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

CGAL 4.3 - 2D Regularized Boolean Set-Operations

All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Groups Pages
List of all members
GeneralPolygonSetDcel Concept Reference
Concepts

## Definition

A doubly-connected edge-list (Dcel for short) data-structure. It consists of three containers of records: vertices \( V\), halfedges \( E\), and faces \( F\). It maintains the incidence relation among them. The halfedges are ordered in pairs sometimes referred to as twins, such that each halfedge pair represent an edge.

A model of the `GeneralPolygonSetDcel` concept must provide the following types and operations. (In addition to the requirements here, the local types `Vertex`,`Halfedge`, `Face`, `Hole`, and `Isolated_vertex` must be models of the concepts `ArrangementDcelVertex`, `ArrangementDcelHalfedge`, `GeneralPolygonSetDcelFace` , `ArrangementDcelHole`, and `ArrangementDcelIsolatedVertex` respectively.) Notice that this concept differs from the concept `ArrangemenDcel` only in the type `Face`.

Has Models:

  `CGAL::Arr_dcel_base<V,H,F>`

  `CGAL::Arr_default_dcel<Traits>`

  `CGAL::Arr_face_extended_dcel<Traits,FData,V,H,F>`

  `CGAL::Arr_extended_dcel<Traits,VData,HData,FData,V,H,F>`

See Also
  `ArrangementDcelVertex`
  `ArrangementDcelHalfedge`
  `GeneralPolygonSetDcelFace`
  `ArrangementDcelHole`
  `ArrangementDcelIsolatedVertex`

## Types
typedef unspecified_type | Vertex
| the vertex type.
typedef unspecified_type | Halfedge
| the halfedge type.
typedef unspecified_type | Face
| the face type.
typedef unspecified_type | Hole
| the hole type.
typedef unspecified_type | Isolated_vertex
| the isolated vertex type.
typedef unspecified_type | Size
| used to represent size values (e.g., `size_t`).

## Iterators
The non-mutable iterators `Vertex_const_iterator`, `Halfedge_const_iterator` and `Face_const_iterator` are also defined.
typedef unspecified_type | Vertex_iterator
| a bidirectional iterator over the vertices. More...
typedef unspecified_type | Halfedge_iterator
| a bidirectional iterator over the halfedges. More...
typedef unspecified_type | Face_iterator
| a bidirectional iterator over the faces. More...

## Creation
| Arr_dcel ()
| constructs an empty Dcel with one unbounded face.
Face * | assign (const Self &other, const Face *uf)
| assigns the contents of the `other` Dcel whose unbounded face is given by `uf`, to `dcel`. More...

## Access Functions
Size | size_of_vertices () const
| returns the number of vertices.
Size | size_of_halfedges () const
| returns the number of halfedges (always even).
Size | size_of_faces () const
| returns the number of faces.
Size | size_of_holes () const
| returns the number of holes (the number of connected components).
Size | size_of_isolated_vertices () const
| returns the number of isolated vertices.

## Iterator Access
The following operations have an equivalent `const` operations that return the corresponding non-mutable iterators:
Vertex_iterator | vertices_begin ()
| returns a begin-iterator of the vertices in `dcel`.
Vertex_iterator | vertices_end ()
| returns a past-the-end iterator of the vertices in `dcel`.
Halfedge_iterator | halfedges_begin ()
| returns a begin-iterator of the halfedges in `dcel`.
Halfedge_iterator | halfedges_end ()
| returns a past-the-end iterator of the halfedges in `dcel`.
Vertex_iterator | faces_begin ()
| returns a begin-iterator of the faces in `dcel`.
Vertex_iterator | faces_end ()
| returns a past-the-end iterator of the faces in `dcel`.

## Modifiers
The following operations allocate a new element of the respective type. Halfedges are always allocated in pairs of opposite halfedges. The halfedges and their opposite pointers are automatically set.
Vertex * | new_vertex ()
| creates a new vertex.
Halfedge * | new_edge ()
| creates a new pair of twin halfedges.
Face * | new_face ()
| creates a new face.
Hole * | new_hole ()
| creates a new hole record.
Isolated_vertex * | new_isolated_vertex ()
| creates a new isolated vertex record.
void | delete_vertex (Vertex *v)
| deletes the vertex `v`.
void | delete_edge (Halfedge *e)
| deletes the halfedge `e` as well as its twin.
void | delete_face (Face *f)
| deletes the face `f`.
void | delete_hole (Hole *ho)
| deletes the hole `ho`.
void | delete_isolated_vertex (Isolated_vertex *iv)
| deletes the isolated vertex `iv`.

## Member Typedef Documentation

typedef unspecified_type GeneralPolygonSetDcel::Face_iterator

a bidirectional iterator over the faces.

Its value-type is `Face`.

typedef unspecified_type GeneralPolygonSetDcel::Halfedge_iterator

a bidirectional iterator over the halfedges.

Its value-type is `Halfedge`.

typedef unspecified_type GeneralPolygonSetDcel::Vertex_iterator

a bidirectional iterator over the vertices.

Its value-type is `Vertex`.

## Member Function Documentation

Face* GeneralPolygonSetDcel::assign | ( | const Self & | other,
|  | const Face * | uf
| ) |  |

assigns the contents of the `other` Dcel whose unbounded face is given by `uf`, to `dcel`.

The function returns a pointer to the unbounded face of `dcel` after the assignment.