Aim: Represents a triangulated surface. The topology is stored with a half-edge data structure. This object stored the positions of vertices in space. If you need further data attached to the surface, you may use property maps (see TriangulatedSurface::makeVertexMap). More...

#include <DGtal/shapes/TriangulatedSurface.h>

Data Structures
struct	IndexedPropertyMap

struct	VertexMap

Public Types
typedef TPoint	Point

typedef TriangulatedSurface< TPoint >	Self

typedef HalfEdgeDataStructure::Size	Size

typedef HalfEdgeDataStructure::Index	Index

typedef HalfEdgeDataStructure::VertexIndex	VertexIndex

typedef HalfEdgeDataStructure::EdgeIndex	EdgeIndex

typedef HalfEdgeDataStructure::FaceIndex	FaceIndex

typedef HalfEdgeDataStructure::Triangle	Triangle

typedef std::vector< Point >	PositionsStorage

typedef std::vector< Triangle >	TriangleStorage

typedef VertexIndex	Vertex

typedef std::set< Vertex >	VertexSet

typedef EdgeIndex	Edge

typedef IntegerSequenceIterator< VertexIndex >	ConstIterator

typedef HalfEdgeDataStructure::HalfEdgeIndex	Arc

typedef HalfEdgeDataStructure::FaceIndex	Face

typedef std::vector< Arc >	ArcRange

typedef std::vector< Face >	FaceRange

typedef std::vector< Vertex >	VertexRange

typedef IndexedPropertyMap< Point >	PositionsMap

Public Member Functions
	BOOST_STATIC_CONSTANT (Face, INVALID_FACE=HALF_EDGE_INVALID_INDEX)

	~TriangulatedSurface ()

	TriangulatedSurface ()

void	clear ()
	Clears everything.

bool	build ()

VertexIndex	addVertex (const Point &vdata)

FaceIndex	addTriangle (VertexIndex v0, VertexIndex v1, VertexIndex v2)

HalfEdgeDataStructure &	heds ()

const HalfEdgeDataStructure &	heds () const

Size	nbArcs () const

Size	nbVertices () const

Size	nbEdges () const

Size	nbFaces () const

long	Euler () const

PositionsMap	positions ()

template<typename AnyData >
IndexedPropertyMap< AnyData >	makeVertexMap () const

template<typename AnyData >
IndexedPropertyMap< AnyData >	makeVertexMap (AnyData value) const

template<typename AnyData >
IndexedPropertyMap< AnyData >	makeEdgeMap () const

template<typename AnyData >
IndexedPropertyMap< AnyData >	makeEdgeMap (AnyData value) const

template<typename AnyData >
IndexedPropertyMap< AnyData >	makeFaceMap () const

template<typename AnyData >
IndexedPropertyMap< AnyData >	makeFaceMap (AnyData value) const

Point &	position (Vertex v)

const Point &	position (Vertex v) const

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

ArcRange	outArcs (const Vertex &v) const

ArcRange	inArcs (const Vertex &v) const

FaceRange	facesAroundVertex (const Vertex &v) const

Vertex	head (const Arc &a) const

Vertex	tail (const Arc &a) const

Arc	opposite (const Arc &a) const

Arc	next (const Arc &a) const

Arc	arc (const Vertex &t, const Vertex &h) const

Face	faceAroundArc (const Arc &a) const

FaceRange	facesAroundArc (const Arc &a) const

VertexRange	verticesAroundFace (const Face &f) const

ArcRange	arcsAroundFace (const Face &f) const

bool	isVertexBoundary (const Vertex &v) const

bool	isArcBoundary (const Arc &v) const

FaceRange	allFaces () const

ArcRange	allArcs () const

VertexRange	allVertices () const

ArcRange	allBoundaryArcs () const

VertexRange	allBoundaryVertices () const

VertexRange	verticesOfFacesAroundArc (const Arc a) const

bool	isFlippable (const Arc a) const

void	flip (const Arc a)

Vertex	split (const Arc a, const Point &data)

bool	isMergeable (const Arc a) const

Vertex	merge (const Arc a, const Point &data)

void	selfDisplay (std::ostream &out) const

bool	isValid () const

Protected Types
typedef HalfEdgeDataStructure::HalfEdge	HalfEdge

Protected Attributes
bool	isHEDSValid
	Indicates if the half-edge structure has been created/updated.

HalfEdgeDataStructure	myHEDS
	The half-edge data structure that stores the topology of the mesh.

PositionsStorage	myPositions
	Stores the information for each Vertex.

TriangleStorage	myTriangles
	Stores the triangles.

