Aim: Represents an embedded mesh as faces and a list of vertices. Vertices may be shared among faces but no specific topology is required. However, you also have methods to navigate between neighbor vertices, faces, etc. The mesh can be equipped with normals at faces and/or vertices. More...

#include <DGtal/shapes/SurfaceMesh.h>

Data Structures
struct	VertexMap

Public Types
typedef TRealPoint	RealPoint

typedef TRealVector	RealVector

typedef SurfaceMesh< RealPoint, RealVector >	Self

typedef RealVector::Component	Scalar

typedef std::vector< Scalar >	Scalars

typedef std::size_t	Size
	The type for counting elements. More...

typedef std::size_t	Index
	The type used for numbering vertices and faces. More...

typedef Index	Face

typedef Index	Edge

typedef Index	Vertex

typedef std::pair< Edge, Scalar >	WeightedEdge

typedef std::pair< Face, Scalar >	WeightedFace

typedef std::vector< Vertex >	Vertices
	The type that defines a list/range of vertices (e.g. to define faces) More...

typedef std::vector< Edge >	Edges
	The type that defines a list/range of edges. More...

typedef std::vector< WeightedEdge >	WeightedEdges

typedef std::vector< Face >	Faces

typedef std::vector< WeightedFace >	WeightedFaces

typedef std::pair< Vertex, Vertex >	VertexPair

typedef std::set< Vertex >	VertexSet

typedef IntegerSequenceIterator< Vertex >	ConstIterator
	Non mutable iterator for visiting vertices. More...

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

void	selfDisplay (std::ostream &out) const

bool	isValid () const

Standard services
	~SurfaceMesh ()=default
	Default destructor. More...

	SurfaceMesh ()=default

	SurfaceMesh (const Self &other)=default

	SurfaceMesh (Self &&other)=default

Self &	operator= (const Self &other)=default

template<typename RealPointIterator , typename VerticesIterator >
	SurfaceMesh (RealPointIterator itPos, RealPointIterator itPosEnd, VerticesIterator itVertices, VerticesIterator itVerticesEnd)

template<typename RealPointIterator , typename VerticesIterator >
bool	init (RealPointIterator itPos, RealPointIterator itPosEnd, VerticesIterator itVertices, VerticesIterator itVerticesEnd)

void	clear ()
	Clears everything. The object is empty. More...

Vertex and face vectors initialization and conversion services
template<typename RealVectorIterator >
bool	setVertexNormals (RealVectorIterator itN, RealVectorIterator itNEnd)

template<typename RealVectorIterator >
bool	setFaceNormals (RealVectorIterator itN, RealVectorIterator itNEnd)

void	computeFaceNormalsFromPositions ()

void	computeFaceNormalsFromVertexNormals ()

void	computeVertexNormalsFromFaceNormals ()

void	computeVertexNormalsFromFaceNormalsWithMaxWeights ()

template<typename AnyRing >
std::vector< AnyRing >	computeFaceValuesFromVertexValues (const std::vector< AnyRing > &vvalues) const

template<typename AnyRing >
std::vector< AnyRing >	computeVertexValuesFromFaceValues (const std::vector< AnyRing > &fvalues) const

std::vector< RealVector >	computeFaceUnitVectorsFromVertexUnitVectors (const std::vector< RealVector > &vuvectors) const

std::vector< RealVector >	computeVertexUnitVectorsFromFaceUnitVectors (const std::vector< RealVector > &fuvectors) const

Accessors
Size	nbVertices () const

Size	nbEdges () const

Size	nbFaces () const

long	Euler () const

Edge	makeEdge (Vertex i, Vertex j) const

const Vertices &	incidentVertices (Face f) const

const Faces &	incidentFaces (Vertex v) const

const Faces &	neighborFaces (Face f) const

const Vertices &	neighborVertices (Vertex v) const

const VertexPair &	edgeVertices (Edge e) const

const Faces &	edgeFaces (Edge e) const

const Faces &	edgeRightFaces (Edge e) const

const Faces &	edgeLeftFaces (Edge e) const

const std::vector< Vertices > &	allIncidentVertices () const

const std::vector< Faces > &	allIncidentFaces () const

const std::vector< Faces > &	allNeighborFaces () const

const std::vector< Vertices > &	allNeighborVertices () const

const std::vector< VertexPair > &	allEdgeVertices () const

const std::vector< Faces > &	allEdgeFaces () const

const std::vector< Faces > &	allEdgeRightFaces () const

const std::vector< Faces > &	allEdgeLeftFaces () const

Other topological services
Edges	computeManifoldBoundaryEdges () const

Edges	computeManifoldInnerEdges () const

Edges	computeManifoldInnerConsistentEdges () const

Edges	computeManifoldInnerUnconsistentEdges () const

Edges	computeNonManifoldEdges () const

bool	isBoundariesManifold (bool checkClosed=true) const

std::vector< Vertices >	computeManifoldBoundaryChains () const

Undirected simple graph services
Size	size () const

Size	bestCapacity () const

Size	degree (const Vertex &v) const

template<typename OutputIterator >
void	writeNeighbors (OutputIterator &it, const Vertex &v) const

template<typename OutputIterator , typename VertexPredicate >
void	writeNeighbors (OutputIterator &it, const Vertex &v, const VertexPredicate &pred) const

ConstIterator	begin () const

ConstIterator	end () const

Geometric services
const std::vector< RealPoint > &	positions () const

RealPoint &	position (Vertex v)

const RealPoint &	position (Vertex v) const

const std::vector< RealVector > &	vertexNormals () const

std::vector< RealVector > &	vertexNormals ()

RealVector &	vertexNormal (Vertex v)

const RealVector &	vertexNormal (Vertex v) const

const std::vector< RealVector > &	faceNormals () const

std::vector< RealVector > &	faceNormals ()

RealVector &	faceNormal (Face f)

const RealVector &	faceNormal (Face f) const

Scalar	averageEdgeLength () const

Scalar	distance (const Vertex i, const Vertex j) const

Scalar	localWindow (Face f) const

void	perturbateWithUniformRandomNoise (Scalar p)

void	perturbateWithAdaptiveUniformRandomNoise (Scalar p)

RealPoint	edgeCentroid (Index e) const

RealPoint	faceCentroid (Index f) const

Scalar	faceArea (Index f) const

Scalars	getMaxWeights (Index v) const

WeightedFaces	computeFacesInclusionsInBall (Scalar r, Index f) const

WeightedFaces	computeFacesInclusionsInBall (Scalar r, Index f, RealPoint p) const

std::tuple< Vertices, WeightedEdges, WeightedFaces >	computeCellsInclusionsInBall (Scalar r, Index f) const

std::tuple< Vertices, WeightedEdges, WeightedFaces >	computeCellsInclusionsInBall (Scalar r, Index f, RealPoint p) const

Scalar	faceInclusionRatio (RealPoint p, Scalar r, Index f) const

Scalar	edgeInclusionRatio (RealPoint p, Scalar r, Index e) const

Scalar	vertexInclusionRatio (RealPoint p, Scalar r, Index v) const

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

Protected Member Functions
void	computeNeighbors ()
	Computes neighboring information. More...

void	computeEdges ()
	Computes edge information. More...

Static Protected Member Functions
static Scalar	rand01 ()

Protected Attributes
std::vector< Vertices >	myIncidentVertices
	For each face, its range of incident vertices. More...

std::vector< Faces >	myIncidentFaces
	For each vertex, its range of incident faces. More...

std::vector< RealPoint >	myPositions
	For each vertex, its position. More...

std::vector< RealVector >	myVertexNormals
	For each vertex, its normal vector. More...

std::vector< RealVector >	myFaceNormals
	For each face, its normal vector. More...

std::vector< Faces >	myNeighborFaces
	For each face, its range of neighbor faces (no particular order) More...

std::vector< Vertices >	myNeighborVertices
	For each vertex, its range of neighbor vertices (no particular order) More...

std::vector< VertexPair >	myEdgeVertices
	For each edge, its two vertices. More...

std::vector< Faces >	myEdgeFaces
	For each edge, its faces (one, two, or more if non manifold) More...

std::vector< Faces >	myEdgeRightFaces

std::vector< Faces >	myEdgeLeftFaces

Detailed Description

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

Aim: Represents an embedded mesh as faces and a list of vertices. Vertices may be shared among faces but no specific topology is required. However, you also have methods to navigate between neighbor vertices, faces, etc. The mesh can be equipped with normals at faces and/or vertices.

Description of template class 'SurfaceMesh'

We sum up below the possible classes for representing meshes:

Mesh represents soaps of triangles with traversal operations but without any link between vertices;
TriangulatedSurface represents 2-manifold triangulated meshes, possibly with boundaries, and provides traversal and neighborhood operations (underlying fast index representation);
PolygonalSurface represents 2-manifold polygonal meshes, possibly with boundaries, and provides traversal and neighborhood operations (underlying fast index representation);
SurfaceMesh represents arbitrary sets of faces with possible connexions between faces, edges and vertices, provides traversal and neighborhood operations (underlying fast index representation), and may represent non manifold meshes.
DigitalSurface is a common interface to represent arbitrary digital surfaces, i.e. boundaries of sets of voxels or interfaces between such sets;
IndexedDigitalSurface is a common interface to represent arbitrary digital surfaces, i.e. boundaries of sets of voxels or interfaces between such sets, but with underlying fast index representation.

