CGAL::Arrangement_2< Traits, Dcel >::Halfedge Class Reference

#include <CGAL/Arrangement_2.h>

Inherits from

Halfedge.

Definition

An object \( e\) of the class Halfedge represents a halfedge in the arrangement.

A halfedge is directed from its source vertex to its target vertex, and has an incident face lying to its left. Each halfedge has a twin halfedge directed in the opposite direction, where the pair of twin halfedges form together an arrangement edge, that is - a \( 1\)-dimensional cell, associated with planar \( x\)-monotone curve.

Halfedges are stored in doubly-connected lists and form chains. These chains define the inner and outer boundaries of connected components.

Creation
	Halfedge ()
	default constructor. More...

Access Functions
All non-const methods listed below also have const counterparts that return constant handles, iterators or circulators:
bool	is_fictitious () const
	returns whether the halfedge is fictitious (i.e., connects two vertices at infinity and is not associated with a valid curve). More...
Vertex_handle	source ()
	returns a handle for the source vertex of e. More...
Vertex_handle	target ()
	returns a handle for the target vertex of e. More...
Arr_halfedge_direction	direction () const
	returns the direction of the halfedge: ARR_LEFT_TO_RIGHT if e's source vertex is lexicographically smaller than it target (so the halfedge is directed from left to right), and ARR_RIGHT_TO_LEFT if it is lexicographically larger than the target (so the halfedge is directed from right to left). More...
Face_handle	face ()
	returns the face that e is incident to (The face lies to the left of e). More...
Halfedge_handle	twin ()
	returns the twin halfedge. More...
Halfedge_handle	prev ()
	returns e's predecessor in the connected component it belongs to. More...
Halfedge_handle	next ()
	returns e's successor in the connected component it belongs to. More...
Ccb_halfedge_circulator	ccb ()
	returns a circulator that allows traversing the halfedges of the connected component boundary (CCB) that contains e. More...
const Traits::X_monotone_curve_2 &	curve () const
	returns the \( x\)-monotone curve associated with e. More...

Constructor & Destructor Documentation

template<typename Traits , typename Dcel >

CGAL::Arrangement_2< Traits, Dcel >::Halfedge::Halfedge

(

)

default constructor.

Member Function Documentation

template<typename Traits , typename Dcel >

Ccb_halfedge_circulator CGAL::Arrangement_2< Traits, Dcel >::Halfedge::ccb

(

)

returns a circulator that allows traversing the halfedges of the connected component boundary (CCB) that contains e.

The circulator is initialized to point to e.

template<typename Traits , typename Dcel >

const Traits::X_monotone_curve_2& CGAL::Arrangement_2< Traits, Dcel >::Halfedge::curve

(

)

const

returns the \( x\)-monotone curve associated with e.

Precondition

e is not a fictitious halfedge.

template<typename Traits , typename Dcel >

Arr_halfedge_direction CGAL::Arrangement_2< Traits, Dcel >::Halfedge::direction

(

)

const

returns the direction of the halfedge: ARR_LEFT_TO_RIGHT if e's source vertex is lexicographically smaller than it target (so the halfedge is directed from left to right), and ARR_RIGHT_TO_LEFT if it is lexicographically larger than the target (so the halfedge is directed from right to left).

template<typename Traits , typename Dcel >

Face_handle CGAL::Arrangement_2< Traits, Dcel >::Halfedge::face

(

)

returns the face that e is incident to (The face lies to the left of e).

template<typename Traits , typename Dcel >

bool CGAL::Arrangement_2< Traits, Dcel >::Halfedge::is_fictitious

(

)

const

returns whether the halfedge is fictitious (i.e., connects two vertices at infinity and is not associated with a valid curve).

template<typename Traits , typename Dcel >

Halfedge_handle CGAL::Arrangement_2< Traits, Dcel >::Halfedge::next

(

)

returns e's successor in the connected component it belongs to.

template<typename Traits , typename Dcel >

Halfedge_handle CGAL::Arrangement_2< Traits, Dcel >::Halfedge::prev

(

)

returns e's predecessor in the connected component it belongs to.

template<typename Traits , typename Dcel >

Vertex_handle CGAL::Arrangement_2< Traits, Dcel >::Halfedge::source

(

)

returns a handle for the source vertex of e.

template<typename Traits , typename Dcel >

Vertex_handle CGAL::Arrangement_2< Traits, Dcel >::Halfedge::target

(

)

returns a handle for the target vertex of e.

template<typename Traits , typename Dcel >

Halfedge_handle CGAL::Arrangement_2< Traits, Dcel >::Halfedge::twin

(

)

returns the twin halfedge.