#include <CGAL/Segment_Delaunay_graph_2.h>

Inherited by CGAL::Segment_Delaunay_graph_hierarchy_2< Gt, STag, DS >.

Definition

The class Segment_Delaunay_graph_2 represents the segment Delaunay graph (which is the dual graph of the 2D segment Voronoi diagram).

Currently it supports only insertions of sites.

Template Parameters

Gt	must be a model of `SegmentDelaunayGraphTraits_2`
DS	must be a model of `SegmentDelaunayGraphDataStructure_2`. `DS` defaults to `CGAL::Triangulation_data_structure_2< CGAL::Segment_Delaunay_graph_vertex_base_2<Gt>, CGAL::Triangulation_face_base_2<Gt> >`.

Traversal of the Segment Delaunay Graph

A segment Delaunay graph can be seen as a container of faces and vertices. Therefore the Segment_Delaunay_graph_2 class provides several iterators and circulators that allow to traverse it (completely or partially).

Is Model Of:: DelaunayGraph_2

See also: DelaunayGraph_2; SegmentDelaunayGraphTraits_2; SegmentDelaunayGraphDataStructure_2; SegmentDelaunayGraphVertexBase_2; TriangulationFaceBase_2; CGAL::Segment_Delaunay_graph_hierarchy_2<Gt,STag,DS>; CGAL::Segment_Delaunay_graph_traits_2<K,MTag>; CGAL::Segment_Delaunay_graph_traits_without_intersections_2<K,MTag>; CGAL::Segment_Delaunay_graph_filtered_traits_2<CK,CM,EK,EM,FK,FM>; CGAL::Segment_Delaunay_graph_filtered_traits_without_intersections_2<CK,CM,EK,EM,FK,FM>; CGAL::Triangulation_data_structure_2<Vb,Fb>; CGAL::Segment_Delaunay_graph_vertex_base_2<Gt,SSTag>; CGAL::Triangulation_face_base_2<Gt>

Examples:: Segment_Delaunay_graph_2/sdg-count-sites.cpp, Segment_Delaunay_graph_2/sdg-fast-sp-polygon.cpp, Segment_Delaunay_graph_2/sdg-fast-sp.cpp, Segment_Delaunay_graph_2/sdg-red-blue-info.cpp, and Segment_Delaunay_graph_2/sdg-voronoi-edges.cpp.

Types
typedef Gt	Geom_traits
	A type for the geometric traits.

typedef DS	Data_structure
	A type for the underlying data structure.

typedef Data_structure	Triangulation_data_structure
	This type has been added so that the `Segment_Delaunay_graph_2` class is a model of the `DelaunayGraph_2` concept.

typedef DS::size_type	size_type
	Size type (an unsigned integral type)

typedef Gt::Point_2	Point_2
	A type for the point defined in the geometric traits.

typedef Gt::Site_2	Site_2
	A type for the segment Delaunay graph site, defined in the geometric traits.

typedef unspecified_type	Point_container
	A type for the container of points.

typedef Point_container::iterator	Point_handle
	A handle for points in the point container.

Iterators and Handles
The vertices and faces of the segment Delaunay graph are accessed through `handles`, `iterators` and `circulators`. The iterators and circulators are all bidirectional and non-mutable. The circulators and iterators are assignable to the corresponding handle types, and they are also convertible to the corresponding handles. The edges of the segment Delaunay graph can also be visited through iterators and circulators, the edge circulators and iterators are also bidirectional and non-mutable. In the following, we call infinite any face or edge incident to the infinite vertex and the infinite vertex itself. Any other feature (face, edge or vertex) of the segment Delaunay graph is said to be finite. Some iterators (the `All` iterators ) allow to visit finite or infinite features while the others (the `Finite` iterators) visit only finite features. Circulators visit both infinite and finite features.
typedef DS::Edge	Edge
	The edge type. More...

typedef DS::Vertex	Vertex
	A type for a vertex.

typedef DS::Face	Face
	A type for a face.

typedef DS::Vertex_handle	Vertex_handle
	A type for a handle to a vertex.

typedef DS::Face_handle	Face_handle
	A type for a handle to a face.

typedef DS::Vertex_circulator	Vertex_circulator
	A type for a circulator over vertices incident to a given vertex.

