CGAL 4.7 - 2D Apollonius Graphs (Delaunay Graphs of Disks): 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 Apollonius Graphs (Delaunay Graphs of Disks)

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2D Apollonius Graphs (Delaunay Graphs of Disks) Reference

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## Concepts

concept | ApolloniusGraphDataStructure_2

The concept `ApolloniusGraphDataStructure_2` refines the concept `TriangulationDataStructure_2`. In addition it provides two methods for the insertion and removal of a degree 2 vertex in the data structure. The insertion method adds a new vertex to the specified edge, thus creating two new edges. Moreover, it creates two new faces that have the two newly created edges in common (see figure below). The removal method performs the reverse operation. More...

concept | ApolloniusGraphHierarchyVertexBase_2

The vertex of an Apollonius graph included in an Apollonius graph hierarchy has to provide some pointers to the corresponding vertices in the graphs of the next and preceding levels. Therefore, the concept `ApolloniusGraphHierarchyVertexBase_2` refines the concept `ApolloniusGraphVertexBase_2`, by adding two vertex handles to the corresponding vertices for the next and previous level graphs. More...

concept | ApolloniusGraphTraits_2

The concept `ApolloniusGraphTraits_2` provides the traits requirements for the `Apollonius_graph_2` class. In particular, it provides a type `Site_2`, which must be a model of the concept `ApolloniusSite_2`. It also provides constructions for sites and several function object types for the predicates. More...

concept | ApolloniusGraphVertexBase_2

The concept `ApolloniusGraphVertexBase_2` describes the requirements for the vertex base class of the `ApolloniusGraphDataStructure_2` concept. A vertex stores an Apollonius site and provides access to one of its incident faces through a `Face_handle`. In addition, it maintains a container of sites. The container stores the hidden sites related to the vertex. More...

concept | ApolloniusSite_2
| The concept `ApolloniusSite_2` provides the requirements for an Apollonius site class. More...