Voronoi_diagram_2<DG,AT,AP>

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CGAL::Voronoi_diagram_2<DG,AT,AP>

Definition

The class Voronoi_diagram_2<DG,AT,AP> provides an adaptor that enables us to view a triangulated Delaunay graph as their dual subdivision, the Voronoi diagram. The class Voronoi_diagram_2<DG,AT,AP> is designed to provide an API that is similar to that of Cgal's arrangements.
The first template parameter of the Voronoi_diagram_2<DG,AT,AP> class corresponds to the triangulated Delaunay graph and must be a model of the DelaunayGraph_2 concept. The second template parameter must be a model of the AdaptationTraits_2 concept. The third template parameter must be a model of the AdaptationPolicy_2 concept. The third template parameter defaults to CGAL::Identity_policy_2<DG,AT>.

#include <CGAL/Voronoi_diagram_2.h>

Refines

DefaultConstructible, CopyConstructible, Assignable

Types

typedef DG	Delaunay_graph;	A type for the dual Delaunay graph.
typedef AT	Adaptation_traits;	A type for the adaptation traits needed by the Voronoi diagram adaptor.
typedef AP	Adaptation_policy;	A type for the adaptation policy used.
typedef Adaptation_traits::Point_2
	Point_2;	A type a point.
typedef Adaptation_traits::Site_2	Site_2;	A type for the sites of the Voronoi diagram.
typedef Delaunay_graph::size_type	size_type;	A type for sizes.
typedef Delaunay_graph::Geom_traits
	Delaunay_geom_traits;	A type for the geometric traits of the Delaunay graph.
typedef Delaunay_graph::Vertex_handle
	Delaunay_vertex_handle;	A type for the vertex handles of the Delaunay graph.
typedef Delaunay_graph::Face_handle
	Delaunay_face_handle;	A type for the face handles of the Delaunay graph.
typedef Delaunay_graph::Edge	Delaunay_edge;	A type for the edges of the Delaunay graph.

Voronoi_diagram_2<DG,AT,AP>::Halfedge
	A type for the halfedges of the Voronoi diagram.
Voronoi_diagram_2<DG,AT,AP>::Vertex
	A type for the vertices of the Voronoi diagram.
Voronoi_diagram_2<DG,AT,AP>::Face
	A type for the faces of the Voronoi diagram.

The vertices, edges and faces of the Voronoi diagram 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.

Voronoi_diagram_2<DG,AT,AP>::Halfedge_handle
	Handle for halfedges.
Voronoi_diagram_2<DG,AT,AP>::Vertex_handle
	Handle for vertices.
Voronoi_diagram_2<DG,AT,AP>::Face_handle
	Handle for faces.
Voronoi_diagram_2<DG,AT,AP>::Edge_iterator
	A type for an iterator over Voronoi edges. Edges are considered non-oriented. Its value type is Halfedge.
Voronoi_diagram_2<DG,AT,AP>::Halfedge_iterator
	A type for an iterator over Voronoi halfedges. Halfedges are oriented and come in pairs. Its value type is Halfedge.
Voronoi_diagram_2<DG,AT,AP>::Face_iterator
	A type for an iterator over Voronoi faces. Its value type is Face.
Voronoi_diagram_2<DG,AT,AP>::Vertex_iterator
	A type for an iterator over Voronoi vertices. Its value type is Vertex.
Voronoi_diagram_2<DG,AT,AP>::Halfedge_around_vertex_circulator
	A type for a circulator over the halfedges that have a common vertex as their target. Its value type is Halfedge.
Voronoi_diagram_2<DG,AT,AP>::Ccb_halfedge_circulator
	A type for a circulator over the halfedges on the boundary of a Voronoi face. Its value type of is Halfedge.
Voronoi_diagram_2<DG,AT,AP>::Unbounded_faces_iterator
	A type for an iterator over the unbounded faces of the Voronoi diagram. Its value type is Face.
Voronoi_diagram_2<DG,AT,AP>::Bounded_faces_iterator
	A type for an iterator over the bounded faces of the Voronoi diagram. Its value type is Face.
Voronoi_diagram_2<DG,AT,AP>::Unbounded_halfedges_iterator
	A type for an iterator over the unbounded halfedges of the Voronoi diagram. Its value type is Halfedge.
Voronoi_diagram_2<DG,AT,AP>::Bounded_halfedges_iterator
	A type for an iterator over the bounded halfedges of the Voronoi diagram. Its value type is Halfedge.
Voronoi_diagram_2<DG,AT,AP>::Site_iterator
	A type for an iterator over the sites of the Voronoi diagram. Its value type is Site_2.

typedef boost::variant<Face_handle,Halfedge_handle,Vertex_handle>
	Locate_result;	The result type of the point location queries.

Creation

Voronoi_diagram_2<DG,AT,AP> vd ( Adaptation_traits at = Adaptation_traits(),
Adaptation_policy ap = Adaptation_policy(),
Delaunay_geom_traits gt = Delaunay_geom_traits());

Creates a Voronoi diagram using at as adaptation traits and ap as adaptation policy; the underlying Delaunay graph is created using gt as geometric traits.