typedef DS::Face_circulator	Face_circulator
	A type for a circulator over faces incident to a given vertex.

typedef DS::Edge_circulator	Edge_circulator
	A type for a circulator over edges incident to a given vertex.

typedef DS::Vertex_iterator	All_vertices_iterator
	A type for an iterator over all vertices.

typedef DS::Face_iterator	All_faces_iterator
	A type for an iterator over all faces.

typedef DS::Edge_iterator	All_edges_iterator
	A type for an iterator over all edges.

typedef unspecified_type	Finite_vertices_iterator
	A type for an iterator over finite vertices.

typedef unspecified_type	Finite_faces_iterator
	A type for an iterator over finite faces.

typedef unspecified_type	Finite_edges_iterator
	A type for an iterator over finite edges.

Site Iterators
The following iterators allow respectively to visit all sites. These iterators are non-mutable, bidirectional and their value type is `Site_2`. They are all invalidated by any change in the segment Delaunay graph.
typedef unspecified_type	Input_sites_iterator
	A type for a bidirectional iterator over all input sites.

typedef unspecified_type	Output_sites_iterator
	A type for a bidirectional iterator over all output sites (the sites in the Delaunay graph).

Input_sites_iterator	input_sites_begin ()
	Starts at an arbitrary input site.

Input_sites_iterator	input_sites_end ()
	Past-the-end iterator.

Output_sites_iterator	output_sites_begin ()
	Starts at an arbitrary output site.

Output_sites_iterator	output_sites_end ()
	Past-the-end iterator.

Creation
In addition to the default and copy constructors the following constructors are defined:
	Segment_Delaunay_graph_2 (Gt gt=Gt())
	Creates the segment Delaunay graph using `gt` as geometric traits.

template<class Input_iterator >
	Segment_Delaunay_graph_2 (Input_iterator first, Input_iterator beyond, Gt gt=Gt())
	Creates the segment Delaunay graph using `gt` as geometric traits and inserts all sites in the range [`first`, `beyond`). More...

Access Functions
Geom_traits	geom_traits ()
	Returns a reference to the segment Delaunay graph traits object.

int	dimension ()
	Returns the dimension of the segment Delaunay graph. More...

size_type	number_of_vertices ()
	Returns the number of finite vertices of the segment Delaunay graph.

size_type	number_of_faces ()
	Returns the number of faces (both finite and infinite) of the segment Delaunay graph.

size_type	number_of_input_sites ()
	Return the number of input sites.

size_type	number_of_output_sites ()
	Return the number of output sites. More...

Face_handle	infinite_face ()
	Returns a face incident to the `infinite_vertex`.

Vertex_handle	infinite_vertex ()
	Returns the `infinite_vertex`.

Vertex_handle	finite_vertex ()
	Returns a vertex distinct from the `infinite_vertex`. More...

Data_structure	data_structure ()
	Returns a reference to the segment Delaunay graph data structure object.

Data_structure	tds ()
	Same as `data_structure()`. More...

Point_container	point_container ()
	Returns a reference to the point container object.

Finite Face, Edge and Vertex Iterators
The following iterators allow respectively to visit finite faces, finite edges and finite vertices of the segment Delaunay graph. These iterators are non-mutable, bidirectional and their value types are respectively `Face`, `Edge` and `Vertex`. They are all invalidated by any change in the segment Delaunay graph.
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.

Infinite Face, Edge, and Vertex Iterators
The following iterators allow respectively to visit all (both finite and infinite) faces, edges and vertices of the segment Delaunay graph. These iterators are non-mutable, bidirectional and their value types are respectively `Face`, `Edge` and `Vertex`. They are all invalidated by any change in the segment Delaunay graph.
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
The `Segment_Delaunay_graph_2` class also provides 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++` moves the circulator counterclockwise around the vertex while the `operator-` moves clockwise. A face circulator is invalidated by any modification of the face pointed to. An edge circulator is invalidated by any modification in one of the two faces incident to the edge pointed to. A vertex circulator is invalidated by any modification in any of the faces adjacent to the vertex pointed to. Applied on the `infinite_vertex` the above methods allow to visit the vertices on the convex hull and the infinite edges and faces. Note that a counterclockwise traversal of the vertices adjacent to the `infinite_vertex` is a clockwise traversal of the convex hull.
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`. More...

