\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 2D Arrangements

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ArrangementDcelHalfedge Concept Reference
DCEL Concepts

## 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.

See Also
  `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.
Vertex * | vertex ()
| returns the target vertex.
Face * | face ()
| returns the incident face. More...
Hole * | hole ()
| 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_curve & | curve ()
| 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.

## Member Function Documentation

X_monotone_curve& ArrangementDcelHalfedge::curve | ( | ) |  |

returns the associated curve.

Precondition
  `e` is associated with a valid curve.

Face* ArrangementDcelHalfedge::face | ( | ) |  |

returns the incident face.

Precondition
  `e` lies on the outer boundary of this face.

Hole* ArrangementDcelHalfedge::hole | ( | ) |  |

returns the hole (inner CCB) `e` belongs to.

Precondition
  `e` lies on a hole inside its incident face.

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.

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.