Voronoi_diagram_2<DG,AT,AP> vd ( Delaunay_graph dg,
bool swap_dg = false,
Adaptation_traits at = Adaptation_traits(),
Adaptation_policy ap = Adaptation_policy());

Creates a Voronoi diagram from the Delaunay graph dg and using at as adaptation traits and ap as adaptation policy. The Delaunay graph dg is fully copied if swap_dg is set to false, or swapped with the one stored internally if swap_dg is set to true.

template<class Iterator>

Voronoi_diagram_2<DG,AT,AP> vd ( Iterator first,
Iterator beyond,
Adaptation_traits at = Adaptation_traits(),
Adaptation_policy ap = Adaptation_policy(),
Delaunay_geom_traits gt = Delaunay_geom_traits());

Creates a Voronoi diagram using as sites the sites in the iterator range [first, beyond), at as adaptation traits and ap as adaptation policy; the underlying Delaunay graph is created using gt as geometric traits. Iterator must be a model of the InputIterator concept and its value type must be Site_2.

Access Methods

Delaunay_graph	vd.dual ()	Returns a const reference to the dual graph, i.e., the Delaunay graph.
Halfedge_handle	vd.dual ( Delaunay_edge e)	Returns a handle to the halfedge in the Voronoi diagram that is dual to the edge e in the Delaunay graph.
Face_handle	vd.dual ( Delaunay_vertex_handle v)
		Returns a handle to the face in the Voronoi diagram that is dual to the vertex corresponding to the vertex handle v in the Delaunay graph.
Vertex_handle	vd.dual ( Delaunay_face_handle f)	Returns a handle to the vertex in the Voronoi diagram that is dual to the face corresponding to the face handle f in the Delaunay graph.
Adaptation_traits	vd.adaptation_traits ()	Returns a reference to the Voronoi traits.
Adaptation_policy	vd.adaptation_policy ()	Returns a reference to the adaptation policy.
size_type	vd.number_of_vertices ()	Returns the number of Voronoi vertices.
size_type	vd.number_of_faces ()	Returns the number of Voronoi faces (bounded and unbounded).
size_type	vd.number_of_halfedges ()	Returns the number of halfedges (bounded and unbounded) in the Voronoi diagram. This is always an even number.
size_type	vd.number_of_connected_components ()
		Returns the number of connected components of the Voronoi skeleton.
Face_handle	vd.unbounded_face ()	Returns one of the unbounded faces of the Voronoi diagram. If no unbounded faces exist (this can happen if the number of sites is zero) the default constructed face handle is returned.
Face_handle	vd.bounded_face ()	Returns one of the bounded faces of the Voronoi diagram. If no bounded faces exist the default constructed face handle is returned.
Halfedge_handle	vd.unbounded_halfedge ()	Returns one of the unbounded halfedges of the Voronoi diagram. If no unbounded halfedges exist the default constructed halfedge handle is returned.
Halfedge_handle	vd.bounded_halfedge ()	Returns one of the bounded halfedges of the Voronoi diagram. If no bounded halfedges exist the default constructed halfedge handle is returned.

Traversal of the Voronoi diagram

A Voronoi diagram can be seen as a container of faces, vertices and halfedges. Therefore the Voronoi diagram provides several iterators and circulators that allow to traverse it.

Iterators

The following iterators allow respectively to visit the faces (all or only the unbounded/bounded ones), edges, halfedges (all or only the unbounded/bounded ones) and vertices of the Voronoi diagram. These iterators are non-mutable, bidirectional and their value types are respectively Face, Halfedge, Halfedge and Vertex. All iterators are convertible to the corresponding handles and are invalidated by any change in the Voronoi diagram.

Face_iterator	vd.faces_begin ()	Starts at an arbitrary Voronoi face.
Face_iterator	vd.faces_end ()	Past-the-end iterator.

Unbounded_faces_iterator	vd.unbounded_faces_begin ()	Starts at an arbitrary unbounded Voronoi face.
Unbounded_faces_iterator	vd.unbounded_faces_end ()	Past-the-end iterator.

Bounded_faces_iterator	vd.bounded_faces_begin ()	Starts at an arbitrary bounded Voronoi face.
Bounded_faces_iterator	vd.bounded_faces_end ()	Past-the-end iterator.

Edge_iterator	vd.edges_begin ()	Starts at an arbitrary Voronoi edge.
Edge_iterator	vd.edges_end ()	Past-the-end iterator.

Halfedge_iterator	vd.halfedges_begin ()	Starts at an arbitrary Voronoi halfedge.
Halfedge_iterator	vd.halfedges_end ()	Past-the-end iterator.

Unbounded_halfedges_iterator	vd.unbounded_halfedges_begin ()	Starts at an arbitrary unbounded Voronoi edge.
Unbounded_halfedges_iterator	vd.unbounded_halfedges_end ()	Past-the-end iterator.

Bounded_halfedges_iterator	vd.bounded_halfedges_begin ()	Starts at an arbitrary bounded Voronoi edge.
Bounded_halfedges_iterator	vd.bounded_halfedges_end ()	Past-the-end iterator.