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`. More...

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`. More...

Predicates
The class `Segment_Delaunay_graph_2` provides methods to test the finite or infinite character of any feature.
bool	is_infinite (Vertex_handle v) const
	`true`, iff `v` is the `infinite_vertex`.

bool	is_infinite (Face_handle f) const
	`true`, iff face `f` is infinite.

bool	is_infinite (Face_handle f, int i) const
	`true`, iff edge `(f,i)` is infinite.

bool	is_infinite (Edge e) const
	`true`, iff edge `e` is infinite.

bool	is_infinite (Edge_circulator ec) const
	`true`, iff edge `*ec` is infinite.

Insertion
template<class Input_iterator >
size_type	insert (Input_iterator first, Input_iterator beyond)
	Inserts the sites in the range [`first`,`beyond`). More...

template<class Input_iterator >
size_type	insert (Input_iterator first, Input_iterator beyond, Tag_false)
	Same as the previous method. More...

template<class Input_iterator >
size_type	insert (Input_iterator first, Input_iterator beyond, Tag_true)
	Decomposes the range [first,beyond) into a range of input points and a range of input segments that are respectively passed to `insert_segments()` and `insert_points()`. More...

template<class PointIterator >
std::size_t	insert_points (PointIterator first, PointIterator beyond)
	Inserts the points in the range [first,beyond) as sites. More...

template<class SegmentIterator >
std::size_t	insert_segments (SegmentIterator first, SegmentIterator beyond)
	Inserts the segments in the range [first,beyond) as sites. More...

template<class PointIterator , class IndicesIterator >
std::size_t	insert_segments (PointIterator points_first, PointIterator points_beyond, IndicesIterator indices_first, IndicesIterator indices_beyond)
	Same as above except that each segment is given as a pair of indices of the points in the range [points_first, points_beyond). More...

Vertex_handle	insert (Point_2 p)
	Inserts the point `p` in the segment Delaunay graph. More...

Vertex_handle	insert (Point_2 p, Vertex_handle vnear)
	Inserts `p` in the segment Delaunay graph using the site associated with `vnear` as an estimate for the nearest neighbor of `p`. More...

Vertex_handle	insert (Point_2 p1, Point_2 p2)
	Inserts the closed segment with endpoints `p1` and `p2` in the segment Delaunay graph. More...

Vertex_handle	insert (Point_2 p1, Point_2 p2, Vertex_handle vnear)
	Inserts the segment whose endpoints are `p1` and `p2` in the segment Delaunay graph using the site associated with `vnear` as an estimate for the nearest neighbor of `p1`. More...

Vertex_handle	insert (Site_2 s)
	Inserts the site `s` in the segment Delaunay graph. More...

Vertex_handle	insert (Site_2 s, Vertex_handle vnear)
	Inserts `s` in the segment Delaunay graph using the site associated with `vnear` as an estimate for the nearest neighbor of `s`, if `s` is a point, or the first endpoint of `s`, if `s` is a segment. More...

Nearest neighbor location
Vertex_handle	nearest_neighbor (Point_2 p)
	Finds the nearest neighbor of the point `p`. More...

Vertex_handle	nearest_neighbor (Point_2 p, Vertex_handle vnear)
	Finds the nearest neighbor of the point `p` using the site associated with `vnear` as an estimate for the nearest neighbor of `p`. More...

I/O
template<class Stream >
Stream &	draw_dual (Stream &str)
	Draws the segment Voronoi diagram to the stream `str`. More...

template<class Stream >
Stream &	draw_skeleton (Stream &str)
	Draws the segment Voronoi diagram to the stream `str`, except the edges of the diagram corresponding to a segment and its endpoints. More...

template<class Stream >
Stream &	draw_dual_edge (Edge e, Stream &str)
	Draws the edge `e` of the segment Voronoi diagram to the stream `str`. More...

template<class Stream >
Stream &	draw_dual_edge (Edge_circulator ec, Stream &str)
	Draws the edge `*ec` of the segment Voronoi diagram to the stream `str`. More...

template<class Stream >
Stream &	draw_dual_edge (All_edges_iterator eit, Stream &str)
	Draws the edge `*eit` of the segment Voronoi diagram to the stream `str`. More...