Detailed Description

template<typename TPoint>
class DGtal::TriangulatedSurface< TPoint >

Aim: Represents a triangulated surface. The topology is stored with a half-edge data structure. This object stored the positions of vertices in space. If you need further data attached to the surface, you may use property maps (see TriangulatedSurface::makeVertexMap).

Description of template class 'TriangulatedSurface'

Except for a few operations, this data structure is rather static. The user must add vertices and triangles, and when finished, call 'build()'.

Model of CUndirectedSimpleGraph: the vertices and edges of the triangulated surface form indeed a graph structure.

Note: Vertices, Arcs, and Faces are all integer ranging from 0 to one less than the total number of the respective elements. You may thus iterate on them by just looping on integers. The index INVALID_FACE is an invalid element (equal to HALF_EDGE_INVALID_INDEX).

Template Parameters

TPoint a type defining the position in space of vertices.

See also: HalfEdgeDataStructure

Note: You may access the underlying half-edge data structure through PolygonalSurface::heds method.

Examples: shapes/viewMarchingCubes.cpp.

Definition at line 85 of file TriangulatedSurface.h.

Member Typedef Documentation

◆ Arc

template<typename TPoint >

typedef HalfEdgeDataStructure::HalfEdgeIndex DGtal::TriangulatedSurface< TPoint >::Arc

Definition at line 111 of file TriangulatedSurface.h.

◆ ArcRange

template<typename TPoint >

typedef std::vector<Arc> DGtal::TriangulatedSurface< TPoint >::ArcRange

Definition at line 113 of file TriangulatedSurface.h.

◆ ConstIterator

template<typename TPoint >

typedef IntegerSequenceIterator< VertexIndex > DGtal::TriangulatedSurface< TPoint >::ConstIterator

Definition at line 108 of file TriangulatedSurface.h.

◆ Edge

template<typename TPoint >

typedef EdgeIndex DGtal::TriangulatedSurface< TPoint >::Edge

Definition at line 107 of file TriangulatedSurface.h.

◆ EdgeIndex

template<typename TPoint >

typedef HalfEdgeDataStructure::EdgeIndex DGtal::TriangulatedSurface< TPoint >::EdgeIndex

Definition at line 93 of file TriangulatedSurface.h.

◆ Face

template<typename TPoint >

typedef HalfEdgeDataStructure::FaceIndex DGtal::TriangulatedSurface< TPoint >::Face

Definition at line 112 of file TriangulatedSurface.h.

◆ FaceIndex

template<typename TPoint >

typedef HalfEdgeDataStructure::FaceIndex DGtal::TriangulatedSurface< TPoint >::FaceIndex

Definition at line 94 of file TriangulatedSurface.h.

◆ FaceRange

template<typename TPoint >

typedef std::vector<Face> DGtal::TriangulatedSurface< TPoint >::FaceRange

Definition at line 114 of file TriangulatedSurface.h.

◆ HalfEdge

template<typename TPoint >

typedef HalfEdgeDataStructure::HalfEdge DGtal::TriangulatedSurface< TPoint >::HalfEdge

protected

Definition at line 214 of file TriangulatedSurface.h.

◆ Index

template<typename TPoint >

typedef HalfEdgeDataStructure::Index DGtal::TriangulatedSurface< TPoint >::Index

Definition at line 91 of file TriangulatedSurface.h.

◆ Point

template<typename TPoint >

typedef TPoint DGtal::TriangulatedSurface< TPoint >::Point

Definition at line 88 of file TriangulatedSurface.h.

◆ PositionsMap

template<typename TPoint >

typedef IndexedPropertyMap< Point > DGtal::TriangulatedSurface< TPoint >::PositionsMap

Definition at line 211 of file TriangulatedSurface.h.

◆ PositionsStorage

template<typename TPoint >

typedef std::vector<Point> DGtal::TriangulatedSurface< TPoint >::PositionsStorage

Definition at line 96 of file TriangulatedSurface.h.

◆ Self

template<typename TPoint >

typedef TriangulatedSurface<TPoint> DGtal::TriangulatedSurface< TPoint >::Self

Definition at line 89 of file TriangulatedSurface.h.

◆ Size

template<typename TPoint >

typedef HalfEdgeDataStructure::Size DGtal::TriangulatedSurface< TPoint >::Size

Definition at line 90 of file TriangulatedSurface.h.

◆ Triangle

template<typename TPoint >

typedef HalfEdgeDataStructure::Triangle DGtal::TriangulatedSurface< TPoint >::Triangle

Definition at line 95 of file TriangulatedSurface.h.