See also SurfaceMeshReader and SurfaceMeshWriter for input/output operations for SurfaceMesh.

Template Parameters

TRealPoint	an arbitrary model of 3D RealPoint.
TRealVector	an arbitrary model of 3D 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/curvature-measures-nc-3d.cpp, geometry/meshes/curvature-measures-nc-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, geometry/meshes/vol-curvature-measures-icnc-XY-3d.cpp, geometry/tools/exampleLatticeBallDelaunay2D.cpp, geometry/tools/exampleLatticeBallDelaunay3D.cpp, geometry/tools/exampleLatticeBallQuickHull3D.cpp, geometry/tools/exampleQuickHull3D.cpp, geometry/tools/exampleRationalBallDelaunay3D.cpp, geometry/tools/exampleRationalBallQuickHull3D.cpp, geometry/volumes/digitalPolyhedronBuilder3D.cpp, geometry/volumes/fullConvexitySphereGeodesics.cpp, geometry/volumes/standardDigitalPolyhedronBuilder3D.cpp, and shapes/exampleSurfaceMesh.cpp.

Definition at line 91 of file SurfaceMesh.h.

Member Typedef Documentation

◆ ConstIterator

template<typename TRealPoint , typename TRealVector >

typedef IntegerSequenceIterator< Vertex > DGtal::SurfaceMesh< TRealPoint, TRealVector >::ConstIterator

Non mutable iterator for visiting vertices.

Definition at line 129 of file SurfaceMesh.h.

◆ Edge

template<typename TRealPoint , typename TRealVector >

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

Definition at line 107 of file SurfaceMesh.h.

◆ Edges

template<typename TRealPoint , typename TRealVector >

typedef std::vector< Edge > DGtal::SurfaceMesh< TRealPoint, TRealVector >::Edges

The type that defines a list/range of edges.

Definition at line 114 of file SurfaceMesh.h.

◆ Face

template<typename TRealPoint , typename TRealVector >

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

Definition at line 106 of file SurfaceMesh.h.

◆ Faces

template<typename TRealPoint , typename TRealVector >

typedef std::vector< Face > DGtal::SurfaceMesh< TRealPoint, TRealVector >::Faces

Definition at line 116 of file SurfaceMesh.h.

◆ Index

template<typename TRealPoint , typename TRealVector >

typedef std::size_t DGtal::SurfaceMesh< TRealPoint, TRealVector >::Index

The type used for numbering vertices and faces.

Definition at line 105 of file SurfaceMesh.h.

◆ RealPoint

template<typename TRealPoint , typename TRealVector >

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

Definition at line 93 of file SurfaceMesh.h.

◆ RealVector

template<typename TRealPoint , typename TRealVector >

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

Definition at line 94 of file SurfaceMesh.h.

◆ Scalar

template<typename TRealPoint , typename TRealVector >

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

Definition at line 100 of file SurfaceMesh.h.

◆ Scalars

template<typename TRealPoint , typename TRealVector >

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

Definition at line 101 of file SurfaceMesh.h.

◆ Self

template<typename TRealPoint , typename TRealVector >

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

Definition at line 95 of file SurfaceMesh.h.

◆ Size

template<typename TRealPoint , typename TRealVector >

typedef std::size_t DGtal::SurfaceMesh< TRealPoint, TRealVector >::Size

The type for counting elements.

Definition at line 103 of file SurfaceMesh.h.

◆ Vertex

template<typename TRealPoint , typename TRealVector >

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

Definition at line 108 of file SurfaceMesh.h.

◆ VertexPair

template<typename TRealPoint , typename TRealVector >

typedef std::pair< Vertex, Vertex > DGtal::SurfaceMesh< TRealPoint, TRealVector >::VertexPair

Definition at line 118 of file SurfaceMesh.h.

◆ VertexSet

template<typename TRealPoint , typename TRealVector >

typedef std::set<Vertex> DGtal::SurfaceMesh< TRealPoint, TRealVector >::VertexSet

Definition at line 121 of file SurfaceMesh.h.

◆ Vertices

template<typename TRealPoint , typename TRealVector >

typedef std::vector< Vertex > DGtal::SurfaceMesh< TRealPoint, TRealVector >::Vertices

The type that defines a list/range of vertices (e.g. to define faces)

Definition at line 112 of file SurfaceMesh.h.

◆ WeightedEdge

template<typename TRealPoint , typename TRealVector >

typedef std::pair< Edge, Scalar > DGtal::SurfaceMesh< TRealPoint, TRealVector >::WeightedEdge

Definition at line 109 of file SurfaceMesh.h.

◆ WeightedEdges

template<typename TRealPoint , typename TRealVector >

typedef std::vector< WeightedEdge > DGtal::SurfaceMesh< TRealPoint, TRealVector >::WeightedEdges

Definition at line 115 of file SurfaceMesh.h.

◆ WeightedFace

template<typename TRealPoint , typename TRealVector >

typedef std::pair< Face, Scalar > DGtal::SurfaceMesh< TRealPoint, TRealVector >::WeightedFace

Definition at line 110 of file SurfaceMesh.h.

◆ WeightedFaces

template<typename TRealPoint , typename TRealVector >

typedef std::vector< WeightedFace > DGtal::SurfaceMesh< TRealPoint, TRealVector >::WeightedFaces

Definition at line 117 of file SurfaceMesh.h.

Constructor & Destructor Documentation

◆ ~SurfaceMesh()

template<typename TRealPoint , typename TRealVector >

DGtal::SurfaceMesh< TRealPoint, TRealVector >::~SurfaceMesh ( )

default

Default destructor.

◆ SurfaceMesh() [1/4]

template<typename TRealPoint , typename TRealVector >

DGtal::SurfaceMesh< TRealPoint, TRealVector >::SurfaceMesh ( )

default

Default constructor.

A typical construction usage is

std::vector< RealPoint > positions = { { 0, 0, 5 }, { 1, 1, 3 }, { -1, 1, 3 }, { -1, -1, 3 }, { 1, -1, 3 } };
std::vector< Vertices  > faces = { { 0, 1, 2 }, { 0, 2, 3 }, { 0, 3, 4 }, { 0, 4, 1 }, { 4, 3, 2, 1 } };
SurfMesh pyramid_mesh;
pyramid_mesh.init( positions.cbegin(), positions.cend(), faces.cbegin(), faces.cend() );

◆ SurfaceMesh() [2/4]

template<typename TRealPoint , typename TRealVector >

DGtal::SurfaceMesh< TRealPoint, TRealVector >::SurfaceMesh ( const Self & other )

default

Default copy constructor.

Parameters

other the object to clone

◆ SurfaceMesh() [3/4]

template<typename TRealPoint , typename TRealVector >

DGtal::SurfaceMesh< TRealPoint, TRealVector >::SurfaceMesh ( Self && other )

default

Default move constructor.

Parameters

other the object to move

◆ SurfaceMesh() [4/4]

template<typename TRealPoint , typename TRealVector >

template<typename RealPointIterator , typename VerticesIterator >

DGtal::SurfaceMesh< TRealPoint, TRealVector >::SurfaceMesh	(	RealPointIterator	itPos,
		RealPointIterator	itPosEnd,
		VerticesIterator	itVertices,
		VerticesIterator	itVerticesEnd
	)

Builds a mesh from vertex positions and polygonal faces.

Template Parameters

RealPointIterator	any forward iterator on RealPoint.
VerticesIterator	any forward iterator on the range of vertices defining a face.

Parameters

itPos	start of range of iterators pointing on the positions of vertices of the mesh
itPosEnd	end of range of iterators pointing on the positions of vertices of the mesh.
itVertices	start of range of iterators pointing on the (oriented) faces of the mesh, each face being a range of vertex indices.
itVerticesEnd	end of range of iterators pointing on the (oriented) faces of the mesh, each face being a range of vertex indices.

A typical construction usage is

std::vector< RealPoint > positions = { { 0, 0, 5 }, { 1, 1, 3 }, { -1, 1, 3 }, { -1, -1, 3 }, { 1, -1, 3 } };
std::vector< Vertices  > faces = { { 0, 1, 2 }, { 0, 2, 3 }, { 0, 3, 4 }, { 0, 4, 1 }, { 4, 3, 2, 1 } };
auto pyramid_mesh = SurfMesh( positions.cbegin(), positions.cend(), faces.cbegin(), faces.cend() );

Member Function Documentation

◆ allEdgeFaces()

template<typename TRealPoint , typename TRealVector >

const std::vector< Faces > & DGtal::SurfaceMesh< TRealPoint, TRealVector >::allEdgeFaces ( ) const

inline

Returns: a const reference to the vector giving for each edge its incident faces (one, two, or more if non manifold)

Definition at line 386 of file SurfaceMesh.h.