template<class Stream >
Stream &	draw_dual_edge (Finite_edges_iterator eit, Stream &str)
	Draws the edge `*eit` of the segment Voronoi diagram to the stream `str`. More...

void	file_output (std::ostream &os)
	Writes the current state of the segment Delaunay graph to an output stream. More...

void	file_input (std::istream &is)
	Reads the state of the segment Delaunay graph from an input stream.

std::ostream &	operator<< (std::ostream &os, Segment_Delaunay_graph_2< Gt, DS > sdg)
	Writes the current state of the segment Delaunay graph to an output stream.

std::istream &	operator>> (std::istream &is, Segment_Delaunay_graph_2< Gt, DS > sdg)
	Reads the state of the segment Delaunay graph from an input stream.

Validity check
bool	is_valid (bool verbose=false, int level=1)
	Checks the validity of the segment Delaunay graph. More...

Miscellaneous
void	clear ()
	Clears all contents of the segment Delaunay graph.

void	swap (Segment_Delaunay_graph_2< Gt, DS > other)
	The segment Delaunay graphs `other` and `*this` are swapped. More...

Member Typedef Documentation

◆ Edge

template<typename Gt , typename DS >

typedef DS::Edge CGAL::Segment_Delaunay_graph_2< Gt, DS >::Edge

The edge type.

The Edge(f,i) is the edge common to faces f and f.neighbor(i). It is also the edge joining the vertices vertex(cw(i)) and vertex(ccw(i)) of f.

Precondition: i must be 0, 1 or 2.

Constructor & Destructor Documentation

◆ Segment_Delaunay_graph_2()

template<typename Gt , typename DS >

template<class Input_iterator >

CGAL::Segment_Delaunay_graph_2< Gt, DS >::Segment_Delaunay_graph_2	(	Input_iterator	first,
		Input_iterator	beyond,
		Gt	gt = `Gt()`
	)

Creates the segment Delaunay graph using gt as geometric traits and inserts all sites in the range [first, beyond).

Precondition: Input_iterator must be a model of InputIterator. The value type of Input_iterator must be either Point_2 or Site_2.

Member Function Documentation

◆ dimension()

template<typename Gt , typename DS >

int CGAL::Segment_Delaunay_graph_2< Gt, DS >::dimension ( )

Returns the dimension of the segment Delaunay graph.

The dimension is \( -1\) if the graph contains no sites, \( 0\) if the graph contains one site, \( 1\) if it contains two sites and \( 2\) if it contains three or more sites.

◆ draw_dual()

template<typename Gt , typename DS >

template<class Stream >

Stream& CGAL::Segment_Delaunay_graph_2< Gt, DS >::draw_dual ( Stream & str )

Draws the segment Voronoi diagram to the stream str.

The following operators must be defined:

Stream& operator<<(Stream&, Gt::Segment_2)

Stream& operator<<(Stream&, Gt::Ray_2)

Stream& operator<<(Stream&, Gt::Line_2)

◆ draw_dual_edge() [1/4]

template<typename Gt , typename DS >

template<class Stream >

Stream& CGAL::Segment_Delaunay_graph_2< Gt, DS >::draw_dual_edge	(	Edge	e,
		Stream &	str
	)

Draws the edge e of the segment Voronoi diagram to the stream str.

The following operators must be defined:

Stream& operator<<(Stream&, Gt::Segment_2)

Stream& operator<<(Stream&, Gt::Ray_2)

Stream& operator<<(Stream&, Gt::Line_2)

Precondition: e must be a finite edge.

◆ draw_dual_edge() [2/4]

template<typename Gt , typename DS >

template<class Stream >

Stream& CGAL::Segment_Delaunay_graph_2< Gt, DS >::draw_dual_edge	(	Edge_circulator	ec,
		Stream &	str
	)

Draws the edge *ec of the segment Voronoi diagram to the stream str.

The following operators must be defined:

Stream& operator<<(Stream&, Gt::Segment_2)

Stream& operator<<(Stream&, Gt::Ray_2)

Stream& operator<<(Stream&, Gt::Line_2)

Precondition: *ec must be a finite edge.

◆ draw_dual_edge() [3/4]

template<typename Gt , typename DS >

template<class Stream >

Stream& CGAL::Segment_Delaunay_graph_2< Gt, DS >::draw_dual_edge	(	All_edges_iterator	eit,
		Stream &	str
	)

Draws the edge *eit of the segment Voronoi diagram to the stream str.