◆ TriangleStorage

template<typename TPoint >

typedef std::vector<Triangle> DGtal::TriangulatedSurface< TPoint >::TriangleStorage

Definition at line 97 of file TriangulatedSurface.h.

◆ Vertex

template<typename TPoint >

typedef VertexIndex DGtal::TriangulatedSurface< TPoint >::Vertex

Definition at line 100 of file TriangulatedSurface.h.

◆ VertexIndex

template<typename TPoint >

typedef HalfEdgeDataStructure::VertexIndex DGtal::TriangulatedSurface< TPoint >::VertexIndex

Definition at line 92 of file TriangulatedSurface.h.

◆ VertexRange

template<typename TPoint >

typedef std::vector<Vertex> DGtal::TriangulatedSurface< TPoint >::VertexRange

Definition at line 115 of file TriangulatedSurface.h.

◆ VertexSet

template<typename TPoint >

typedef std::set<Vertex> DGtal::TriangulatedSurface< TPoint >::VertexSet

Definition at line 101 of file TriangulatedSurface.h.

Constructor & Destructor Documentation

◆ ~TriangulatedSurface()

template<typename TPoint >

DGtal::TriangulatedSurface< TPoint >::~TriangulatedSurface ( )

inline

Destructor.

Definition at line 222 of file TriangulatedSurface.h.

222{}

◆ TriangulatedSurface()

template<typename TPoint >

DGtal::TriangulatedSurface< TPoint >::TriangulatedSurface ( )

inline

Constructor.

Definition at line 227 of file TriangulatedSurface.h.

227: isHEDSValid( false ) {}

DGtal::TriangulatedSurface::isHEDSValid

bool isHEDSValid

Indicates if the half-edge structure has been created/updated.

Definition TriangulatedSurface.h:660

Member Function Documentation

◆ addTriangle()

template<typename TPoint >

FaceIndex DGtal::TriangulatedSurface< TPoint >::addTriangle	(	VertexIndex	v0,
		VertexIndex	v1,
		VertexIndex	v2 )

Adds a new triangle of vertices v0, v1, v2 to the surface.

Returns: the corresponding index of the triangle.

Referenced by makeTwoTriangles().

◆ addVertex()

template<typename TPoint >

VertexIndex DGtal::TriangulatedSurface< TPoint >::addVertex ( const Point & vdata )

Adds a new vertex to the surface with data vdata.

Parameters

vdata the data associated to this new vertex.

Returns: the new index given to this vertex.

Referenced by makeTwoTriangles().

◆ allArcs()

template<typename TPoint >

ArcRange DGtal::TriangulatedSurface< TPoint >::allArcs ( ) const

Returns: the range of all arcs of the triangulated surface, i.e. an array containing 0, 1, 2, ..., nbArcs()-1.

◆ allBoundaryArcs()

template<typename TPoint >

ArcRange DGtal::TriangulatedSurface< TPoint >::allBoundaryArcs ( ) const

This set of arcs is sufficient for displaying the boundary of the surface.

Returns: the array of all arcs (oriented edges) lying on the boundary of the surface (in no particular order).

Referenced by SCENARIO().

◆ allBoundaryVertices()

template<typename TPoint >

VertexRange DGtal::TriangulatedSurface< TPoint >::allBoundaryVertices ( ) const

This set of arcs is sufficient for displaying the boundary of the surface.

Returns: the array of vertices lying on the boundary of the surface (in no particular order).

Referenced by SCENARIO().

◆ allFaces()

template<typename TPoint >

FaceRange DGtal::TriangulatedSurface< TPoint >::allFaces ( ) const

Returns: the range of all faces of the triangulated surface, i.e. an array containing 0, 1, 2, ..., nbVertices()-1.

◆ allVertices()

template<typename TPoint >

VertexRange DGtal::TriangulatedSurface< TPoint >::allVertices ( ) const

Returns: the range of all vertices of the triangulated surface, i.e. an array containing 0, 1, 2, ..., nbVertices()-1.

Referenced by laplacian().

◆ arc()

template<typename TPoint >

Arc DGtal::TriangulatedSurface< TPoint >::arc	(	const Vertex &	t,
		const Vertex &	h ) const

[t] and [h] should be adjacent vertices.

Parameters

t	the vertex at the tail of the arc.
h	the vertex at the head of the arc.

Returns: the arc (tail, head)

Referenced by SCENARIO(), and SCENARIO().