387 { return myEdgeFaces; }

DGtal::SurfaceMesh::myEdgeFaces

std::vector< Faces > myEdgeFaces

For each edge, its faces (one, two, or more if non manifold)

Definition: SurfaceMesh.h:891

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myEdgeFaces.

◆ allEdgeLeftFaces()

template<typename TRealPoint , typename TRealVector >

const std::vector< Faces > & DGtal::SurfaceMesh< TRealPoint, TRealVector >::allEdgeLeftFaces ( ) const

inline

Returns: a const reference to the vector giving for each edge its incident faces to its left (zero if open, one, or more if non manifold).

Note: an edge is stored as a vertex pair (i,j), i < j. So a face to its left, being defined ccw, means that the face is some (..., i, j, ... ).

Definition at line 406 of file SurfaceMesh.h.

407 { return myEdgeLeftFaces; }

DGtal::SurfaceMesh::myEdgeLeftFaces

std::vector< Faces > myEdgeLeftFaces

Definition: SurfaceMesh.h:903

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myEdgeLeftFaces.

◆ allEdgeRightFaces()

template<typename TRealPoint , typename TRealVector >

const std::vector< Faces > & DGtal::SurfaceMesh< TRealPoint, TRealVector >::allEdgeRightFaces ( ) const

inline

Returns: a const reference to the vector giving for each edge its incident faces to its right (zero if open, one, or more if non manifold).

Note: an edge is stored as a vertex pair (i,j), i < j. So a face to its right, being defined ccw, means that the face is some (..., j, i, ... ).

Definition at line 396 of file SurfaceMesh.h.

397 { return myEdgeRightFaces; }

DGtal::SurfaceMesh::myEdgeRightFaces

std::vector< Faces > myEdgeRightFaces

Definition: SurfaceMesh.h:897

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myEdgeRightFaces.

◆ allEdgeVertices()

template<typename TRealPoint , typename TRealVector >

const std::vector< VertexPair > & DGtal::SurfaceMesh< TRealPoint, TRealVector >::allEdgeVertices ( ) const

inline

Returns: a const reference to the vector giving for each edge its two vertices (as a pair (i,j), i<j).

Note: edges are sorted in increasing order.

Definition at line 381 of file SurfaceMesh.h.

382 { return myEdgeVertices; }

DGtal::SurfaceMesh::myEdgeVertices

std::vector< VertexPair > myEdgeVertices

For each edge, its two vertices.

Definition: SurfaceMesh.h:889

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myEdgeVertices.

Referenced by main().

◆ allIncidentFaces()

template<typename TRealPoint , typename TRealVector >

const std::vector< Faces > & DGtal::SurfaceMesh< TRealPoint, TRealVector >::allIncidentFaces ( ) const

inline

Returns: a const reference to the vector giving for each vertex its incident faces.

Definition at line 367 of file SurfaceMesh.h.

368 { return myIncidentFaces; }

DGtal::SurfaceMesh::myIncidentFaces

std::vector< Faces > myIncidentFaces

For each vertex, its range of incident faces.

Definition: SurfaceMesh.h:877

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myIncidentFaces.

◆ allIncidentVertices()

template<typename TRealPoint , typename TRealVector >

const std::vector< Vertices > & DGtal::SurfaceMesh< TRealPoint, TRealVector >::allIncidentVertices ( ) const

inline

Returns: a const reference to the vector giving for each face its incident vertices.

Definition at line 362 of file SurfaceMesh.h.

363 { return myIncidentVertices; }

DGtal::SurfaceMesh::myIncidentVertices

std::vector< Vertices > myIncidentVertices

For each face, its range of incident vertices.

Definition: SurfaceMesh.h:875

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myIncidentVertices.

Referenced by main().

◆ allNeighborFaces()

template<typename TRealPoint , typename TRealVector >

const std::vector< Faces > & DGtal::SurfaceMesh< TRealPoint, TRealVector >::allNeighborFaces ( ) const

inline

Returns: a const reference to the vector of neighbor faces for each face.

Definition at line 371 of file SurfaceMesh.h.

372 { return myNeighborFaces; }

DGtal::SurfaceMesh::myNeighborFaces

std::vector< Faces > myNeighborFaces

For each face, its range of neighbor faces (no particular order)

Definition: SurfaceMesh.h:885

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myNeighborFaces.

◆ allNeighborVertices()

template<typename TRealPoint , typename TRealVector >

const std::vector< Vertices > & DGtal::SurfaceMesh< TRealPoint, TRealVector >::allNeighborVertices ( ) const

inline

Returns: a const reference to the vector of neighbor vertices for each vertex.

Definition at line 375 of file SurfaceMesh.h.

376 { return myNeighborVertices; }

DGtal::SurfaceMesh::myNeighborVertices

std::vector< Vertices > myNeighborVertices

For each vertex, its range of neighbor vertices (no particular order)

Definition: SurfaceMesh.h:887

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myNeighborVertices.

◆ averageEdgeLength()

template<typename TRealPoint , typename TRealVector >

Scalar DGtal::SurfaceMesh< TRealPoint, TRealVector >::averageEdgeLength ( ) const

Returns: the average of the length of edges.

◆ begin()

template<typename TRealPoint , typename TRealVector >

ConstIterator DGtal::SurfaceMesh< TRealPoint, TRealVector >::begin ( ) const

inline

Returns: a (non mutable) iterator pointing on the first vertex.

Definition at line 616 of file SurfaceMesh.h.

617 { return ConstIterator( 0 ); }

DGtal::SurfaceMesh::ConstIterator

IntegerSequenceIterator< Vertex > ConstIterator

Non mutable iterator for visiting vertices.

Definition: SurfaceMesh.h:129

◆ bestCapacity()

template<typename TRealPoint , typename TRealVector >

Size DGtal::SurfaceMesh< TRealPoint, TRealVector >::bestCapacity ( ) const

inline

Returns: an estimate of the maximum number of neighbors for this adjacency

Note: chosen here to be 8. Number of neighbors is 6 on average for planar triangulations.

Definition at line 559 of file SurfaceMesh.h.

560 { return 8; }

◆ BOOST_STATIC_ASSERT()

template<typename TRealPoint , typename TRealVector >

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

◆ clear()

template<typename TRealPoint , typename TRealVector >

void DGtal::SurfaceMesh< TRealPoint, TRealVector >::clear ( )

Clears everything. The object is empty.

◆ computeCellsInclusionsInBall() [1/2]

template<typename TRealPoint , typename TRealVector >

std::tuple< Vertices, WeightedEdges, WeightedFaces > DGtal::SurfaceMesh< TRealPoint, TRealVector >::computeCellsInclusionsInBall	(	Scalar	r,
		Index	f
	)		const

Given a ball of radius r centered on the centroid of face f, return the vertices/edges/faces having an non empty intersection with this ball, each edge/face weighted by its ratio of inclusion (in the range [0,1] where 0 is empty intersection and 1 is completely included).

Parameters

r	the radius of the ball.
f	the face where the ball is centered.

Returns: the range of vertices/edges/faces having an non empty intersection with this ball, each edge/face weighted by its ratio of inclusion (in the range [0,1] where 0 is empty intersection and 1 is completely included).

Note: a vertex is either included or not, so no weight is necessary.

Referenced by DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::measure().

◆ computeCellsInclusionsInBall() [2/2]

template<typename TRealPoint , typename TRealVector >

std::tuple< Vertices, WeightedEdges, WeightedFaces > DGtal::SurfaceMesh< TRealPoint, TRealVector >::computeCellsInclusionsInBall	(	Scalar	r,
		Index	f,
		RealPoint	p
	)		const

Given a ball of radius r centered on a point p belonging to face f, return the vertices/edges/faces having an non empty intersection with this ball, each edge/face weighted by its ratio of inclusion (in the range [0,1] where 0 is empty intersection and 1 is completely included).

Parameters

r	the radius of the ball.
f	the face where the ball is centered.
p	the position on the face where the ball is centered.

Returns: the range of vertices/edges/faces having an non empty intersection with this ball, each edge/face weighted by its ratio of inclusion (in the range [0,1] where 0 is empty intersection and 1 is completely included).

Note: a vertex is either included or not, so no weight is necessary.

◆ computeEdges()

template<typename TRealPoint , typename TRealVector >

void DGtal::SurfaceMesh< TRealPoint, TRealVector >::computeEdges ( )

protected

Computes edge information.

◆ computeFaceNormalsFromPositions()

template<typename TRealPoint , typename TRealVector >

void DGtal::SurfaceMesh< TRealPoint, TRealVector >::computeFaceNormalsFromPositions ( )

Uses the positions of vertices to compute a normal vector to each face of the mesh. It computes the barycenter, triangulates implicitly the face to build the normal vector from the average of implicit triangle normals.