The following operators must be defined:

Stream& operator<<(Stream&, Gt::Segment_2)

Stream& operator<<(Stream&, Gt::Ray_2)

Stream& operator<<(Stream&, Gt::Line_2)

Precondition: *eit must be a finite edge.

◆ draw_dual_edge() [4/4]

template<typename Gt , typename DS >

template<class Stream >

Stream& CGAL::Segment_Delaunay_graph_2< Gt, DS >::draw_dual_edge	(	Finite_edges_iterator	eit,
		Stream &	str
	)

Draws the edge *eit of the segment Voronoi diagram to the stream str.

The following operators must be defined:

Stream& operator<<(Stream&, Gt::Segment_2)

Stream& operator<<(Stream&, Gt::Ray_2)

Stream& operator<<(Stream&, Gt::Line_2)

◆ draw_skeleton()

template<typename Gt , typename DS >

template<class Stream >

Stream& CGAL::Segment_Delaunay_graph_2< Gt, DS >::draw_skeleton ( Stream & str )

Draws the segment Voronoi diagram to the stream str, except the edges of the diagram corresponding to a segment and its endpoints.

The following operators must be defined:

Stream& operator<<(Stream&, Gt::Segment_2)

Stream& operator<<(Stream&, Gt::Ray_2)

Stream& operator<<(Stream&, Gt::Line_2)

◆ file_output()

template<typename Gt , typename DS >

void CGAL::Segment_Delaunay_graph_2< Gt, DS >::file_output ( std::ostream & os )

Writes the current state of the segment Delaunay graph to an output stream.

In particular, all sites in the diagram are written to the stream (represented through appropriate input sites), as well as the underlying combinatorial data structure.

◆ finite_vertex()

template<typename Gt , typename DS >

Vertex_handle CGAL::Segment_Delaunay_graph_2< Gt, DS >::finite_vertex ( )

Returns a vertex distinct from the infinite_vertex.

Precondition: The number of sites in the segment Delaunay graph must be at least one.

◆ incident_edges()

template<typename Gt , typename DS >

Edge_circulator CGAL::Segment_Delaunay_graph_2< Gt, DS >::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 is incident to vertex v.

◆ incident_faces()

template<typename Gt , typename DS >

Face_circulator CGAL::Segment_Delaunay_graph_2< Gt, DS >::incident_faces	(	Vertex_handle	v,
		Face_handle	f
	)

Starts at face f.

Precondition: Face f is incident to vertex v.

◆ incident_vertices()

template<typename Gt , typename DS >

Vertex_circulator CGAL::Segment_Delaunay_graph_2< Gt, DS >::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 is incident to vertex v.

◆ insert() [1/9]

template<typename Gt , typename DS >

template<class Input_iterator >

size_type CGAL::Segment_Delaunay_graph_2< Gt, DS >::insert	(	Input_iterator	first,
		Input_iterator	beyond
	)

Inserts the sites in the range [first,beyond).

The number of additional sites inserted in the Delaunay graph is returned. Input_iterator must be a model of InputIterator and its value type must be either Point_2 or Site_2.

◆ insert() [2/9]

template<typename Gt , typename DS >

template<class Input_iterator >

size_type CGAL::Segment_Delaunay_graph_2< Gt, DS >::insert	(	Input_iterator	first,
		Input_iterator	beyond,
		Tag_false
	)

Same as the previous method.

Input_iterator must be a model of InputIterator and its value type must be either Point_2 or Site_2.

◆ insert() [3/9]

template<typename Gt , typename DS >

template<class Input_iterator >

size_type CGAL::Segment_Delaunay_graph_2< Gt, DS >::insert	(	Input_iterator	first,
		Input_iterator	beyond,
		Tag_true
	)

Decomposes the range [first,beyond) into a range of input points and a range of input segments that are respectively passed to insert_segments() and insert_points().

Non-input sites are first random_shuffled and then inserted one by one. Input_iterator must be a model of InputIterator and its value type must be either Point_2, Segment_2 or Site_2.

Returns: the number of sites inserted in the Delaunay graph

◆ insert() [4/9]

template<typename Gt , typename DS >

Vertex_handle CGAL::Segment_Delaunay_graph_2< Gt, DS >::insert ( Point_2 p )

Inserts the point p in the segment Delaunay graph.