◆ arcsAroundFace()

template<typename TPoint >

ArcRange DGtal::TriangulatedSurface< TPoint >::arcsAroundFace ( const Face & f ) const

Parameters

f	any valid face on the surface. (open or closed ).

Note: By construction, each anArc returned by the method on a face f is such that this->faceAroundArc(anArc) == f.

Returns: the sequence of arcs that touches this face in their natural order (the range size should be 3).

Referenced by SCENARIO().

◆ begin()

template<typename TPoint >

ConstIterator DGtal::TriangulatedSurface< TPoint >::begin ( ) const

inline

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

Definition at line 398 of file TriangulatedSurface.h.

399 { return ConstIterator( 0 ); }

DGtal::TriangulatedSurface::ConstIterator

IntegerSequenceIterator< VertexIndex > ConstIterator

Definition TriangulatedSurface.h:108

Referenced by SCENARIO().

◆ bestCapacity()

template<typename TPoint >

Size DGtal::TriangulatedSurface< TPoint >::bestCapacity ( ) const

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.

◆ BOOST_STATIC_CONSTANT()

template<typename TPoint >

DGtal::TriangulatedSurface< TPoint >::BOOST_STATIC_CONSTANT	(	Face	,
		INVALID_FACE	= HALF_EDGE_INVALID_INDEX )

◆ build()

template<typename TPoint >

bool DGtal::TriangulatedSurface< TPoint >::build ( )

Builds the half-edge data structure from the given triangles and vertices. After that, the surface is valid.

Returns: true if everything went allright, false if it was not possible to build a consistent data structure (e.g., butterfly neighborhoods).

Referenced by makeTwoTriangles().

◆ clear()

template<typename TPoint >

void DGtal::TriangulatedSurface< TPoint >::clear ( )

Clears everything.

◆ degree()

template<typename TPoint >

Size DGtal::TriangulatedSurface< TPoint >::degree ( const Vertex & v ) const

Parameters

v	any vertex

Returns: the number of neighbors of this vertex

Referenced by SCENARIO().

◆ end()

template<typename TPoint >

ConstIterator DGtal::TriangulatedSurface< TPoint >::end ( ) const

inline

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

Definition at line 402 of file TriangulatedSurface.h.

403 { return ConstIterator( nbVertices() ); }

DGtal::TriangulatedSurface::nbVertices

Size nbVertices() const

Definition TriangulatedSurface.h:263

References DGtal::TriangulatedSurface< TPoint >::nbVertices().

Referenced by SCENARIO().

◆ Euler()

template<typename TPoint >

long DGtal::TriangulatedSurface< TPoint >::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 274 of file TriangulatedSurface.h.

274{ return myHEDS.Euler(); }

DGtal::HalfEdgeDataStructure::Euler

long Euler() const

Definition HalfEdgeDataStructure.h:379

DGtal::TriangulatedSurface::myHEDS

HalfEdgeDataStructure myHEDS

The half-edge data structure that stores the topology of the mesh.

Definition TriangulatedSurface.h:662

References DGtal::HalfEdgeDataStructure::Euler(), and DGtal::TriangulatedSurface< TPoint >::myHEDS.

Referenced by SCENARIO().

◆ faceAroundArc()

template<typename TPoint >

Face DGtal::TriangulatedSurface< TPoint >::faceAroundArc ( const Arc & a ) const

Convenience method for computing the face incident to a given arc. There is at most one face that borders an arc for triangulated surface since it is a combinatorial 2-manifold.

Parameters

a	any arc on the surface.

Returns: the face around the given arc or the InvalidFace if the arc was a boundary arc.

Referenced by SCENARIO().

◆ facesAroundArc()

template<typename TPoint >

FaceRange DGtal::TriangulatedSurface< TPoint >::facesAroundArc ( const Arc & a ) const

Computes the faces incident to a given arc. There is only one for triangulated surface since it is a combinatorial 2-manifold.

Parameters

a	any arc on the surface.

Returns: a vector containing the faces incident to this arc.

◆ facesAroundVertex()

template<typename TPoint >

FaceRange DGtal::TriangulatedSurface< TPoint >::facesAroundVertex ( const Vertex & v ) const

Parameters

v	any vertex of the surface.

Returns: the faces containing this vertex [v].

Referenced by laplacian().

◆ flip()

template<typename TPoint >

void DGtal::TriangulatedSurface< TPoint >::flip ( const Arc a )

Flip the edge associated to arc a.

Parameters

a	any valid arc.

Precondition: the edge must be flippable, isFlippable( a ) == true

See also: isFlippable

Postcondition: After flip the arc a corresponding to the flipped edge (if you reflip it you get your former triangulation).

