CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge Class Reference

#include <CGAL/Voronoi_diagram_2.h>

Definition

The class Halfedge is the class provided by the Voronoi_diagram_2<DG,AT,AP> class for Voronoi halfedges.

Below we present its interface.

Is Model Of:

DefaultConstructible

CopyConstructible

Assignable

EqualityComparable

LessThanComparable

See also

CGAL::Voronoi_diagram_2<DG,AT,AP>

CGAL::Voronoi_diagram_2<DG,AT,AP>::Vertex

CGAL::Voronoi_diagram_2<DG,AT,AP>::Face

DelaunayGraph_2

Types
typedef unspecified_type	Vertex
	A type for the vertices of the Voronoi diagram. More...
typedef unspecified_type	Face
	A type for the faces of the Voronoi diagram. More...
typedef unspecified_type	Vertex_handle
	Handle for the vertices of the Voronoi diagram. More...
typedef unspecified_type	Face_handle
	Handle for the faces of the Voronoi diagram. More...
typedef unspecified_type	Halfedge_handle
	Handle for the halfedges of the Voronoi diagram. More...
typedef unspecified_type	Ccb_halfedge_circulator
	A type for a bidirectional circulator over the halfedges of the boundary of a Voronoi face. More...
typedef unspecified_type	Delaunay_graph
	A type for the Delaunay graph. More...
typedef Delaunay_graph::Edge	Delaunay_edge
	A type for the dual edge in the Delaunay graph. More...
typedef Delaunay_graph::Vertex_handle	Delaunay_vertex_handle
	A type for vertex handles in the Delaunay graph. More...

Access Methods
Halfedge_handle	twin ()
	Returns the twin halfedge. More...
Halfedge_handle	opposite ()
	Same as e.twin(). More...
Halfedge_handle	next ()
	Returns the next halfedge in the counterclockwise sense around the boundary of the face that e is incident to. More...
Halfedge_handle	previous ()
	Returns the previous halfedge in the counterclockwise sense around the boundary of the adjacent face. More...
Face_handle	face ()
	Returns the face that e is incident to. More...
Vertex_handle	source ()
	Returns the source vertex of e. More...
Vertex_handle	target ()
	Returns the target vertex of e. More...
Ccb_halfedge_circulator	ccb ()
	Returns a bidirectional circulator to traverse the halfedges on the boundary of the Voronoi face containing e. More...
Delaunay_edge	dual ()
	Returns the corresponding dual edge in the Delaunay graph. More...
In the four methods below we consider Voronoi halfedges to be "parallel" to the \( x\)-axis, oriented from left to right.
Delaunay_vertex_handle	up ()
	Returns a handle to the vertex in the Delaunay graph corresponding to the defining site above the Voronoi edge. More...
Delaunay_vertex_handle	down ()
	Returns a handle to the vertex in the Delaunay graph corresponding to the defining site below the Voronoi edge. More...
Delaunay_vertex_handle	left ()
	Returns a handle to the vertex in the Delaunay graph corresponding to the defining site to the left of the Voronoi edge. More...
Delaunay_vertex_handle	right ()
	Returns a handle to the vertex in the Delaunay graph corresponding to the defining site to the right of the Voronoi edge. More...

Predicate Methods
bool	has_source ()
	Returns true iff the halfedge corresponds to a bisecting segment or a bisecting ray oriented appropriately so that its apex is its source. More...
bool	has_target ()
	Returns true iff the halfedge corresponds to a bisecting segment or a bisecting ray oriented appropriately so that its apex is its target. More...
bool	is_unbounded ()
	Returns true iff the source or the target of the halfedge does not exist, i.e., if either of has_source() or has_target() return false. More...
bool	is_bisector ()
	Returns true iff the Voronoi edge is an entire bisector. More...
bool	is_segment ()
	Returns true iff the Voronoi edge has both a source and a target Voronoi vertex. More...
bool	is_ray ()
	Returns true iff the Voronoi edge has either a source or a target Voronoi vertex, but not both; in other words it is a bisecting ray. More...
bool	is_valid ()
	Returns true if the following conditions are met: the halfedge is not a rejected edge with respect to the chosen adaptation policy; the twin edge of its twin edge is itself; its adjacent face is not a rejected face with respect to the chosen adaptation policy; its source and target vertices are valid (provided they exist, of course); the previous of its next halfedge is itself and the next of its previous halfedge is itself. More...

Member Typedef Documentation

template<typename DG , typename AT , typename AP >

typedef unspecified_type CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::Ccb_halfedge_circulator

A type for a bidirectional circulator over the halfedges of the boundary of a Voronoi face.

The value type of the circulator is CGAL::Voronoi_diagram_2<DG,AT,AP>::Halfedge and is convertible to Halfedge_handle.

template<typename DG , typename AT , typename AP >

typedef Delaunay_graph::Edge CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::Delaunay_edge

A type for the dual edge in the Delaunay graph.

template<typename DG , typename AT , typename AP >

typedef unspecified_type CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::Delaunay_graph

A type for the Delaunay graph.