Vertex_iterator	vd.vertices_begin ()	Starts at an arbitrary Voronoi vertex.
Vertex_iterator	vd.vertices_end ()	Past-the-end iterator.

The following iterator provides access to the sites that define the Voronoi diagram. Its value type is Site_2. It is invalidated by any change in the Voronoi diagram.

Site_iterator	vd.sites_begin ()	Starts at an arbitrary site.
Site_iterator	vd.sites_end ()	Past-the-end iterator.

Circulators

The Voronoi diagram adaptor also provides circulators that allow to visit all halfedges whose target is a given vertex - this is the Halfedge_around_vertex_circulator, as well as all halfedges on the boundary of a Voronoi face - this is the Ccb_halfedge_circulator. These circulators are non-mutable and bidirectional. The operator operator++ moves the former circulator counterclockwise around the vertex while the operator-- moves clockwise. The latter circulator is moved by the operator operator++ to the next halfedge on the boundary in the counterclockwise sense, while operator-- moves clockwise. When the Ccb_halfedge_circulator is defined over an infinite Voronoi face f, then applying operator++ to a circulator corresponding to a halfedge whose target is not finite moves to the next infinite (or semi-infinite) halfedge of f in the counterclockwise sense. Similarly, applying operator++ to a circulator corresponding to a halfedge whose source is not finite, moves to the previous infinite (or semi-infinite) halfedge of f in the clockwise sense. The Halfedge_around_vertex_circulator circulator is invalidated by any modification in the faces adjacent to the vertex over which it is defined. The Ccb_halfedge_circulator is invalidated by any modification in the face over which it is defined.

Ccb_halfedge_circulator

vd.ccb_halfedges ( Face_handle f)

Returns a circulator over the halfedges on the boundary of f. The circulator is initialized to an arbitrary halfedge on the boundary of the Voronoi face f.

Ccb_halfedge_circulator

vd.ccb_halfedges ( Face_handle f, Halfedge_handle h)

Returns a circulator over the halfedges on the boundary of f. The circulator is initialized with the halfedge h.

Precondition:

The halfedge h must lie on the boundary of f.

Halfedge_around_vertex_circulator

vd.incident_halfedges ( Vertex_handle v)

Returns a circulator over the halfedges whose target is the Voronoi vertex v. The circulator is initialized to an arbitrary halfedge incident to v.

Halfedge_around_vertex_circulator

vd.incident_halfedges ( Vertex_handle v, Halfedge_handle h)

Returns a circulator over the halfedges whose target is the Voronoi vertex v. The circulator is initialized with the halfedge h.

Precondition:

The vertex v must be the target vertex of the halfedge h.

Insertion

Face_handle	vd.insert ( Site_2 t)	Inserts the site t in the Voronoi diagram. A handle to the face corresponding to the Voronoi face of t in the Voronoi diagram is returned. If t has an empty Voronoi cell, the default constructed face handle is returned. This method is supported only if Voronoi_traits::Has_inserter is set to CGAL::Tag_true.
template<class Iterator>
size_type	vd.insert ( Iterator first, Iterator beyond)
		Inserts, in the Voronoi diagram, the sites in the iterator range [first, beyond). The value type of Iterator must be Site_2. The number of sites in the iterator range is returned. This method is supported only if Voronoi_traits::Has_inserter is set to CGAL::Tag_true.

Queries

Locate_result

vd.locate ( Point_2 p)

Performs point location for the query point p. In other words, the face, halfedge or vertex of the Voronoi diagram is found on which the point p lies. This method is supported only if Voronoi_traits::Has_nearest_site_2 is set to CGAL::Tag_true.

Precondition:

The Voronoi diagram must contain at least one face.

I/O

void	vd.file_output ( std::ostream& os)
		Writes the current state of the Voronoi diagram to the output stream os. The following operator must be defined: std::ostream& operator<<(std::ostream&, Delaunay_graph)
void	vd.file_input ( std::istream& is)	Reads the current state of the Voronoi diagram from the input stream is. The following operator must be defined: std::istream& operator>>(std::istream&, Delaunay_graph)

std::ostream&	std::ostream& os << vd	Writes the current state of the Voronoi diagram to the output stream os. The following operator must be defined: std::ostream& operator<<(std::ostream&, Delaunay_graph)
std::istream&	std::istream& is >> vd	Reads the current state of the Voronoi diagram from the input stream is. The following operator must be defined: std::istream& operator>>(std::istream&, Delaunay_graph)

Validity check

bool

vd.is_valid ()

Checks the validity of the dual Delaunay graph and the Voronoi diagram adaptor.

Miscellaneous

void	vd.clear ()	Clears all contents of the Voronoi diagram.
void	vd.swap ( other)	The Voronoi diagrams other and vd are swapped. vd.swap(other) should be preferred to vd = other or to vd(other) if other is deleted afterwards.

CGAL::Voronoi_diagram_2<DG,AT,AP>

Definition

Refines

Types

Creation

Access Methods

Traversal of the Voronoi diagram

Iterators

Circulators

Insertion

Queries

I/O

Validity check

Miscellaneous

See Also