DelaunayGraph_2 Concept Reference

Definition

The concept DelaunayGraph_2 defines the requirements for the first template parameter of the Voronoi_diagram_2<DG,AT,AP> class. The DelaunayGraph_2 concept essentially defines the requirements that a class representing a Delaunay graph must obey so that the Voronoi diagram adaptor can adapt it.

Refines

CopyConstructible

Assignable

DefaultConstructible

Traversal of the Delaunay graph

A model of the DelaunayGraph_2 concept must provide several iterators and circulators that allow to traverse it (completely or partially). All iterators and circulators must be convertible to the corresponding handles.

Has Models:

CGAL::Delaunay_triangulation_2<Traits,Tds>

CGAL::Regular_triangulation_2<Traits,Tds>

CGAL::Triangulation_hierarchy_2<Tr> provided that Tr is a model of DelaunayGraph_2

CGAL::Segment_Delaunay_graph_2<Gt,DS>

CGAL::Segment_Delaunay_graph_hierarchy_2<Gt,STag,DS>

CGAL::Apollonius_graph_2<Gt,Agds>

CGAL::Apollonius_graph_hierarchy_2<Gt,Agds>

See also

AdaptationTraits_2

AdaptationPolicy_2

CGAL::Voronoi_diagram_2<DG,AT,AP>

Types
typedef unspecified_type	size_type
	A type for sizes.
typedef unspecified_type	Geom_traits
	A type for the geometric traits associated with the Delaunay graph.
typedef unspecified_type	Triangulation_data_structure
	A type for the underlying triangulation data structure.
typedef unspecified_type	Vertex
	A type for the vertices of the Delaunay graph.
typedef unspecified_type	Face
	A type for the faces of the Delaunay graph.
typedef std::pair< Face_handle, int >	Edge
	The type of the edges of the Delaunay graph.
typedef unspecified_type	Vertex_handle
	Handle to the vertices of the Delaunay graph.
typedef unspecified_type	Face_handle
	Handle to the faces of the Delaunay graph.
The following iterators and circulators must be defined. All iterators and circulators must be assignable and convertible to their corresponding handles.
typedef unspecified_type	All_edges_iterator
	A type for an iterator over all edges of the Delaunay graph.
typedef unspecified_type	Finite_edges_iterator
	A type for an iterator over the finite edges of the Delaunay graph.
typedef unspecified_type	All_faces_iterator
	A type for an iterator over all faces of the Delaunay graph.
typedef unspecified_type	Finite_faces_iterator
	A type for an iterator over the finite faces of the Delaunay graph.
typedef unspecified_type	All_vertices_iterator
	A type for an iterator over all vertices of the Delaunay graph.
typedef unspecified_type	Finite_vertices_iterator
	A type for an iterator over the finite vertices of the Delaunay graph.
typedef unspecified_type	Face_circulator
	A type for a circulator over the adjacent faces of a vertex of the Delaunay graph.
typedef unspecified_type	Vertex_circulator
	A type for a circulator over the adjacent vertices of a vertex of the Delaunay graph.
typedef unspecified_type	Edge_circulator
	A type for a circulator over the adjacent edges of a vertex of the Delaunay graph.

Creation
In addition to the default and copy constructors, as well as the assignment operator, the following constructors are required.
	DelaunayGraph_2 (Geom_traits gt)
	Constructor that takes an instance of the geometric traits.
template<class It >
	DelaunayGraph_2 (It first, It beyond)
	Constructor that takes an iterator range.
template<class It >
	DelaunayGraph_2 (It first, It beyond, Geom_traits gt)
	Constructor that takes an iterator range and an instance of the geometric traits.

Access methods
Triangulation_data_structure	tds ()
	Returns a reference to the underlying triangulation data structure.
Geom_traits	geom_traits ()
	Returns a reference to the geometric traits object.
Vertex_handle	infinite_vertex ()
	Returns a handle to the infinite vertex.
Vertex_handle	finite_vertex ()
	Returns a handle to a finite vertex, provided there exists one.
Face_handle	infinite_face ()
	Returns a handle to a face incident to the infinite vertex.
int	dimension ()
	Returns the dimension of the Delaunay graph.
size_type	number_of_vertices ()
	Returns the number of finite vertices.
size_type	number_of_faces ()
	Returns the number of faces (both finite and infinite).

Finite Face, Edge and Vertex Iterators
The following iterators must allow, respectively, to visit finite faces, finite edges and finite vertices of the Delaunay graph. These iterators must be non-mutable, bidirectional and their value types are respectively Face, Edge and Vertex.
Finite_vertices_iterator	finite_vertices_begin ()
	Starts at an arbitrary finite vertex.
Finite_vertices_iterator	finite_vertices_end ()
	Past-the-end iterator.
Finite_edges_iterator	finite_edges_begin ()
	Starts at an arbitrary finite edge.
Finite_edges_iterator	finite_edges_end ()
	Past-the-end iterator.
Finite_faces_iterator	finite_faces_begin ()
	Starts at an arbitrary finite face.
Finite_faces_iterator	finite_faces_end () const
	Past-the-end iterator.

All Face, Edge and Vertex Iterators
The following iterators must allow, respectively, to visit all (both finite and infinite) faces, edges and vertices of the Delaunay graph. These iterators are non-mutable, bidirectional and their value types are respectively Face, Edge and Vertex.
All_vertices_iterator	all_vertices_begin ()
	Starts at an arbitrary vertex.
All_vertices_iterator	all_vertices_end ()
	Past-the-end iterator.
All_edges_iterator	all_edges_begin ()
	Starts at an arbitrary edge.
All_edges_iterator	all_edges_end ()
	Past-the-end iterator.
All_faces_iterator	all_faces_begin ()
	Starts at an arbitrary face.
All_faces_iterator	all_faces_end ()
	Past-the-end iterator.