It is a model of the DelaunayGraph_2 concept.

template<typename DG , typename AT , typename AP >

typedef Delaunay_graph::Vertex_handle CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::Delaunay_vertex_handle

A type for vertex handles in the Delaunay graph.

template<typename DG , typename AT , typename AP >

typedef unspecified_type CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::Face

A type for the faces of the Voronoi diagram.

template<typename DG , typename AT , typename AP >

typedef unspecified_type CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::Face_handle

Handle for the faces of the Voronoi diagram.

template<typename DG , typename AT , typename AP >

typedef unspecified_type CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::Halfedge_handle

Handle for the halfedges of the Voronoi diagram.

template<typename DG , typename AT , typename AP >

typedef unspecified_type CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::Vertex

A type for the vertices of the Voronoi diagram.

template<typename DG , typename AT , typename AP >

typedef unspecified_type CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::Vertex_handle

Handle for the vertices of the Voronoi diagram.

Member Function Documentation

template<typename DG , typename AT , typename AP >

Ccb_halfedge_circulator CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::ccb

(

)

Returns a bidirectional circulator to traverse the halfedges on the boundary of the Voronoi face containing e.

The circulator is initialized to e. Applying operator++ (resp. operator-) to this circulator returns the next halfedge on the boundary of the face containing e in the counterclockwise (resp. clockwise) sense.

template<typename DG , typename AT , typename AP >

Delaunay_vertex_handle CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::down

(

)

Returns a handle to the vertex in the Delaunay graph corresponding to the defining site below the Voronoi edge.

template<typename DG , typename AT , typename AP >

Delaunay_edge CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::dual

(

)

Returns the corresponding dual edge in the Delaunay graph.

template<typename DG , typename AT , typename AP >

Face_handle CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::face

(

)

Returns the face that e is incident to.

template<typename DG , typename AT , typename AP >

bool CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::has_source

(

)

Returns true iff the halfedge corresponds to a bisecting segment or a bisecting ray oriented appropriately so that its apex is its source.

template<typename DG , typename AT , typename AP >

bool CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::has_target

(

)

Returns true iff the halfedge corresponds to a bisecting segment or a bisecting ray oriented appropriately so that its apex is its target.

template<typename DG , typename AT , typename AP >

bool CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::is_bisector

(

)

Returns true iff the Voronoi edge is an entire bisector.

template<typename DG , typename AT , typename AP >

bool CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::is_ray

(

)

Returns true iff the Voronoi edge has either a source or a target Voronoi vertex, but not both; in other words it is a bisecting ray.

template<typename DG , typename AT , typename AP >

bool CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::is_segment

(

)

Returns true iff the Voronoi edge has both a source and a target Voronoi vertex.

template<typename DG , typename AT , typename AP >

bool CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::is_unbounded

(

)

Returns true iff the source or the target of the halfedge does not exist, i.e., if either of has_source() or has_target() return false.

template<typename DG , typename AT , typename AP >

bool CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::is_valid

(

)

Returns true if the following conditions are met: the halfedge is not a rejected edge with respect to the chosen adaptation policy; the twin edge of its twin edge is itself; its adjacent face is not a rejected face with respect to the chosen adaptation policy; its source and target vertices are valid (provided they exist, of course); the previous of its next halfedge is itself and the next of its previous halfedge is itself.

template<typename DG , typename AT , typename AP >

Delaunay_vertex_handle CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::left

(

)

Returns a handle to the vertex in the Delaunay graph corresponding to the defining site to the left of the Voronoi edge.

Precondition

has_source() must be true.

template<typename DG , typename AT , typename AP >

Halfedge_handle CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::next

(

)

Returns the next halfedge in the counterclockwise sense around the boundary of the face that e is incident to.

template<typename DG , typename AT , typename AP >

Halfedge_handle CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::opposite

(

)

Same as e.twin().

template<typename DG , typename AT , typename AP >

Halfedge_handle CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::previous

(

)

Returns the previous halfedge in the counterclockwise sense around the boundary of the adjacent face.

template<typename DG , typename AT , typename AP >

Delaunay_vertex_handle CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::right

(

)

Returns a handle to the vertex in the Delaunay graph corresponding to the defining site to the right of the Voronoi edge.

Precondition

has_target() must be true.

template<typename DG , typename AT , typename AP >

Vertex_handle CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::source

(

)

Returns the source vertex of e.

Precondition

The source vertex must exist, i.e., has_source() must return true.

template<typename DG , typename AT , typename AP >

Vertex_handle CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::target

(

)

Returns the target vertex of e.

Precondition

The target vertex must exist, i.e., has_target() must return true.

template<typename DG , typename AT , typename AP >

Halfedge_handle CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::twin

(

)

Returns the twin halfedge.

template<typename DG , typename AT , typename AP >

Delaunay_vertex_handle CGAL::Voronoi_diagram_2< DG, AT, AP >::Halfedge::up

(

)

Returns a handle to the vertex in the Delaunay graph corresponding to the defining site above the Voronoi edge.