CGAL 5.3 - 2D Arrangements
ArrangementDcelHalfedge Concept Reference

## Definition

A halfedge record in a DCEL data structure. Two halfedges with opposite directions always form an edge (a halfedge pair). The halfedges form together chains, defining the boundaries of connected components, such that all halfedges along a chain have the same incident face. Note that the chain the halfedge belongs to may form the outer boundary of a bounded face (an outer CCB) or the boundary of a hole inside a face (an inner CCB).

An edge is always associated with a curve, but the halfedge records only store a pointer to the associated curve, and the actual curve objects are stored elsewhere. Two opposite halfedges are always associated with the same curve.

ArrangementDcel
ArrangementDcelVertex
ArrangementDcelFace
ArrangementDcelHole

## Types

typedef unspecified_type Vertex
the corresponding DCEL vertex type.

typedef unspecified_type Face
the corresponding DCEL face type.

typedef unspecified_type Hole
the corresponding DCEL hole type.

typedef unspecified_type X_monotone_curve
the curve type associated with the edge.

## Creation

Arr_dcel_halfedge ()
default constructor.

void assign (const Self &other)
assigns e with the contents of the other halfedge.

## Access Functions

Arr_halfedge_direction direction () const
returns ARR_LEFT_TO_RIGHT if e's source vertex is lexicographically smaller than it target, and ARR_RIGHT_TO_LEFT if it is lexicographically larger than the target.

bool is_on_hole () const
determines whether the e lies on an outer CCB of a bounded face, or on an inner CCB (a hole inside a face). More...

All functions below also have const counterparts, returning non-mutable pointers or references:

Halfedge * opposite ()
returns the twin halfedge.

Halfedge * prev ()
returns the previous halfedge along the chain.

Halfedge * next ()
returns the next halfedge along the chain.

Vertexvertex ()
returns the target vertex.

Faceface ()
returns the incident face. More...

Holehole ()
returns the hole (inner CCB) e belongs to. More...

bool has_null_curve () const
returns whether the vertex is not associated with a valid curve.

X_monotone_curvecurve ()
returns the associated curve. More...

## Modifiers

void set_opposite (Halfedge *opp)
sets the opposite halfedge.

void set_direction (Arr_halfedge_direction dir)
sets the lexicographical order between e's source and target vertices to be dir. More...

void set_prev (Halfedge *prev)
sets the previous halfedge of e along the chain, and updates the cross-pointer prev->next().

void set_next (Halfedge *next)
sets the next halfedge of e along the chain, and updates the cross-pointer next->prev().

void set_vertex (Vertex *v)
sets the target vertex.

void set_face (Face *f)
sets the incident face, marking that e lies on the outer CCB of the face f.

void set_hole (Hole *ho)
sets the incident hole, marking that e lies on an inner CCB.

void set_curve (X_monotone_curve *c)
sets the associated curve of e and its opposite halfedge.

## ◆ curve()

 X_monotone_curve& ArrangementDcelHalfedge::curve ( )

returns the associated curve.

Precondition
e is associated with a valid curve.

## ◆ face()

 Face* ArrangementDcelHalfedge::face ( )

returns the incident face.

Precondition
e lies on the outer boundary of this face.

## ◆ hole()

 Hole* ArrangementDcelHalfedge::hole ( )

returns the hole (inner CCB) e belongs to.

Precondition
e lies on a hole inside its incident face.

## ◆ is_on_hole()

 bool ArrangementDcelHalfedge::is_on_hole ( ) const

determines whether the e lies on an outer CCB of a bounded face, or on an inner CCB (a hole inside a face).

The function returns true if e lies on a hole.

## ◆ set_direction()

 void ArrangementDcelHalfedge::set_direction ( Arr_halfedge_direction dir )

sets the lexicographical order between e's source and target vertices to be dir.

The direction of the opposite halfedge is also set to the opposite direction.