CGAL::Triangulation_data_structure_2< VertexBase, FaceBase > Class Template Reference

#include <CGAL/Triangulation_data_structure_2.h>

Definition

template<typename VertexBase, typename FaceBase>
class CGAL::Triangulation_data_structure_2< VertexBase, FaceBase >

The class Triangulation_data_structure_2 is a model for the TriangulationDataStructure_2 concept.

It can be used to represent an orientable 2D triangulation embedded in a space of any dimension.

The vertices and faces are stored in two nested containers, which are implemented using Compact_container. The class may offer some flexibility for the choice of container in the future, in the form of additional template parameters.

Template Parameters

VertexBase	must be a model of TriangulationDSVertexBase_2. The default is Triangulation_ds_vertex_base_2<TDS>.
FaceBase	must be a model of TriangulationDSFaceBase_2. The default is Triangulation_ds_face_base_2<TDS>.

Is model of

TriangulationDataStructure_2

Modifiers

In addition to the modifiers required by the TriangulationDataStructure_2 concept, the Triangulation_data_structure_2 class supports also the modifiers below. Note also that the modifiers below guarantee the combinatorial validity of the resulting data structure.

Illustrations

The join and split operations.

Insertion and removal of degree 2 vertices.

Types
typedef Triangulation_data_structure_2< VertexBase, FaceBase >	Tds
typedef VertexBase::template Rebind_TDS< Tds >::Other	Vertex
	The vertex type.
typedef FaceBase::template Rebind_TDS< Tds >::Other	Face
	The face type.

Ranges
Advanced In addition to the interface documented in the concept, the class offers the following types.
typedef Compact_container< Vertex >	Vertex_range
	Vertex container type.
typedef Compact_container< Face >	Face_range
	Face container type.

Operations
Advanced In addition to the interface documented in the concept, the class offers the following functions.
Face_range &	faces () const
	returns a reference to the container of faces.
Face_range &	faces ()
	returns a reference to the container of faces.
Vertex_range &	vertices () const
	returns a reference to the container of vertices.
Vertex_range &	vertices ()
	returns a reference to the container of vertices.

Modifiers
Vertex_handle	join_vertices (Face_handle f, int i)
	joins the vertices that are endpoints of the edge (f,i), and returns a vertex handle to common vertex (see Fig. figtdssplitjoin).
Vertex_handle	join_vertices (Edge e)
	joins the vertices that are endpoints of the edge e, and returns a vertex handle to common vertex.
Vertex_handle	join_vertices (Edge_iterator eit)
	joins the vertices that are endpoints of the edge *eit, and returns a vertex handle to common vertex.
Vertex_handle	join_vertices (Edges_circulator ec)
	joins the vertices that are endpoints of the edge *ec, and returns a vertex handle to common vertex.
boost::tuples::tuple< Vertex_handle, Vertex_handle, Face_handle, Face_handle >	split_vertex (Vertex_handle v, Face_handle f1, Face_handle f2)
	splits the vertex v into two vertices v1 and v2.
Vertex_handle	insert_degree_2 (Face_handle f, int i)
	inserts a degree two vertex and two faces adjacent to it that have two common edges.
void	remove_degree_2 (Vertex_handle v)
	removes a degree 2 vertex and the two faces adjacent to it.

Member Typedef Documentation

Face

template<typename VertexBase , typename FaceBase >

typedef FaceBase::template Rebind_TDS<Tds>::Other CGAL::Triangulation_data_structure_2< VertexBase, FaceBase >::Face

The face type.

See also

Section The Rebind Mechanism

Vertex

template<typename VertexBase , typename FaceBase >

typedef VertexBase::template Rebind_TDS<Tds>::Other CGAL::Triangulation_data_structure_2< VertexBase, FaceBase >::Vertex

The vertex type.

See also

Section The Rebind Mechanism

Member Function Documentation

insert_degree_2()

template<typename VertexBase , typename FaceBase >

Vertex_handle CGAL::Triangulation_data_structure_2< VertexBase, FaceBase >::insert_degree_2	(	Face_handle	f,
		int	i
	)

inserts a degree two vertex and two faces adjacent to it that have two common edges.

The edge defined by the face handle f and the integer i is duplicated. It returns a handle to the vertex created (see Fig. figtdsirdeg2).

join_vertices()

template<typename VertexBase , typename FaceBase >

Vertex_handle CGAL::Triangulation_data_structure_2< VertexBase, FaceBase >::join_vertices	(	Face_handle	f,
		int	i
	)

joins the vertices that are endpoints of the edge (f,i), and returns a vertex handle to common vertex (see Fig. figtdssplitjoin).

Precondition

f must be different from Face_handle() and i must be 0, 1 or 2.

remove_degree_2()

template<typename VertexBase , typename FaceBase >

void CGAL::Triangulation_data_structure_2< VertexBase, FaceBase >::remove_degree_2

(

Vertex_handle

v

)

removes a degree 2 vertex and the two faces adjacent to it.

The two edges of the star of v that are not incident to it are collapsed (see Fig. figtdsirdeg2).

Precondition

The degree of v must be equal to 2.

split_vertex()

template<typename VertexBase , typename FaceBase >

boost::tuples::tuple< Vertex_handle, Vertex_handle, Face_handle, Face_handle > CGAL::Triangulation_data_structure_2< VertexBase, FaceBase >::split_vertex	(	Vertex_handle	v,
		Face_handle	f1,
		Face_handle	f2
	)

splits the vertex v into two vertices v1 and v2.

The common faces f and g of v1 and v2 are created after (in the counter-clockwise sense) the faces f1 and f2. The 4-tuple (v1,v2,f,g) is returned (see Fig. figtdssplitjoin).

Precondition

dimension() must be equal to 2, f1 and f2 must be different from Face_handle() and v must be a vertex of both f1 and f2.