CGAL 4.7 - 2D Arrangements: DCEL Concepts

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

CGAL 4.7 - 2D Arrangements

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DCEL Concepts
Concepts

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## Concepts

concept | ArrangementDcel

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. More...

concept | ArrangementDcelFace
| A face record in a Dcel data structure. A face may either be unbounded, otherwise it has an incident halfedge along the chain defining its outer boundary. A face may also contain holes and isolated vertices in its interior. More...
concept | ArrangementDcelHalfedge

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). More...

concept | ArrangementDcelHole
| A hole record in a Dcel data structure, which stores the face that contains the hole in its interior, along with an iterator for the hole in the holes' container of this face. More...
concept | ArrangementDcelIsolatedVertex
| An isolated vertex-information record in a Dcel data structure, which stores the face that contains the isolated vertex in its interior, along with an iterator for the isolated vertex in the isolated vertices' container of this face. More...
concept | ArrangementDcelVertex
| A vertex record in a Dcel data structure. A vertex is always associated with a point. However, the vertex record only stores a pointer to the associated point, and the actual `Point` object is stored elsewhere. More...
concept | ArrangementDcelWithRebind
| The concept `ArrangementDcelWithRebind` refines the `ArrangementDcel` concept by adding a policy clone idiom in form of a rebind struct-template. More...