Face, Edge and Vertex Circulators
A model of the DelaunayGraph_2 concept must also provide circulators that allow to visit, respectively, all faces or edges incident to a given vertex or all vertices adjacent to a given vertex. These circulators are non-mutable and bidirectional. The operator operator++ must move the circulator counterclockwise around the vertex while the operator- must move the circulator clockwise.
Face_circulator	incident_faces (Vertex_handle v)
	Starts at an arbitrary face incident to v.
Face_circulator	incident_faces (Vertex_handle v, Face_handle f)
	Starts at face f.
Edge_circulator	incident_edges (Vertex_handle v)
	Starts at an arbitrary edge incident to v.
Edge_circulator	incident_edges (Vertex_handle v, Face_handle f)
	Starts at the first edge of f incident to v, in counterclockwise order around v.
Vertex_circulator	incident_vertices (Vertex_handle v)
	Starts at an arbitrary vertex incident to v.
Vertex_circulator	incident_vertices (Vertex_handle v, Face_handle f)
	Starts at the first vertex of f adjacent to v in counterclockwise order around v.

Predicates
A model of the DelaunayGraph_2 concept must provide methods to test the finite or infinite character of any feature.
bool	is_infinite (Vertex_handle v)
	true, iff v is the infinite_vertex.
bool	is_infinite (Face_handle f)
	true, iff face f is infinite.
bool	is_infinite (Face_handle f, int i)
	true, iff edge (f,i) is infinite.
bool	is_infinite (Edge e)
	true, iff edge e is infinite.
bool	is_infinite (Edge_circulator ec)
	true, iff edge *ec is infinite.

Validity check
bool	is_valid (bool verbose=false)
	Checks the validity of the Delaunay graph.

Miscellaneous
void	clear ()
	Clears all contents of the Delaunay graph.
void	swap (DelaunayGraph_2 other)
	The Delaunay graphs other and dg are swapped.

Member Typedef Documentation

All_edges_iterator

typedef unspecified_type DelaunayGraph_2::All_edges_iterator

A type for an iterator over all edges of the Delaunay graph.

Its value type must be Edge.

All_faces_iterator

typedef unspecified_type DelaunayGraph_2::All_faces_iterator

A type for an iterator over all faces of the Delaunay graph.

Its value type must be Face.

All_vertices_iterator

typedef unspecified_type DelaunayGraph_2::All_vertices_iterator

A type for an iterator over all vertices of the Delaunay graph.

Its value type must be Vertex.

Edge_circulator

typedef unspecified_type DelaunayGraph_2::Edge_circulator

A type for a circulator over the adjacent edges of a vertex of the Delaunay graph.

Its value type must be Edge.

Face_circulator

typedef unspecified_type DelaunayGraph_2::Face_circulator

A type for a circulator over the adjacent faces of a vertex of the Delaunay graph.

Its value type must be Face.

Finite_edges_iterator

typedef unspecified_type DelaunayGraph_2::Finite_edges_iterator

A type for an iterator over the finite edges of the Delaunay graph.

Its value type must be Edge.

Finite_faces_iterator

typedef unspecified_type DelaunayGraph_2::Finite_faces_iterator

A type for an iterator over the finite faces of the Delaunay graph.

Its value type must be Face.

Finite_vertices_iterator

typedef unspecified_type DelaunayGraph_2::Finite_vertices_iterator

A type for an iterator over the finite vertices of the Delaunay graph.

Its value type must be Vertex.

Triangulation_data_structure

typedef unspecified_type DelaunayGraph_2::Triangulation_data_structure

A type for the underlying triangulation data structure.

It must be a model of the concept TriangulationDataStructure_2.

Vertex_circulator

typedef unspecified_type DelaunayGraph_2::Vertex_circulator

A type for a circulator over the adjacent vertices of a vertex of the Delaunay graph.

Its value type must be Vertex.

Constructor & Destructor Documentation

DelaunayGraph_2() [1/2]

template<class It >

DelaunayGraph_2::DelaunayGraph_2	(	It	first,
		It	beyond
	)

Constructor that takes an iterator range.

The value type of the iterator must be the type of the sites of the Delaunay graph.

DelaunayGraph_2() [2/2]

template<class It >

DelaunayGraph_2::DelaunayGraph_2	(	It	first,
		It	beyond,
		Geom_traits	gt
	)

Constructor that takes an iterator range and an instance of the geometric traits.

The value type of the iterator must be the type of the sites of the Delaunay graph.

Member Function Documentation

incident_edges()

Edge_circulator DelaunayGraph_2::incident_edges	(	Vertex_handle	v,
		Face_handle	f
	)

Starts at the first edge of f incident to v, in counterclockwise order around v.

Precondition

Face f must be incident to vertex v.

incident_faces()

Face_circulator DelaunayGraph_2::incident_faces	(	Vertex_handle	v,
		Face_handle	f
	)

Starts at face f.

Precondition

Face f must be incident to vertex v.

incident_vertices()

Vertex_circulator DelaunayGraph_2::incident_vertices	(	Vertex_handle	v,
		Face_handle	f
	)

Starts at the first vertex of f adjacent to v in counterclockwise order around v.

Precondition

Face f must be incident to vertex v.

is_valid()

bool DelaunayGraph_2::is_valid

(

bool

verbose = false

)

Checks the validity of the Delaunay graph.

If verbose is true a short message is sent to std::cerr.

swap()

void DelaunayGraph_2::swap

(

DelaunayGraph_2

other

)

The Delaunay graphs other and dg are swapped.

dg.swap(other) should be preferred to dg= other or to dg(other) if other is deleted afterwards.