Note: Time complexity is O(1).

Referenced by SCENARIO().

◆ head()

template<typename TPoint >

Vertex DGtal::TriangulatedSurface< TPoint >::head ( const Arc & a ) const

Parameters

a	any arc (s,t)

Returns: the vertex t

Referenced by laplacian(), and SCENARIO().

◆ heds() [1/2]

template<typename TPoint >

HalfEdgeDataStructure & DGtal::TriangulatedSurface< TPoint >::heds ( )

inline

Returns: (setter) a reference to the topological structure of the triangulated surface (an half-edge data structure).

Definition at line 251 of file TriangulatedSurface.h.

251{ return myHEDS; }

References DGtal::TriangulatedSurface< TPoint >::myHEDS.

◆ heds() [2/2]

template<typename TPoint >

const HalfEdgeDataStructure & DGtal::TriangulatedSurface< TPoint >::heds ( ) const

inline

Returns: (getter) a const reference to the topological structure of the triangulated surface (an half-edge data structure).

Definition at line 255 of file TriangulatedSurface.h.

255{ return myHEDS; }

References DGtal::TriangulatedSurface< TPoint >::myHEDS.

◆ inArcs()

template<typename TPoint >

ArcRange DGtal::TriangulatedSurface< TPoint >::inArcs ( const Vertex & v ) const

Parameters

v	any vertex of the surface.

Returns: the ingoing arcs to [v]

◆ isArcBoundary()

template<typename TPoint >

bool DGtal::TriangulatedSurface< TPoint >::isArcBoundary ( const Arc & v ) const

Parameters

v any arc.

Returns: 'true' if and only if arc v lies on a boundary (note that the opposite arc does not lie on the boundary).

Note: O(1) operation

◆ isFlippable()

template<typename TPoint >

bool DGtal::TriangulatedSurface< TPoint >::isFlippable ( const Arc a ) const

An edge is (topologically) flippable iff: (1) it does not lie on the boundary, (2) it is bordered by two triangles, (3) the two other vertices of the quad are not already neighbors. (2) is always true for a triangulated surface.

Parameters

a any arc.

Returns: 'true' if the edge containing a is topologically flippable.

Note: Time complexity is O(1).

Referenced by SCENARIO().

◆ isMergeable()

template<typename TPoint >

bool DGtal::TriangulatedSurface< TPoint >::isMergeable ( const Arc a ) const

An edge is (topologically) mergeable iff: (1) it is bordered by two triangles, (2) there is no boundary vertex in the two triangles bordering the edge.

Parameters

a any arc.

Returns: 'true' if the edge containing a is topologically mergeable.

Note: Time complexity is O(1).

◆ isValid()

template<typename TPoint >

bool DGtal::TriangulatedSurface< TPoint >::isValid ( ) const

Checks the validity/consistency of the object.

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

◆ isVertexBoundary()

template<typename TPoint >

bool DGtal::TriangulatedSurface< TPoint >::isVertexBoundary ( const Vertex & v ) const

Parameters

v	any vertex.

Returns: 'true' if and only if vertex v lies on a boundary.

Note: O(1) operation

◆ makeEdgeMap() [1/2]

template<typename TPoint >

template<typename AnyData >

IndexedPropertyMap< AnyData > DGtal::TriangulatedSurface< TPoint >::makeEdgeMap ( ) const

inline

Returns: an edge property map that associates some data to any edge.

Definition at line 300 of file TriangulatedSurface.h.

    {
      return IndexedPropertyMap< AnyData >( *this, nbEdges() );
    }

References DGtal::TriangulatedSurface< TPoint >::nbEdges().

◆ makeEdgeMap() [2/2]

template<typename TPoint >

template<typename AnyData >

IndexedPropertyMap< AnyData > DGtal::TriangulatedSurface< TPoint >::makeEdgeMap ( AnyData value ) const

inline

Parameters

value the value that is given to all edges at initialization.

Returns: an edge property map that associates some data to any edge.

Definition at line 308 of file TriangulatedSurface.h.

    {
      return IndexedPropertyMap< AnyData >( *this, nbEdges(), value );
    }

References DGtal::TriangulatedSurface< TPoint >::nbEdges().

◆ makeFaceMap() [1/2]

template<typename TPoint >

template<typename AnyData >

IndexedPropertyMap< AnyData > DGtal::TriangulatedSurface< TPoint >::makeFaceMap ( ) const

inline

Returns: a face property map that associates some data to any face.

Definition at line 315 of file TriangulatedSurface.h.