◆ computeFaceNormalsFromVertexNormals()

template<typename TRealPoint , typename TRealVector >

void DGtal::SurfaceMesh< TRealPoint, TRealVector >::computeFaceNormalsFromVertexNormals ( )

Uses the normals associated with vertices to compute a normal vector to each face of the mesh. It simply averages the normals at every incident vertex.

◆ computeFacesInclusionsInBall() [1/2]

template<typename TRealPoint , typename TRealVector >

WeightedFaces DGtal::SurfaceMesh< TRealPoint, TRealVector >::computeFacesInclusionsInBall	(	Scalar	r,
		Index	f
	)		const

Given a ball of radius r centered on the centroid of face f, return the faces having a non empty intersection with this ball, each one weighted by its ratio of inclusion (in the range [0,1] where 0 is empty intersection and 1 is completely included).

Parameters

r	the radius of the ball.
f	the face where the ball is centered.

Returns: the range of faces having an non empty intersection with this ball, each one weighted by its ratio of inclusion (in the range [0,1] where 0 is empty intersection and 1 is completely included).

Note: For faces, the ratio is the approximated area of the face part inside the ball and the face area. The approximation is estimated by computing the distance of face vertices and face barycenter to the ball center and by linear interpolation of the results.

Referenced by DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::measure().

◆ computeFacesInclusionsInBall() [2/2]

template<typename TRealPoint , typename TRealVector >

WeightedFaces DGtal::SurfaceMesh< TRealPoint, TRealVector >::computeFacesInclusionsInBall	(	Scalar	r,
		Index	f,
		RealPoint	p
	)		const

Given a ball of radius r centered on a point p belonging to face f, return the faces having a non empty intersection with this ball, each one weighted by its ratio of inclusion (in the range [0,1] where 0 is empty intersection and 1 is completely included).

Parameters

r	the radius of the ball.
f	the face where the ball is centered.
p	the position on the face where the ball is centered.

Returns: the range of faces having an non empty intersection with this ball, each one weighted by its ratio of inclusion (in the range [0,1] where 0 is empty intersection and 1 is completely included).

Note: For faces, the ratio is the approximated area of the face part inside the ball and the face area. The approximation is estimated by computing the distance of face vertices and face barycenter to the ball center and by linear interpolation of the results.

◆ computeFaceUnitVectorsFromVertexUnitVectors()

template<typename TRealPoint , typename TRealVector >

std::vector< RealVector > DGtal::SurfaceMesh< TRealPoint, TRealVector >::computeFaceUnitVectorsFromVertexUnitVectors ( const std::vector< RealVector > & vuvectors ) const

Parameters

vuvectors any vector of unit vectors on vertices.

Returns: a vector of unit vectors on faces approximating vuvectors.

◆ computeFaceValuesFromVertexValues()

template<typename TRealPoint , typename TRealVector >

template<typename AnyRing >

std::vector< AnyRing > DGtal::SurfaceMesh< TRealPoint, TRealVector >::computeFaceValuesFromVertexValues ( const std::vector< AnyRing > & vvalues ) const

Parameters

vvalues any vector of vertex values.

Returns: a vector of face values approximating vvalues.

Template Parameters

AnyRing any summable and averagable type.

Referenced by main(), and saveToObj().

◆ computeManifoldBoundaryChains()

template<typename TRealPoint , typename TRealVector >

std::vector< Vertices > DGtal::SurfaceMesh< TRealPoint, TRealVector >::computeManifoldBoundaryChains ( ) const

inline

Extract the boundary of a surface mesh as a collection of sequences of vertices. The boundaries must be 1d manifold polygonal curves.

Precondition: the boundaries must be manifold.

Returns: a vector of polygonal simple curves (vector of vertices).

Definition at line 473 of file SurfaceMesh.h.

    {
      std::vector<Vertices> boundaries;
      Vertices boundary;
      auto MBE = this->computeManifoldBoundaryEdges();
      std::map<Vertex,bool> visited;
      std::map<Vertex,Vertices> adjacent;
      
      ASSERT_MSG(MBE.size()>0,"The surface mesh must have boundary edges");
      ASSERT_MSG(this->isBoundariesManifold(), "The surface mesh mush have manifold boundaries");
      
      //Coompute adjecency relationships
      for (auto e : MBE)
      {
        auto ij = this->edgeVertices(e);
        visited[ij.first] = false;
        visited[ij.second] = false;
        adjacent[ij.first].push_back(ij.second);
        adjacent[ij.second].push_back(ij.first);
      }
      
      auto boundary_it = visited.begin();
      
      while(boundary_it != visited.end() )
      {
        Vertex first = (*boundary_it).first;
        visited[first] = true;
        boundary.clear();
        boundary.push_back(first);
        
        Vertex current = first;
        size_t nb_iter = 0;
        bool pushed=false;
        
        while ((!pushed) && (nb_iter < MBE.size()*2))
        {
          bool ok = false;
          for (auto other : adjacent[current])
            if (!visited[other])
            {
              boundary.push_back(other);
              current = other;
              visited[other] = true;
              ok = true;
              break;
            }
          if (!ok)
          {
            //all neighboors are visited
            for (auto other : adjacent[current])
              if (other == first)
              {
                boundaries.push_back(boundary);
                pushed = true;
                break;
              }
            //if first vertex isn't found then this chain is not
            //homeomorphic to a circle, hence isn't added to boundaries
          }
          nb_iter++;
        }
        boundary_it = std::find_if(visited.begin(), visited.end(),
                                   []
                                   (std::pair<Vertex,bool> x){return !x.second;});
      }
      return boundaries;
    }

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::computeManifoldBoundaryEdges(), DGtal::SurfaceMesh< TRealPoint, TRealVector >::edgeVertices(), and DGtal::SurfaceMesh< TRealPoint, TRealVector >::isBoundariesManifold().

◆ computeManifoldBoundaryEdges()

template<typename TRealPoint , typename TRealVector >

Edges DGtal::SurfaceMesh< TRealPoint, TRealVector >::computeManifoldBoundaryEdges ( ) const

Returns: the edges that lie on the boundary of the mesh, i.e. they have only one incident face.

Referenced by DGtal::SurfaceMesh< TRealPoint, TRealVector >::computeManifoldBoundaryChains(), DGtal::SurfaceMesh< TRealPoint, TRealVector >::isBoundariesManifold(), SCENARIO(), and TEST_CASE().

◆ computeManifoldInnerConsistentEdges()

template<typename TRealPoint , typename TRealVector >

Edges DGtal::SurfaceMesh< TRealPoint, TRealVector >::computeManifoldInnerConsistentEdges ( ) const

Returns: the edges that lie on the inside of the mesh, with consistent local orientation, i.e. they have one left incident face, and one right incident face.

◆ computeManifoldInnerEdges()

template<typename TRealPoint , typename TRealVector >

Edges DGtal::SurfaceMesh< TRealPoint, TRealVector >::computeManifoldInnerEdges ( ) const

Returns: the edges that lie on the inside of the mesh, with two incident faces, consistently oriented or not.

Note: union of computeManifoldInnerConsistentEdges and computeManifoldInnerUnconsistentEdges

◆ computeManifoldInnerUnconsistentEdges()

template<typename TRealPoint , typename TRealVector >

Edges DGtal::SurfaceMesh< TRealPoint, TRealVector >::computeManifoldInnerUnconsistentEdges ( ) const

Returns: the edges that have two incident faces, but not correctly oriented, i.e. they may have two left incident faces and no right incident face, or two right incident faces and no left incident face.

◆ computeNeighbors()

template<typename TRealPoint , typename TRealVector >

void DGtal::SurfaceMesh< TRealPoint, TRealVector >::computeNeighbors ( )

protected

Computes neighboring information.

◆ computeNonManifoldEdges()

template<typename TRealPoint , typename TRealVector >

Edges DGtal::SurfaceMesh< TRealPoint, TRealVector >::computeNonManifoldEdges ( ) const

Returns: the edges that are non manifold, i.e. neither boundary or inner edges: they may have more than two incident faces, or two left incident faces for instance.

Referenced by SCENARIO().

◆ computeVertexNormalsFromFaceNormals()

template<typename TRealPoint , typename TRealVector >

void DGtal::SurfaceMesh< TRealPoint, TRealVector >::computeVertexNormalsFromFaceNormals ( )

Uses the normals associated with faces to compute a normal vector to each vertex of the mesh. It simply averages the normals of every incident face.

◆ computeVertexNormalsFromFaceNormalsWithMaxWeights()

template<typename TRealPoint , typename TRealVector >

void DGtal::SurfaceMesh< TRealPoint, TRealVector >::computeVertexNormalsFromFaceNormalsWithMaxWeights ( )

Uses the normals associated with faces to compute a normal vector to each vertex of the mesh. It uses the weights proposed by [84] for combining face information into vertex information.

◆ computeVertexUnitVectorsFromFaceUnitVectors()

template<typename TRealPoint , typename TRealVector >

std::vector< RealVector > DGtal::SurfaceMesh< TRealPoint, TRealVector >::computeVertexUnitVectorsFromFaceUnitVectors ( const std::vector< RealVector > & fuvectors ) const

Parameters

fuvectors any vector of unit vectors on faces.