If p has already been inserted, then the vertex handle of its already inserted copy is returned. If p has not been inserted yet, the vertex handle of p is returned.

◆ insert() [5/9]

template<typename Gt , typename DS >

Vertex_handle CGAL::Segment_Delaunay_graph_2< Gt, DS >::insert	(	Point_2	p,
		Vertex_handle	vnear
	)

Inserts p in the segment Delaunay graph using the site associated with vnear as an estimate for the nearest neighbor of p.

The vertex handle returned has the same semantics as the vertex handle returned by the method Vertex_handle insert(Point_2 p).

◆ insert() [6/9]

template<typename Gt , typename DS >

Vertex_handle CGAL::Segment_Delaunay_graph_2< Gt, DS >::insert	(	Point_2	p1,
		Point_2	p2
	)

Inserts the closed segment with endpoints p1 and p2 in the segment Delaunay graph.

If the segment has already been inserted in the Delaunay graph then the vertex handle of its already inserted copy is returned. If the segment does not intersect any segment in the existing diagram, the vertex handle corresponding to its corresponding open segment is returned. Finally, if the segment intersects other segments in the existing Delaunay graph, the vertex handle to one of its open subsegments is returned.

◆ insert() [7/9]

template<typename Gt , typename DS >

Vertex_handle CGAL::Segment_Delaunay_graph_2< Gt, DS >::insert	(	Point_2	p1,
		Point_2	p2,
		Vertex_handle	vnear
	)

Inserts the segment whose endpoints are p1 and p2 in the segment Delaunay graph using the site associated with vnear as an estimate for the nearest neighbor of p1.

The vertex handle returned has the same semantics as the vertex handle returned by the method Vertex_handle insert(Point_2 p1, Point_2 p2).

◆ insert() [8/9]

template<typename Gt , typename DS >

Vertex_handle CGAL::Segment_Delaunay_graph_2< Gt, DS >::insert ( Site_2 s )

Inserts the site s in the segment Delaunay graph.

The vertex handle returned has the same semantics as the vertex handle returned by the methods Vertex_handle insert(Point_2 p) and Vertex_handle insert(Point_2 p1, Point_2 p2), depending on whether s represents a point or a segment respectively.

Precondition: s.is_input() must be true.

◆ insert() [9/9]

template<typename Gt , typename DS >

Vertex_handle CGAL::Segment_Delaunay_graph_2< Gt, DS >::insert	(	Site_2	s,
		Vertex_handle	vnear
	)

Inserts s in the segment Delaunay graph using the site associated with vnear as an estimate for the nearest neighbor of s, if s is a point, or the first endpoint of s, if s is a segment.

The vertex handle returned has the same semantics as the vertex handle returned by the method Vertex_handle insert(Site_2 s).

Precondition: s.is_input() must be true.

◆ insert_points()

template<typename Gt , typename DS >

template<class PointIterator >

std::size_t CGAL::Segment_Delaunay_graph_2< Gt, DS >::insert_points	(	PointIterator	first,
		PointIterator	beyond
	)

Inserts the points in the range [first,beyond) as sites.

Note that this function is not guaranteed to insert the points following the order of PointInputIterator, as spatial_sort() is used to improve efficiency.

Returns: the number of points inserted in the Delaunay graph

Template Parameters

PointIterator must be an input iterator Point_2 or Site_2 as value_type.

◆ insert_segments() [1/2]

template<typename Gt , typename DS >

template<class SegmentIterator >

std::size_t CGAL::Segment_Delaunay_graph_2< Gt, DS >::insert_segments	(	SegmentIterator	first,
		SegmentIterator	beyond
	)

Inserts the segments in the range [first,beyond) as sites.

Note that this function is not guaranteed to insert the segments following the order of SegmentIterator, as spatial_sort() is used to improve efficiency.

Returns: the number of segments inserted in the Delaunay graph

Template Parameters

SegmentIterator must be an input iterator with Site_2, Segment_2 or std::pair<Point_2,Point_2> as value type.