    {
      return IndexedPropertyMap< AnyData >( *this, nbFaces() );
    }

References DGtal::TriangulatedSurface< TPoint >::nbFaces().

◆ makeFaceMap() [2/2]

template<typename TPoint >

template<typename AnyData >

IndexedPropertyMap< AnyData > DGtal::TriangulatedSurface< TPoint >::makeFaceMap ( AnyData value ) const

inline

Parameters

value the value that is given to all faces at initialization.

Returns: a face property map that associates some data to any face.

Definition at line 323 of file TriangulatedSurface.h.

    {
      return IndexedPropertyMap< AnyData >( *this, nbFaces(), value );
    }

References DGtal::TriangulatedSurface< TPoint >::nbFaces().

◆ makeVertexMap() [1/2]

template<typename TPoint >

template<typename AnyData >

IndexedPropertyMap< AnyData > DGtal::TriangulatedSurface< TPoint >::makeVertexMap ( ) const

inline

Returns: a vertex property map that associates some data to any vertex.

Definition at line 285 of file TriangulatedSurface.h.

    {
      return IndexedPropertyMap< AnyData >( *this, nbVertices() );
    }

References DGtal::TriangulatedSurface< TPoint >::nbVertices().

◆ makeVertexMap() [2/2]

template<typename TPoint >

template<typename AnyData >

IndexedPropertyMap< AnyData > DGtal::TriangulatedSurface< TPoint >::makeVertexMap ( AnyData value ) const

inline

Parameters

value the value that is given to all vertices at initialization.

Returns: a vertex property map that associates some data to any vertex.

Definition at line 293 of file TriangulatedSurface.h.

    {
      return IndexedPropertyMap< AnyData >( *this, nbVertices(), value );
    }

References DGtal::TriangulatedSurface< TPoint >::nbVertices().

◆ merge()

template<typename TPoint >

Vertex DGtal::TriangulatedSurface< TPoint >::merge	(	const Arc	a,
		const Point &	data )

Merges the edge specified by the arc a.

Parameters

a	any valid arc.
data	the position for the merged vertex.

Returns: the index of the merged vertex (which is the tail of the arc a)..

Precondition: the edge must be mergeable, isMergeable( a ) == true

See also: isMergeable

Note: Time complexity is O(1).

Todo: We could also merge boundary triangles.

Note: All the underlying data-structure is renumbered so that vertex, edge, face and half-edge indices are consecutive. In other words, since 1 vertex, 3 edges, 2 faces and 6 half-edges have been deleted, then the last vertices, edges, faces, half-edges have been renumbered into the freed indices. For instance, the vertex head(a) does not exist anymore (but has been replaced by a renumbered vertex).

◆ nbArcs()

template<typename TPoint >

Size DGtal::TriangulatedSurface< TPoint >::nbArcs ( ) const

inline

Returns: the number of half edges in the structure.

Definition at line 260 of file TriangulatedSurface.h.

260{ return myHEDS.nbHalfEdges(); }

DGtal::HalfEdgeDataStructure::nbHalfEdges

Size nbHalfEdges() const

Definition HalfEdgeDataStructure.h:367

References DGtal::TriangulatedSurface< TPoint >::myHEDS, and DGtal::HalfEdgeDataStructure::nbHalfEdges().

Referenced by SCENARIO(), and SCENARIO().

◆ nbEdges()

template<typename TPoint >

Size DGtal::TriangulatedSurface< TPoint >::nbEdges ( ) const

inline

Returns: the number of unoriented edges in the structure.

Definition at line 266 of file TriangulatedSurface.h.

266{ return myHEDS.nbEdges(); }

DGtal::HalfEdgeDataStructure::nbEdges

Size nbEdges() const

Definition HalfEdgeDataStructure.h:373

References DGtal::TriangulatedSurface< TPoint >::myHEDS, and DGtal::HalfEdgeDataStructure::nbEdges().

Referenced by DGtal::TriangulatedSurface< TPoint >::makeEdgeMap(), DGtal::TriangulatedSurface< TPoint >::makeEdgeMap(), SCENARIO(), and SCENARIO().

◆ nbFaces()

template<typename TPoint >

Size DGtal::TriangulatedSurface< TPoint >::nbFaces ( ) const

inline

Returns: the number of faces in the structure.

Definition at line 269 of file TriangulatedSurface.h.

269{ return myHEDS.nbFaces(); }

DGtal::HalfEdgeDataStructure::nbFaces

Size nbFaces() const

Definition HalfEdgeDataStructure.h:376

References DGtal::TriangulatedSurface< TPoint >::myHEDS, and DGtal::HalfEdgeDataStructure::nbFaces().