Returns: a vector of unit vectors on vertices approximating fuvectors.

◆ computeVertexValuesFromFaceValues()

template<typename TRealPoint , typename TRealVector >

template<typename AnyRing >

std::vector< AnyRing > DGtal::SurfaceMesh< TRealPoint, TRealVector >::computeVertexValuesFromFaceValues ( const std::vector< AnyRing > & fvalues ) const

Parameters

fvalues any vector of vertex values.

Returns: a vector of vertex values approximating fvalues.

Template Parameters

AnyRing any summable and averagable type.

◆ degree()

template<typename TRealPoint , typename TRealVector >

Size DGtal::SurfaceMesh< TRealPoint, TRealVector >::degree ( const Vertex & v ) const

inline

Parameters

v	any vertex

Returns: the number of neighbors of this vertex

Definition at line 567 of file SurfaceMesh.h.

568 { return myNeighborVertices[ v ].size(); }

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myNeighborVertices.

◆ distance()

template<typename TRealPoint , typename TRealVector >

Scalar DGtal::SurfaceMesh< TRealPoint, TRealVector >::distance	(	const Vertex	i,
		const Vertex	j
	)		const

inline

Returns: the Euclidean distance between any two vertices i and j.

Parameters

i	first vertex
j	second vertex

Definition at line 692 of file SurfaceMesh.h.

    {
      //unrolling for compiler optimization
      const auto p=this->myPositions[ i ];
      const auto q=this->myPositions[ j ];
      return std::sqrt( (p[0]-q[0])*(p[0]-q[0]) + (p[1]-q[1])*(p[1]-q[1])+ (p[2]-q[2])*(p[2]-q[2]));
    }

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myPositions.

◆ edgeCentroid()

template<typename TRealPoint , typename TRealVector >

RealPoint DGtal::SurfaceMesh< TRealPoint, TRealVector >::edgeCentroid ( Index e ) const

Parameters

e	any valid edge index.

Returns: the centroid (or barycenter) of edge f.

◆ edgeFaces()

template<typename TRealPoint , typename TRealVector >

const Faces & DGtal::SurfaceMesh< TRealPoint, TRealVector >::edgeFaces ( Edge e ) const

inline

Parameters

e any edge

Returns: a const reference to the range giving for edge e its incident faces (one, two, or more if non manifold)

Definition at line 335 of file SurfaceMesh.h.

336 { return myEdgeFaces[ e ]; }

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myEdgeFaces.

◆ edgeInclusionRatio()

template<typename TRealPoint , typename TRealVector >

Scalar DGtal::SurfaceMesh< TRealPoint, TRealVector >::edgeInclusionRatio	(	RealPoint	p,
		Scalar	r,
		Index	e
	)		const

Computes an approximation of the inclusion ratio of a given edge e with a ball of radius r and center p.

Parameters

p	the center of the ball.
r	the radius of the ball.
e	any index of edge.

Returns: the inclusion ratio as a scalar between 0 (no intersection) and 1 (inclusion).

Note: The approximation is estimated by computing the distance of edge vertices and edge midpoint to the ball center and by linear interpolation of the results.

◆ edgeLeftFaces()

template<typename TRealPoint , typename TRealVector >

const Faces & DGtal::SurfaceMesh< TRealPoint, TRealVector >::edgeLeftFaces ( Edge e ) const

inline

Parameters

e any edge

Returns: a const reference to the range giving for edge e its incident faces to its left (zero if open, one, or more if non manifold).

Note: an edge is stored as a vertex pair (i,j), i < j. So a face to its left, being defined ccw, means that the face is some (..., i, j, ... ).

Definition at line 357 of file SurfaceMesh.h.

358 { return myEdgeLeftFaces[ e ]; }

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myEdgeLeftFaces.

◆ edgeRightFaces()

template<typename TRealPoint , typename TRealVector >

const Faces & DGtal::SurfaceMesh< TRealPoint, TRealVector >::edgeRightFaces ( Edge e ) const

inline

Parameters

e any edge

Returns: a const reference to the range giving for edge e its incident faces to its right (zero if open, one, or more if non manifold).

Note: an edge is stored as a vertex pair (i,j), i < j. So a face to its right, being defined ccw, means that the face is some (..., j, i, ... ).

Definition at line 346 of file SurfaceMesh.h.

347 { return myEdgeRightFaces[ e ]; }

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myEdgeRightFaces.

◆ edgeVertices()

template<typename TRealPoint , typename TRealVector >

const VertexPair & DGtal::SurfaceMesh< TRealPoint, TRealVector >::edgeVertices ( Edge e ) const

inline

Parameters

e any edge

Returns: a const reference to the vector giving for edge e its two vertices (as a pair (i,j), i<j).

Definition at line 329 of file SurfaceMesh.h.

330 { return myEdgeVertices[ e ]; }

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myEdgeVertices.

Referenced by DGtal::SurfaceMesh< TRealPoint, TRealVector >::computeManifoldBoundaryChains(), DGtal::SurfaceMesh< TRealPoint, TRealVector >::isBoundariesManifold(), and TEST_CASE().

◆ end()

template<typename TRealPoint , typename TRealVector >

ConstIterator DGtal::SurfaceMesh< TRealPoint, TRealVector >::end ( ) const

inline

Returns: a (non mutable) iterator pointing after the last vertex.

Definition at line 620 of file SurfaceMesh.h.

621 { return ConstIterator( nbVertices() ); }

DGtal::SurfaceMesh::nbVertices

Size nbVertices() const

Definition: SurfaceMesh.h:280

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::nbVertices().

◆ Euler()

template<typename TRealPoint , typename TRealVector >

long DGtal::SurfaceMesh< TRealPoint, TRealVector >::Euler ( ) const

inline

Returns: the euler characteristic of the triangulated surface (a famous topological invariant that is the number of vertices minus the number of edges plus the number of faces).

Definition at line 294 of file SurfaceMesh.h.

295 { return nbVertices() - nbEdges() + nbFaces(); }

DGtal::SurfaceMesh::nbFaces

Size nbFaces() const

Definition: SurfaceMesh.h:288

DGtal::SurfaceMesh::nbEdges

Size nbEdges() const

Definition: SurfaceMesh.h:284

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::nbEdges(), DGtal::SurfaceMesh< TRealPoint, TRealVector >::nbFaces(), and DGtal::SurfaceMesh< TRealPoint, TRealVector >::nbVertices().

Referenced by SCENARIO().

◆ faceArea()

template<typename TRealPoint , typename TRealVector >

Scalar DGtal::SurfaceMesh< TRealPoint, TRealVector >::faceArea ( Index f ) const

Parameters

f	any valid face index.

Returns: the area of face f.

◆ faceCentroid()

template<typename TRealPoint , typename TRealVector >

RealPoint DGtal::SurfaceMesh< TRealPoint, TRealVector >::faceCentroid ( Index f ) const

Parameters

f	any valid face index.

Returns: the centroid (or barycenter) of face f.

◆ faceInclusionRatio()

template<typename TRealPoint , typename TRealVector >

Scalar DGtal::SurfaceMesh< TRealPoint, TRealVector >::faceInclusionRatio	(	RealPoint	p,
		Scalar	r,
		Index	f
	)		const

Computes an approximation of the inclusion ratio of a given face f with a ball of radius r and center p.

Parameters

p	the center of the ball.
r	the radius of the ball.
f	any index of face.

Returns: the inclusion ratio as a scalar between 0 (no intersection) and 1 (inclusion).

Note: The approximation is estimated by computing the distance of face vertices and face barycenter to the ball center and by linear interpolation of the results.

◆ faceNormal() [1/2]

template<typename TRealPoint , typename TRealVector >

RealVector & DGtal::SurfaceMesh< TRealPoint, TRealVector >::faceNormal ( Face f )

inline

Mutable accessor to face normal.

Parameters

f any face.

Returns: the mutable normal associated to f.

Definition at line 677 of file SurfaceMesh.h.

678 { return myFaceNormals[ f ]; }

DGtal::SurfaceMesh::myFaceNormals

std::vector< RealVector > myFaceNormals

For each face, its normal vector.

Definition: SurfaceMesh.h:883

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myFaceNormals.

◆ faceNormal() [2/2]

template<typename TRealPoint , typename TRealVector >

const RealVector & DGtal::SurfaceMesh< TRealPoint, TRealVector >::faceNormal ( Face f ) const

inline

Const accessor to face normal.

Parameters

f any face.

Returns: the non-mutable normal associated to f.

Definition at line 683 of file SurfaceMesh.h.

684 { return myFaceNormals[ f ]; }

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myFaceNormals.

◆ faceNormals() [1/2]

template<typename TRealPoint , typename TRealVector >

std::vector< RealVector > & DGtal::SurfaceMesh< TRealPoint, TRealVector >::faceNormals ( )

inline

Returns: a reference to the vector of normals to faces.

Definition at line 671 of file SurfaceMesh.h.