◆ insert_segments() [2/2]

template<typename Gt , typename DS >

template<class PointIterator , class IndicesIterator >

std::size_t CGAL::Segment_Delaunay_graph_2< Gt, DS >::insert_segments	(	PointIterator	points_first,
		PointIterator	points_beyond,
		IndicesIterator	indices_first,
		IndicesIterator	indices_beyond
	)

Same as above except that each segment is given as a pair of indices of the points in the range [points_first, points_beyond).

The indices must start from 0 to std::distance(points_first, points_beyond)

Template Parameters

PointIterator	is an input iterator with `Point_2` as value type.
IndicesIterator	is an input iterator with `std::pair<std::size_t, std::size_t>` as value type.

◆ is_valid()

template<typename Gt , typename DS >

bool CGAL::Segment_Delaunay_graph_2< Gt, DS >::is_valid	(	bool	verbose = `false`,
		int	level = `1`
	)

Checks the validity of the segment Delaunay graph.

If verbose is true a short message is sent to std::cerr. If level is 0, only the data structure is validated. If level is 1, then both the data structure and the segment Delaunay graph are validated. Negative values of level always return true, and values greater than 1 are equivalent to level being 1.

◆ nearest_neighbor() [1/2]

template<typename Gt , typename DS >

Vertex_handle CGAL::Segment_Delaunay_graph_2< Gt, DS >::nearest_neighbor ( Point_2 p )

Finds the nearest neighbor of the point p.

In other words it finds the site whose segment Voronoi diagram cell contains p. Ties are broken arbitrarily and one of the nearest neighbors of p is returned. If there are no sites in the segment Delaunay graph Vertex_handle() is returned.

◆ nearest_neighbor() [2/2]

template<typename Gt , typename DS >

Vertex_handle CGAL::Segment_Delaunay_graph_2< Gt, DS >::nearest_neighbor	(	Point_2	p,
		Vertex_handle	vnear
	)

Finds the nearest neighbor of the point p using the site associated with vnear as an estimate for the nearest neighbor of p.

Ties are broken arbitrarily and one of the nearest neighbors of p is returned. If there are no sites in the segment Delaunay graph Vertex_handle() is returned.

◆ number_of_output_sites()

template<typename Gt , typename DS >

size_type CGAL::Segment_Delaunay_graph_2< Gt, DS >::number_of_output_sites ( )

Return the number of output sites.

This is equal to the number of vertices in the segment Delaunay graph.

◆ swap()

template<typename Gt , typename DS >

void CGAL::Segment_Delaunay_graph_2< Gt, DS >::swap ( Segment_Delaunay_graph_2< Gt, DS > other )

The segment Delaunay graphs other and *this are swapped.

For a segment Delaunay graph sdg, the operation sdg.swap(other) should be preferred to sdg= other or to sdg(other) if other is deleted afterwards.

◆ tds()

template<typename Gt , typename DS >

Data_structure CGAL::Segment_Delaunay_graph_2< Gt, DS >::tds ( )

Same as data_structure().

It has been added for compliance to the DelaunayGraph_2 concept.

Definition

Types

Iterators and Handles

Site Iterators

Creation

Access Functions

Finite Face, Edge and Vertex Iterators

Infinite Face, Edge, and Vertex Iterators

Face, Edge and Vertex Circulators

Predicates

Insertion

Nearest neighbor location

I/O

Validity check

Miscellaneous

Member Typedef Documentation

◆ Edge

Constructor & Destructor Documentation

◆ Segment_Delaunay_graph_2()

Member Function Documentation

◆ dimension()

◆ draw_dual()

◆ draw_dual_edge() [1/4]

◆ draw_dual_edge() [2/4]

◆ draw_dual_edge() [3/4]

◆ draw_dual_edge() [4/4]

◆ draw_skeleton()

◆ file_output()

◆ finite_vertex()

◆ incident_edges()

◆ incident_faces()

◆ incident_vertices()

◆ insert() [1/9]

◆ insert() [2/9]

◆ insert() [3/9]

◆ insert() [4/9]

◆ insert() [5/9]

◆ insert() [6/9]

◆ insert() [7/9]

◆ insert() [8/9]

◆ insert() [9/9]

◆ insert_points()

◆ insert_segments() [1/2]

◆ insert_segments() [2/2]

◆ is_valid()

◆ nearest_neighbor() [1/2]

◆ nearest_neighbor() [2/2]

◆ number_of_output_sites()

◆ swap()

◆ tds()