Referenced by laplacian(), DGtal::TriangulatedSurface< TPoint >::makeFaceMap(), DGtal::TriangulatedSurface< TPoint >::makeFaceMap(), SCENARIO(), and SCENARIO().

◆ nbVertices()

template<typename TPoint >

Size DGtal::TriangulatedSurface< TPoint >::nbVertices ( ) const

inline

Returns: the number of vertices in the structure.

Definition at line 263 of file TriangulatedSurface.h.

263{ return myHEDS.nbVertices(); }

DGtal::HalfEdgeDataStructure::nbVertices

Size nbVertices() const

Definition HalfEdgeDataStructure.h:370

References DGtal::TriangulatedSurface< TPoint >::myHEDS, and DGtal::HalfEdgeDataStructure::nbVertices().

Referenced by DGtal::TriangulatedSurface< TPoint >::end(), laplacian(), DGtal::TriangulatedSurface< TPoint >::makeVertexMap(), DGtal::TriangulatedSurface< TPoint >::makeVertexMap(), SCENARIO(), and SCENARIO().

◆ next()

template<typename TPoint >

Arc DGtal::TriangulatedSurface< TPoint >::next ( const Arc & a ) const

Constant-time access to the next arc

Parameters

a	any arc (s,t)

Returns: the next arc

Referenced by laplacian().

◆ opposite()

template<typename TPoint >

Arc DGtal::TriangulatedSurface< TPoint >::opposite ( const Arc & a ) const

Parameters

a	any arc (s,t)

Returns: the arc (t,s)

Referenced by laplacian().

◆ outArcs()

template<typename TPoint >

ArcRange DGtal::TriangulatedSurface< TPoint >::outArcs ( const Vertex & v ) const

Parameters

v	any vertex of the surface.

Returns: the outgoing arcs from [v]

Referenced by laplacian().

◆ position() [1/2]

template<typename TPoint >

Point & DGtal::TriangulatedSurface< TPoint >::position ( Vertex v )

Mutable accessor to vertex data.

Parameters

v	any vertex.

Returns: the mutable data associated to v.

Referenced by laplacian().

◆ position() [2/2]

template<typename TPoint >

const Point & DGtal::TriangulatedSurface< TPoint >::position ( Vertex v ) const

Const accessor to vertex data.

Parameters

v	any vertex.

Returns: the non-mutable data associated to v.

◆ positions()

template<typename TPoint >

PositionsMap DGtal::TriangulatedSurface< TPoint >::positions ( )

inline

Returns: the property map stored in the surface that defines vertex positions.

Note: The returned map only references what is stored in the surface.

Definition at line 278 of file TriangulatedSurface.h.

    {
      return PositionsMap( *this, myPositions );
    }

References DGtal::TriangulatedSurface< TPoint >::myPositions.

Referenced by SCENARIO().

◆ selfDisplay()

template<typename TPoint >

void DGtal::TriangulatedSurface< TPoint >::selfDisplay ( std::ostream & out ) const

Writes/Displays the object on an output stream.

Parameters

out	the output stream where the object is written.

◆ size()

template<typename TPoint >

Size DGtal::TriangulatedSurface< TPoint >::size ( ) const

Returns: the number of vertices of the surface.

Referenced by SCENARIO().

◆ split()

template<typename TPoint >

Vertex DGtal::TriangulatedSurface< TPoint >::split	(	const Arc	a,
		const Point &	data )

Splits the edge specified by the arc a. The two faces incident to a are split into four faces.

Parameters

a	any valid arc.
data	the position for the newly created vertex.

Returns: the index of the created vertex.

Precondition: the edge must be flippable, isFlippable( a ) == true

See also: isFlippable

Note: Time complexity is O(1).

◆ tail()

template<typename TPoint >

Vertex DGtal::TriangulatedSurface< TPoint >::tail ( const Arc & a ) const

Parameters

a	any arc (s,t)

Returns: the vertex s

◆ verticesAroundFace()

template<typename TPoint >

VertexRange DGtal::TriangulatedSurface< TPoint >::verticesAroundFace ( const Face & f ) const

If f is incident to the arcs (s,t) and (t,u) (say), then (s,t,u) is a subsequence of the returned sequence.

Parameters

f	any valid face on the surface (open or closed ).

Returns: the sequence of vertices that touches this face. The order follows the order of incident arcs (the range size should be 3).

Referenced by laplacian(), and SCENARIO().