672 { return myFaceNormals; }

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myFaceNormals.

◆ faceNormals() [2/2]

template<typename TRealPoint , typename TRealVector >

const std::vector< RealVector > & DGtal::SurfaceMesh< TRealPoint, TRealVector >::faceNormals ( ) const

inline

Returns: a const reference to the vector of normals to faces.

Definition at line 667 of file SurfaceMesh.h.

668 { return myFaceNormals; }

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myFaceNormals.

◆ getMaxWeights()

template<typename TRealPoint , typename TRealVector >

Scalars DGtal::SurfaceMesh< TRealPoint, TRealVector >::getMaxWeights ( Index v ) const

Parameters

v	any valid vertex index.

Returns: the Max's weights for each incident face to v, in the same order as myIncidentFaces[ v ].

Note: Used in computeVertexNormalsFromFaceNormalsWithMaxWeights, see [84]

◆ incidentFaces()

template<typename TRealPoint , typename TRealVector >

const Faces & DGtal::SurfaceMesh< TRealPoint, TRealVector >::incidentFaces ( Vertex v ) const

inline

Parameters

v	any vertex

Returns: a const reference to the range giving for vertex v its incident faces.

Definition at line 313 of file SurfaceMesh.h.

314 { return myIncidentFaces[ v ]; }

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myIncidentFaces.

Referenced by DGtal::PolygonalCalculus< TRealPoint, TRealVector >::computeVertexNormal(), DGtal::PolygonalCalculus< TRealPoint, TRealVector >::doubledGlobalLumpedMassMatrix(), and DGtal::PolygonalCalculus< TRealPoint, TRealVector >::globalLumpedMassMatrix().

◆ incidentVertices()

template<typename TRealPoint , typename TRealVector >

const Vertices & DGtal::SurfaceMesh< TRealPoint, TRealVector >::incidentVertices ( Face f ) const

inline

Parameters

f any face

Returns: a const reference to the range giving for face f its incident vertices.

Definition at line 307 of file SurfaceMesh.h.

308 { return myIncidentVertices[ f ]; }

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myIncidentVertices.

Referenced by DGtal::PolygonalCalculus< TRealPoint, TRealVector >::globalConnectionLaplace(), DGtal::PolygonalCalculus< TRealPoint, TRealVector >::globalLaplaceBeltrami(), DGtal::PolygonalCalculus< TRealPoint, TRealVector >::shapeOperator(), DGtal::PolygonalCalculus< TRealPoint, TRealVector >::Tf(), DGtal::PolygonalCalculus< TRealPoint, TRealVector >::transportAndFormatVectorField(), DGtal::PolygonalCalculus< TRealPoint, TRealVector >::updateFaceDegree(), DGtal::PolygonalCalculus< TRealPoint, TRealVector >::vectorArea(), and DGtal::PolygonalCalculus< TRealPoint, TRealVector >::X().

◆ init()

template<typename TRealPoint , typename TRealVector >

template<typename RealPointIterator , typename VerticesIterator >

bool DGtal::SurfaceMesh< TRealPoint, TRealVector >::init	(	RealPointIterator	itPos,
		RealPointIterator	itPosEnd,
		VerticesIterator	itVertices,
		VerticesIterator	itVerticesEnd
	)

Initializes a mesh from vertex positions and polygonal faces (clears everything before).

Template Parameters

RealPointIterator	any forward iterator on RealPoint.
VerticesIterator	any forward iterator on a range of vertices.

Parameters

itPos	start of range of iterators pointing on the positions of vertices of the mesh
itPosEnd	end of range of iterators pointing on the positions of vertices of the mesh.
itVertices	start of range of iterators pointing on the (oriented) faces of the mesh, each face being a range of vertex indices.
itVerticesEnd	end of range of iterators pointing on the (oriented) faces of the mesh, each face being a range of vertex indices.

A typical construction usage is

std::vector< RealPoint > positions = { { 0, 0, 5 }, { 1, 1, 3 }, { -1, 1, 3 }, { -1, -1, 3 }, { 1, -1, 3 } };
std::vector< Vertices  > faces = { { 0, 1, 2 }, { 0, 2, 3 }, { 0, 3, 4 }, { 0, 4, 1 }, { 4, 3, 2, 1 } };
SurfMesh pyramid_mesh;
pyramid_mesh.init( positions.cbegin(), positions.cend(), faces.cbegin(), faces.cend() );

Referenced by main().

◆ isBoundariesManifold()

template<typename TRealPoint , typename TRealVector >

bool DGtal::SurfaceMesh< TRealPoint, TRealVector >::isBoundariesManifold ( bool checkClosed = true ) const

inline

Returns: true if the boundary edges define a collection of manifold 1d polygonal curves (at most 2 adjecent edges per vertex). If checkClosed is set to true, we also check that all polygonal curves are closed.

The method returns false if the surface mesh has no boundary.

Parameters

checkClosed if true, we check that each vertex has exactly two adejcent edges.

Definition at line 446 of file SurfaceMesh.h.

    {
      //computes unordered list of boundary vertices
      std::map<Vertex,Vertices> adjacent;
      auto MBE = this->computeManifoldBoundaryEdges();
      if (MBE.size()==0) return false;
      
      for (auto e : MBE)
      {
        auto ij = this->edgeVertices(e);
        adjacent[ij.first].push_back(ij.second);
        if (adjacent[ij.first].size()>2) return false;
        adjacent[ij.second].push_back(ij.first);
        if (adjacent[ij.second].size()>2)  return false;
      }
      //we may check if all curves are closed.
      if (checkClosed)
        for(const auto &adj : adjacent)
          if (adj.second.size() != 2) return false;
      return true;
    }

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::computeManifoldBoundaryEdges(), and DGtal::SurfaceMesh< TRealPoint, TRealVector >::edgeVertices().

Referenced by DGtal::SurfaceMesh< TRealPoint, TRealVector >::computeManifoldBoundaryChains().

◆ isValid()

template<typename TRealPoint , typename TRealVector >

bool DGtal::SurfaceMesh< TRealPoint, TRealVector >::isValid ( ) const

Checks the validity/consistency of the object.

Returns: 'true' if the object is valid, 'false' otherwise.

◆ localWindow()

template<typename TRealPoint , typename TRealVector >

Scalar DGtal::SurfaceMesh< TRealPoint, TRealVector >::localWindow ( Face f ) const

Parameters

f	any valid face index

Returns: the average distance between the centroid of face f and its vertices.

◆ makeEdge()

template<typename TRealPoint , typename TRealVector >

Edge DGtal::SurfaceMesh< TRealPoint, TRealVector >::makeEdge	(	Vertex	i,
		Vertex	j
	)		const

Parameters

i	any vertex of the mesh
j	any vertex of the mesh

Returns: the edge index of edge (i,j) or nbEdges() if this edge does not exist.

Note: O(log E) time complexity.

◆ nbEdges()

template<typename TRealPoint , typename TRealVector >

Size DGtal::SurfaceMesh< TRealPoint, TRealVector >::nbEdges ( ) const

inline

Returns: the number of (unordered) edges of the mesh.

Definition at line 284 of file SurfaceMesh.h.

285 { return myEdgeVertices.size(); }

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myEdgeVertices.

Referenced by DGtal::SurfaceMesh< TRealPoint, TRealVector >::Euler(), main(), and SCENARIO().

◆ nbFaces()

template<typename TRealPoint , typename TRealVector >

Size DGtal::SurfaceMesh< TRealPoint, TRealVector >::nbFaces ( ) const

inline

Returns: the number of faces of the mesh.

Definition at line 288 of file SurfaceMesh.h.

289 { return myIncidentVertices.size(); }

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myIncidentVertices.

Referenced by DGtal::SurfaceMesh< TRealPoint, TRealVector >::Euler(), DGtal::PolygonalCalculus< TRealPoint, TRealVector >::getOperatorCacheMatrix(), DGtal::PolygonalCalculus< TRealPoint, TRealVector >::getOperatorCacheVector(), DGtal::PolygonalCalculus< TRealPoint, TRealVector >::globalConnectionLaplace(), DGtal::PolygonalCalculus< TRealPoint, TRealVector >::globalLaplaceBeltrami(), main(), DGtal::PolygonalCalculus< TRealPoint, TRealVector >::nbFaces(), saveToObj(), SCENARIO(), TEST_CASE(), and DGtal::PolygonalCalculus< TRealPoint, TRealVector >::updateFaceDegree().

◆ nbVertices()

template<typename TRealPoint , typename TRealVector >

Size DGtal::SurfaceMesh< TRealPoint, TRealVector >::nbVertices ( ) const

inline

Returns: the number of vertices of the mesh.

Definition at line 280 of file SurfaceMesh.h.

281 { return myIncidentFaces.size(); }

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myIncidentFaces.

◆ neighborFaces()

template<typename TRealPoint , typename TRealVector >

const Faces & DGtal::SurfaceMesh< TRealPoint, TRealVector >::neighborFaces ( Face f ) const

inline

Parameters

f any face

Returns: a const reference to the range of neighbor faces for face f.

