

DGtal::CorrectedNormalCurrentComputer< TRealPoint, TRealVector >::CorrectedNormalCurrentComputer	(	ConstAlias< SurfaceMesh >	aMesh,
		bool	unit_u = false )

Constructor from mesh.

Parameters

aMesh	any simplified mesh that is referenced in this object.
unit_u	when set to 'true' tells the computer to normalize corrected normals in curvature formulae. For instance, for the Gaussian curvature, it induces exact Gaussian curvature computation with spherical triangles.

Member Function Documentation

◆ BOOST_STATIC_ASSERT()

template<typename TRealPoint , typename TRealVector >

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

◆ computeMu0()

template<typename TRealPoint , typename TRealVector >

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

Returns: the \( \mu_0 \) corrected curvature measure, i.e. the area measure.

◆ computeMu0ConstantU()

template<typename TRealPoint , typename TRealVector >

ScalarMeasure DGtal::CorrectedNormalCurrentComputer< TRealPoint, TRealVector >::computeMu0ConstantU ( ) const

protected

Returns: the \( \mu_0 \) corrected curvature measure, i.e. the area measure, when corrected normals are constant per face.

Precondition: ! myMesh.faceNormals().empty()

◆ computeMu0InterpolatedU()

template<typename TRealPoint , typename TRealVector >

ScalarMeasure DGtal::CorrectedNormalCurrentComputer< TRealPoint, TRealVector >::computeMu0InterpolatedU ( ) const

protected

Returns: the \( \mu_0 \) corrected curvature measure, i.e. the area measure, when corrected normals are interpolated per face.

Precondition: ! myMesh.vertexNormals().empty()

◆ computeMu1()

template<typename TRealPoint , typename TRealVector >

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

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

◆ computeMu1ConstantU()

template<typename TRealPoint , typename TRealVector >

ScalarMeasure DGtal::CorrectedNormalCurrentComputer< TRealPoint, TRealVector >::computeMu1ConstantU ( ) const

protected

Returns: the \( \mu_1 \) corrected curvature measure, i.e. twice the mean curvature measure, when corrected normals are constant per face.

Precondition: ! myMesh.faceNormals().empty()

◆ computeMu1InterpolatedU()

template<typename TRealPoint , typename TRealVector >

ScalarMeasure DGtal::CorrectedNormalCurrentComputer< TRealPoint, TRealVector >::computeMu1InterpolatedU ( ) const

protected

Returns: the \( \mu_1 \) corrected curvature measure, i.e. twice the mean curvature measure, when corrected normals are interpolated per face.

Precondition: ! myMesh.vertexNormals().empty()

◆ computeMu2()

template<typename TRealPoint , typename TRealVector >

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

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

◆ computeMu2ConstantU()

template<typename TRealPoint , typename TRealVector >

ScalarMeasure DGtal::CorrectedNormalCurrentComputer< TRealPoint, TRealVector >::computeMu2ConstantU ( ) const

protected

Returns: the \( \mu_2 \) corrected curvature measure, i.e. the Gaussian curvature measure, when corrected normals are constant per face.

Precondition: ! myMesh.faceNormals().empty()

◆ computeMu2InterpolatedU()

template<typename TRealPoint , typename TRealVector >

ScalarMeasure DGtal::CorrectedNormalCurrentComputer< TRealPoint, TRealVector >::computeMu2InterpolatedU ( ) const

protected

Returns: the \( \mu_2 \) corrected curvature measure, i.e. the Gaussian curvature measure, when corrected normals are interpolated per face.

Precondition: ! myMesh.vertexNormals().empty()

◆ computeMuXY()

template<typename TRealPoint , typename TRealVector >

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

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

◆ computeMuXYConstantU()

template<typename TRealPoint , typename TRealVector >

TensorMeasure DGtal::CorrectedNormalCurrentComputer< TRealPoint, TRealVector >::computeMuXYConstantU ( ) const

protected

Returns: the \( \mu^{X,Y} \) corrected curvature measure, i.e. the anisotropic tensor curvature measure, when corrected normals are constant per face.

Precondition: ! myMesh.faceNormals().empty()

◆ computeMuXYInterpolatedU()

template<typename TRealPoint , typename TRealVector >

TensorMeasure DGtal::CorrectedNormalCurrentComputer< TRealPoint, TRealVector >::computeMuXYInterpolatedU ( ) const

protected

Returns: the \( \mu^{X,Y} \) corrected curvature measure, i.e. the anisotropic tensor curvature measure, when corrected normals are interpolated per face.

Precondition: ! myMesh.vertexNormals().empty()

◆ GaussianCurvature()

template<typename TRealPoint , typename TRealVector >

static Scalar DGtal::CorrectedNormalCurrentComputer< 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 135 of file CorrectedNormalCurrentComputer.h.

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

◆ meanCurvature()

template<typename TRealPoint , typename TRealVector >

static Scalar DGtal::CorrectedNormalCurrentComputer< 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 126 of file CorrectedNormalCurrentComputer.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::CorrectedNormalCurrentComputer< 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 149 of file CorrectedNormalCurrentComputer.h.

    {
      muXY += muXY.transpose();
      muXY *= 0.5;
      const double   coef_N = 1000.0 * mu0;
      // Trick to force orthogonality to normal vector.
      // (see @cite lachaud2020interpolated, section 2) 
      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::CorrectedNormalCurrentComputer< TRealPoint, TRealVector >::dimension = RealPoint::dimension

static

Definition at line 74 of file CorrectedNormalCurrentComputer.h.

◆ myMesh

template<typename TRealPoint , typename TRealVector >

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

protected

A reference to the mesh over which computations are done.

Definition at line 176 of file CorrectedNormalCurrentComputer.h.

◆ myUnitU

template<typename TRealPoint , typename TRealVector >

bool DGtal::CorrectedNormalCurrentComputer< TRealPoint, TRealVector >::myUnitU

protected

Tells if we should use a normalized unit vector or not for interpolated curvature measures.

Definition at line 179 of file CorrectedNormalCurrentComputer.h.

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

CorrectedNormalCurrentComputer.h

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Member Functions

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

◆ CorrectedNormalCurrentComputer()

Member Function Documentation

◆ BOOST_STATIC_ASSERT()

◆ computeMu0()

◆ computeMu0ConstantU()

◆ computeMu0InterpolatedU()

◆ computeMu1()

◆ computeMu1ConstantU()

◆ computeMu1InterpolatedU()

◆ computeMu2()

◆ computeMu2ConstantU()

◆ computeMu2InterpolatedU()

◆ computeMuXY()

◆ computeMuXYConstantU()

◆ computeMuXYInterpolatedU()

◆ GaussianCurvature()

◆ meanCurvature()

◆ principalCurvatures()

Field Documentation

◆ dimension

◆ myMesh

◆ myUnitU