◆ verticesOfFacesAroundArc()

template<typename TPoint >

VertexRange DGtal::TriangulatedSurface< TPoint >::verticesOfFacesAroundArc ( const Arc a ) const

Parameters

a any arc.

Returns: either the four vertices of the two triangles bordering a, or the three vertices if this is an edge on the boundary.

Note: O(1) operation; Order is, if arc a is (s,t), and a belongs to triangle (s,t,u) and opposite arc belongs to triangle (t,s,v): (t,u,s,v), (t,u,s), (t,s,v)

Referenced by SCENARIO().

◆ writeNeighbors() [1/2]

template<typename TPoint >

template<typename OutputIterator >

void DGtal::TriangulatedSurface< TPoint >::writeNeighbors	(	OutputIterator &	it,
		const Vertex &	v ) const

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

◆ writeNeighbors() [2/2]

template<typename TPoint >

template<typename OutputIterator , typename VertexPredicate >

void DGtal::TriangulatedSurface< TPoint >::writeNeighbors	(	OutputIterator &	it,
		const Vertex &	v,
		const VertexPredicate &	pred ) const

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

Field Documentation

◆ isHEDSValid

template<typename TPoint >

bool DGtal::TriangulatedSurface< TPoint >::isHEDSValid

protected

Indicates if the half-edge structure has been created/updated.

Definition at line 660 of file TriangulatedSurface.h.

◆ myHEDS

template<typename TPoint >

HalfEdgeDataStructure DGtal::TriangulatedSurface< TPoint >::myHEDS

protected

The half-edge data structure that stores the topology of the mesh.

Definition at line 662 of file TriangulatedSurface.h.

Referenced by DGtal::TriangulatedSurface< TPoint >::Euler(), DGtal::TriangulatedSurface< TPoint >::heds(), DGtal::TriangulatedSurface< TPoint >::heds(), DGtal::TriangulatedSurface< TPoint >::nbArcs(), DGtal::TriangulatedSurface< TPoint >::nbEdges(), DGtal::TriangulatedSurface< TPoint >::nbFaces(), and DGtal::TriangulatedSurface< TPoint >::nbVertices().

◆ myPositions

template<typename TPoint >

PositionsStorage DGtal::TriangulatedSurface< TPoint >::myPositions

protected

Stores the information for each Vertex.

Definition at line 664 of file TriangulatedSurface.h.

Referenced by DGtal::TriangulatedSurface< TPoint >::positions().

◆ myTriangles

template<typename TPoint >

TriangleStorage DGtal::TriangulatedSurface< TPoint >::myTriangles

protected

Stores the triangles.

Definition at line 666 of file TriangulatedSurface.h.

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

TriangulatedSurface.h

Data Structures

Public Types

Public Member Functions

Protected Types

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ Arc

◆ ArcRange

◆ ConstIterator

◆ Edge

◆ EdgeIndex

◆ Face

◆ FaceIndex

◆ FaceRange

◆ HalfEdge

◆ Index

◆ Point

◆ PositionsMap

◆ PositionsStorage

◆ Self

◆ Size

◆ Triangle

◆ TriangleStorage

◆ Vertex

◆ VertexIndex

◆ VertexRange

◆ VertexSet

Constructor & Destructor Documentation

◆ ~TriangulatedSurface()

◆ TriangulatedSurface()

Member Function Documentation

◆ addTriangle()

◆ addVertex()

◆ allArcs()

◆ allBoundaryArcs()

◆ allBoundaryVertices()

◆ allFaces()

◆ allVertices()

◆ arc()

◆ arcsAroundFace()

◆ begin()

◆ bestCapacity()

◆ BOOST_STATIC_CONSTANT()

◆ build()

◆ clear()

◆ degree()

◆ end()

◆ Euler()

◆ faceAroundArc()

◆ facesAroundArc()

◆ facesAroundVertex()

◆ flip()

◆ head()

◆ heds() [1/2]

◆ heds() [2/2]

◆ inArcs()

◆ isArcBoundary()

◆ isFlippable()

◆ isMergeable()

◆ isValid()

◆ isVertexBoundary()

◆ makeEdgeMap() [1/2]

◆ makeEdgeMap() [2/2]

◆ makeFaceMap() [1/2]

◆ makeFaceMap() [2/2]

◆ makeVertexMap() [1/2]

◆ makeVertexMap() [2/2]

◆ merge()

◆ nbArcs()

◆ nbEdges()

◆ nbFaces()

◆ nbVertices()

◆ next()

◆ opposite()

◆ outArcs()

◆ position() [1/2]

◆ position() [2/2]

◆ positions()

◆ selfDisplay()