Definition at line 318 of file SurfaceMesh.h.

319 { return myNeighborFaces[ f ]; }

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myNeighborFaces.

◆ neighborVertices()

template<typename TRealPoint , typename TRealVector >

const Vertices & DGtal::SurfaceMesh< TRealPoint, TRealVector >::neighborVertices ( Vertex v ) const

inline

Parameters

v	any vertex

Returns: a const reference to the range of neighbor vertices for vertex v.

Definition at line 323 of file SurfaceMesh.h.

324 { return myNeighborVertices[ v ]; }

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myNeighborVertices.

Referenced by DGtal::PolygonalCalculus< TRealPoint, TRealVector >::Tv().

◆ operator=()

template<typename TRealPoint , typename TRealVector >

Self & DGtal::SurfaceMesh< TRealPoint, TRealVector >::operator= ( const Self & other )

default

Default assignment constructor.

Parameters

other the object to clone

Returns: a reference to 'this'.

◆ perturbateWithAdaptiveUniformRandomNoise()

template<typename TRealPoint , typename TRealVector >

void DGtal::SurfaceMesh< TRealPoint, TRealVector >::perturbateWithAdaptiveUniformRandomNoise ( Scalar p )

Perturbate the positions with a uniform random noise of 'p * averageLocalEdgeLength' along arbitrary directions.

Parameters

p	any positive real value.

◆ perturbateWithUniformRandomNoise()

template<typename TRealPoint , typename TRealVector >

void DGtal::SurfaceMesh< TRealPoint, TRealVector >::perturbateWithUniformRandomNoise ( Scalar p )

Perturbate the positions with a uniform random noise of 'p * averageEdgeLength' along arbitrary directions.

Parameters

p	any positive real value.

◆ position() [1/2]

template<typename TRealPoint , typename TRealVector >

RealPoint & DGtal::SurfaceMesh< TRealPoint, TRealVector >::position ( Vertex v )

inline

Mutable accessor to vertex position.

Parameters

v	any vertex.

Returns: the mutable position associated to v.

Definition at line 637 of file SurfaceMesh.h.

638 { return myPositions[ v ]; }

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myPositions.

Referenced by main(), DGtal::PolygonalCalculus< TRealPoint, TRealVector >::PolygonalCalculus(), TEST_CASE(), DGtal::PolygonalCalculus< TRealPoint, TRealVector >::Tf(), and DGtal::PolygonalCalculus< TRealPoint, TRealVector >::Tv().

◆ position() [2/2]

template<typename TRealPoint , typename TRealVector >

const RealPoint & DGtal::SurfaceMesh< TRealPoint, TRealVector >::position ( Vertex v ) const

inline

Const accessor to vertex position.

Parameters

v	any vertex.

Returns: the non-mutable position associated to v.

Definition at line 643 of file SurfaceMesh.h.

644 { return myPositions[ v ]; }

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myPositions.

◆ positions()

template<typename TRealPoint , typename TRealVector >

const std::vector< RealPoint > & DGtal::SurfaceMesh< TRealPoint, TRealVector >::positions ( ) const

inline

Returns: a const reference to the vector of positions (of vertices).

Definition at line 631 of file SurfaceMesh.h.

632 { return myPositions; }

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myPositions.

◆ rand01()

template<typename TRealPoint , typename TRealVector >

static Scalar DGtal::SurfaceMesh< TRealPoint, TRealVector >::rand01 ( )

inlinestaticprotected

Returns: a random number between 0.0 and 1.0

Definition at line 918 of file SurfaceMesh.h.

919 { return (Scalar) rand() / (Scalar) RAND_MAX; }

DGtal::SurfaceMesh::Scalar

RealVector::Component Scalar

Definition: SurfaceMesh.h:100

◆ selfDisplay()

template<typename TRealPoint , typename TRealVector >

void DGtal::SurfaceMesh< TRealPoint, TRealVector >::selfDisplay ( std::ostream & out ) const

Writes/Displays the object on an output stream.

Parameters

out	the output stream where the object is written.

◆ setFaceNormals()

template<typename TRealPoint , typename TRealVector >

template<typename RealVectorIterator >

bool DGtal::SurfaceMesh< TRealPoint, TRealVector >::setFaceNormals	(	RealVectorIterator	itN,
		RealVectorIterator	itNEnd
	)

Given a range of real vectors, sets the normals of every face to the given vectors.

◆ setVertexNormals()

template<typename TRealPoint , typename TRealVector >

template<typename RealVectorIterator >

bool DGtal::SurfaceMesh< TRealPoint, TRealVector >::setVertexNormals	(	RealVectorIterator	itN,
		RealVectorIterator	itNEnd
	)

Given a range of real vectors, sets the normals of every vertex to the given vectors.

◆ size()

template<typename TRealPoint , typename TRealVector >

Size DGtal::SurfaceMesh< TRealPoint, TRealVector >::size ( ) const

inline

Returns: the number of vertices of the surface.

Definition at line 550 of file SurfaceMesh.h.

551 { return nbVertices(); }

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::nbVertices().

◆ vertexInclusionRatio()

template<typename TRealPoint , typename TRealVector >

Scalar DGtal::SurfaceMesh< TRealPoint, TRealVector >::vertexInclusionRatio	(	RealPoint	p,
		Scalar	r,
		Index	v
	)		const

Computes the inclusion ratio of a given vertex v with a ball of radius r and center p.

Parameters

p	the center of the ball.
r	the radius of the ball.
v	any index of vertex.

Returns: the inclusion ratio as a scalar, either 0 (no intersection) or 1 (inclusion).

◆ vertexNormal() [1/2]

template<typename TRealPoint , typename TRealVector >

RealVector & DGtal::SurfaceMesh< TRealPoint, TRealVector >::vertexNormal ( Vertex v )

inline

Mutable accessor to vertex normal.

Parameters

v	any vertex.

Returns: the mutable normal associated to v.

Definition at line 657 of file SurfaceMesh.h.

658 { return myVertexNormals[ v ]; }

DGtal::SurfaceMesh::myVertexNormals

std::vector< RealVector > myVertexNormals

For each vertex, its normal vector.

Definition: SurfaceMesh.h:881

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myVertexNormals.

◆ vertexNormal() [2/2]

template<typename TRealPoint , typename TRealVector >

const RealVector & DGtal::SurfaceMesh< TRealPoint, TRealVector >::vertexNormal ( Vertex v ) const

inline

Const accessor to vertex normal.

Parameters

v	any vertex.

Returns: the non-mutable normal associated to v.

Definition at line 663 of file SurfaceMesh.h.

664 { return myVertexNormals[ v ]; }

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myVertexNormals.

◆ vertexNormals() [1/2]

template<typename TRealPoint , typename TRealVector >

std::vector< RealVector > & DGtal::SurfaceMesh< TRealPoint, TRealVector >::vertexNormals ( )

inline

Returns: a reference to the vector of normals to vertices.

Definition at line 651 of file SurfaceMesh.h.

652 { return myVertexNormals; }

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myVertexNormals.

◆ vertexNormals() [2/2]

template<typename TRealPoint , typename TRealVector >

const std::vector< RealVector > & DGtal::SurfaceMesh< TRealPoint, TRealVector >::vertexNormals ( ) const

inline

Returns: a const reference to the vector of normals to vertices.

Definition at line 647 of file SurfaceMesh.h.

648 { return myVertexNormals; }

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myVertexNormals.

◆ writeNeighbors() [1/2]

template<typename TRealPoint , typename TRealVector >

template<typename OutputIterator >

void DGtal::SurfaceMesh< TRealPoint, TRealVector >::writeNeighbors	(	OutputIterator &	it,
		const Vertex &	v
	)		const

inline

Writes the neighbors of a vertex using an output iterator

Template Parameters

OutputIterator the type of an output iterator writing in a container of vertices.

Parameters

it	the output iterator
v	the vertex whose neighbors will be writen

Definition at line 582 of file SurfaceMesh.h.

    {
      for ( auto&& nv : myNeighborVertices[ v ] )
        *it++ = nv;
    }

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myNeighborVertices.

◆ writeNeighbors() [2/2]

template<typename TRealPoint , typename TRealVector >

template<typename OutputIterator , typename VertexPredicate >

void DGtal::SurfaceMesh< TRealPoint, TRealVector >::writeNeighbors	(	OutputIterator &	it,
		const Vertex &	v,
		const VertexPredicate &	pred
	)		const

inline

Writes the neighbors of a vertex which satisfy a predicate using an output iterator

Template Parameters

OutputIterator	the type of an output iterator writing in a container of vertices.
VertexPredicate	the type of the predicate

Parameters

it	the output iterator
v	the vertex whose neighbors will be written
pred	the predicate that must be satisfied

Definition at line 607 of file SurfaceMesh.h.

    {
      for ( auto&& nv : myNeighborVertices[ v ] )
        if ( pred( nv ) ) *it++ = nv;
    }

References DGtal::SurfaceMesh< TRealPoint, TRealVector >::myNeighborVertices.

