\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.5.1 - 2D Arrangements
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CGAL::Arrangement_2< Traits, Dcel >::Halfedge Class Reference
DCEL

#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.
 

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).
 
Vertex_handle source ()
 returns a handle for the source vertex of e.
 
Vertex_handle target ()
 returns a handle for the target vertex of e.
 
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).
 
Face_handle face ()
 returns the face that e is incident to (The face lies to the left of e).
 
Halfedge_handle twin ()
 returns the twin halfedge.
 
Halfedge_handle prev ()
 returns e's predecessor in the connected component it belongs to.
 
Halfedge_handle next ()
 returns e's successor in the connected component it belongs to.
 
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...
 

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.