Field Documentation

◆ dimension

template<typename TRealPoint , typename TRealVector >

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

static

Definition at line 97 of file SurfaceMesh.h.

◆ myEdgeFaces

template<typename TRealPoint , typename TRealVector >

std::vector< Faces > DGtal::SurfaceMesh< TRealPoint, TRealVector >::myEdgeFaces

protected

For each edge, its faces (one, two, or more if non manifold)

Definition at line 891 of file SurfaceMesh.h.

Referenced by DGtal::SurfaceMesh< TRealPoint, TRealVector >::allEdgeFaces(), and DGtal::SurfaceMesh< TRealPoint, TRealVector >::edgeFaces().

◆ myEdgeLeftFaces

template<typename TRealPoint , typename TRealVector >

std::vector< Faces > DGtal::SurfaceMesh< TRealPoint, TRealVector >::myEdgeLeftFaces

protected

For each edge, its faces to its left (zero if open, one, or more if non manifold).

Note: an edge is stored as a vertex pair (i,j), i < j. So a face to its left, being defined ccw, means that the face is some (..., i, j, ... ).

Definition at line 903 of file SurfaceMesh.h.

Referenced by DGtal::SurfaceMesh< TRealPoint, TRealVector >::allEdgeLeftFaces(), and DGtal::SurfaceMesh< TRealPoint, TRealVector >::edgeLeftFaces().

◆ myEdgeRightFaces

template<typename TRealPoint , typename TRealVector >

std::vector< Faces > DGtal::SurfaceMesh< TRealPoint, TRealVector >::myEdgeRightFaces

protected

For each edge, its faces to its right (zero if open, one, or more if non manifold).

Note: an edge is stored as a vertex pair (i,j), i < j. So a face to its right, being defined ccw, means that the face is some (..., j, i, ... ).

Definition at line 897 of file SurfaceMesh.h.

Referenced by DGtal::SurfaceMesh< TRealPoint, TRealVector >::allEdgeRightFaces(), and DGtal::SurfaceMesh< TRealPoint, TRealVector >::edgeRightFaces().

◆ myEdgeVertices

template<typename TRealPoint , typename TRealVector >

std::vector< VertexPair > DGtal::SurfaceMesh< TRealPoint, TRealVector >::myEdgeVertices

protected

For each edge, its two vertices.

Definition at line 889 of file SurfaceMesh.h.

Referenced by DGtal::SurfaceMesh< TRealPoint, TRealVector >::allEdgeVertices(), DGtal::SurfaceMesh< TRealPoint, TRealVector >::edgeVertices(), and DGtal::SurfaceMesh< TRealPoint, TRealVector >::nbEdges().

◆ myFaceNormals

template<typename TRealPoint , typename TRealVector >

std::vector< RealVector > DGtal::SurfaceMesh< TRealPoint, TRealVector >::myFaceNormals

protected

For each face, its normal vector.

Definition at line 883 of file SurfaceMesh.h.

Referenced by DGtal::SurfaceMesh< TRealPoint, TRealVector >::faceNormal(), and DGtal::SurfaceMesh< TRealPoint, TRealVector >::faceNormals().

◆ myIncidentFaces

template<typename TRealPoint , typename TRealVector >

std::vector< Faces > DGtal::SurfaceMesh< TRealPoint, TRealVector >::myIncidentFaces

protected

For each vertex, its range of incident faces.

Definition at line 877 of file SurfaceMesh.h.

Referenced by DGtal::SurfaceMesh< TRealPoint, TRealVector >::allIncidentFaces(), DGtal::SurfaceMesh< TRealPoint, TRealVector >::incidentFaces(), and DGtal::SurfaceMesh< TRealPoint, TRealVector >::nbVertices().

◆ myIncidentVertices

template<typename TRealPoint , typename TRealVector >

std::vector< Vertices > DGtal::SurfaceMesh< TRealPoint, TRealVector >::myIncidentVertices

protected

For each face, its range of incident vertices.

Definition at line 875 of file SurfaceMesh.h.

Referenced by DGtal::SurfaceMesh< TRealPoint, TRealVector >::allIncidentVertices(), DGtal::SurfaceMesh< TRealPoint, TRealVector >::incidentVertices(), and DGtal::SurfaceMesh< TRealPoint, TRealVector >::nbFaces().

◆ myNeighborFaces

template<typename TRealPoint , typename TRealVector >

std::vector< Faces > DGtal::SurfaceMesh< TRealPoint, TRealVector >::myNeighborFaces

protected

For each face, its range of neighbor faces (no particular order)

Definition at line 885 of file SurfaceMesh.h.

Referenced by DGtal::SurfaceMesh< TRealPoint, TRealVector >::allNeighborFaces(), and DGtal::SurfaceMesh< TRealPoint, TRealVector >::neighborFaces().

◆ myNeighborVertices

template<typename TRealPoint , typename TRealVector >

std::vector< Vertices > DGtal::SurfaceMesh< TRealPoint, TRealVector >::myNeighborVertices

protected

For each vertex, its range of neighbor vertices (no particular order)

Definition at line 887 of file SurfaceMesh.h.

Referenced by DGtal::SurfaceMesh< TRealPoint, TRealVector >::allNeighborVertices(), DGtal::SurfaceMesh< TRealPoint, TRealVector >::degree(), DGtal::SurfaceMesh< TRealPoint, TRealVector >::neighborVertices(), and DGtal::SurfaceMesh< TRealPoint, TRealVector >::writeNeighbors().

◆ myPositions

template<typename TRealPoint , typename TRealVector >

std::vector< RealPoint > DGtal::SurfaceMesh< TRealPoint, TRealVector >::myPositions

protected

For each vertex, its position.

Definition at line 879 of file SurfaceMesh.h.

Referenced by DGtal::SurfaceMesh< TRealPoint, TRealVector >::distance(), DGtal::SurfaceMesh< TRealPoint, TRealVector >::position(), and DGtal::SurfaceMesh< TRealPoint, TRealVector >::positions().

◆ myVertexNormals

template<typename TRealPoint , typename TRealVector >

std::vector< RealVector > DGtal::SurfaceMesh< TRealPoint, TRealVector >::myVertexNormals

protected

For each vertex, its normal vector.

Definition at line 881 of file SurfaceMesh.h.

Referenced by DGtal::SurfaceMesh< TRealPoint, TRealVector >::vertexNormal(), and DGtal::SurfaceMesh< TRealPoint, TRealVector >::vertexNormals().

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

SurfaceMesh.h

Data Structures

Public Types

Public Member Functions

Static Public Attributes

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ ConstIterator

◆ Edge

◆ Edges

◆ Face

◆ Faces

◆ Index

◆ RealPoint

◆ RealVector

◆ Scalar

◆ Scalars

◆ Self

◆ Size

◆ Vertex

◆ VertexPair

◆ VertexSet

◆ Vertices

◆ WeightedEdge

◆ WeightedEdges

◆ WeightedFace

◆ WeightedFaces

Constructor & Destructor Documentation

◆ ~SurfaceMesh()

◆ SurfaceMesh() [1/4]

◆ SurfaceMesh() [2/4]

◆ SurfaceMesh() [3/4]

◆ SurfaceMesh() [4/4]

Member Function Documentation

◆ allEdgeFaces()

◆ allEdgeLeftFaces()

◆ allEdgeRightFaces()

◆ allEdgeVertices()

◆ allIncidentFaces()

◆ allIncidentVertices()

◆ allNeighborFaces()

◆ allNeighborVertices()

◆ averageEdgeLength()

◆ begin()

◆ bestCapacity()

◆ BOOST_STATIC_ASSERT()

◆ clear()

◆ computeCellsInclusionsInBall() [1/2]

◆ computeCellsInclusionsInBall() [2/2]

◆ computeEdges()

◆ computeFaceNormalsFromPositions()

◆ computeFaceNormalsFromVertexNormals()

◆ computeFacesInclusionsInBall() [1/2]

◆ computeFacesInclusionsInBall() [2/2]

◆ computeFaceUnitVectorsFromVertexUnitVectors()

◆ computeFaceValuesFromVertexValues()

◆ computeManifoldBoundaryChains()

◆ computeManifoldBoundaryEdges()

◆ computeManifoldInnerConsistentEdges()

◆ computeManifoldInnerEdges()

◆ computeManifoldInnerUnconsistentEdges()

◆ computeNeighbors()

◆ computeNonManifoldEdges()

◆ computeVertexNormalsFromFaceNormals()

◆ computeVertexNormalsFromFaceNormalsWithMaxWeights()

◆ computeVertexUnitVectorsFromFaceUnitVectors()

◆ computeVertexValuesFromFaceValues()

◆ degree()

◆ distance()

◆ edgeCentroid()

◆ edgeFaces()

◆ edgeInclusionRatio()

◆ edgeLeftFaces()

◆ edgeRightFaces()

◆ edgeVertices()

◆ end()

◆ Euler()

◆ faceArea()