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CGAL 4.8 - 2D Apollonius Graphs (Delaunay Graphs of Disks)

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2D Apollonius Graphs (Delaunay Graphs of Disks) Reference

##

Menelaos Karavelas and Mariette Yvinec
Algorithms for computing the Apollonius graph in two dimensions. The Apollonius graph is the dual of the Apollonius diagram, also known as the additively weighted Voronoi diagram. The latter can be thought of as the Voronoi diagram of a set of disks under the Euclidean metric, and it is a generalization of the standard Voronoi diagram for points. The algorithms provided are dynamic.

Introduced in: CGAL 3.0
Depends on: 2D Triangulation Data Structure
BibTeX: cgal:ky-ag2-16a
License: GPL
Windows Demo: 2D Apollonius Graph
Common Demo Dlls: dlls

An Apollonius graph is the dual of the Apollonius diagram, also known as the additively weighted Voronoi diagram. It is essentially the Voronoi diagram of a set of disks, where the distance of a point of the plane from a disk is defined as the Euclidean distance of the point and the center of the circle, minus the radius of the disk.

CGAL provides the class `CGAL::Apollonius_graph_2<Gt,Agds>` for computing the 2D Apollonius graph. The two template parameters must be models of the `ApolloniusGraphTraits_2` and `ApolloniusGraphDataStructure_2` concepts. The first concept is related to the geometric objects and predicates associated with Apollonius graphs, whereas the second concept refers to the data structure used to represent the Apollonius graph. The classes `Apollonius_graph_traits_2<K,Method_tag>` and `Triangulation_data_structure_2<Vb,Fb>` are models of the aforementioned concepts.

## Classified Reference Pages

## Concepts

- `ApolloniusSite_2`
- `ApolloniusGraphDataStructure_2`
- `ApolloniusGraphVertexBase_2`
- `ApolloniusGraphTraits_2`
- `ApolloniusGraphHierarchyVertexBase_2`

## Classes

- `CGAL::Apollonius_graph_2<Gt,Agds>`
- `CGAL::Apollonius_site_2<K>`
- `CGAL::Apollonius_graph_vertex_base_2<Gt,StoreHidden>`
- `CGAL::Apollonius_graph_traits_2<K,Method_tag>`
- `CGAL::Apollonius_graph_filtered_traits_2<CK,CM,EK,EM,FK,FM>`
- `CGAL::Apollonius_graph_hierarchy_2<Gt,Agds>`
- `CGAL::Apollonius_graph_hierarchy_vertex_base_2<Agvb>`

## Modules
| Concepts

## Classes
class | CGAL::Apollonius_graph_2< Gt, Agds >
| The class `Apollonius_graph_2` represents the Apollonius graph. More...
class | CGAL::Apollonius_graph_filtered_traits_2< CK, CM, EK, EM, FK, FM >
| The class `Apollonius_graph_filtered_traits_2` provides a model for the `ApolloniusGraphTraits_2` concept. More...
class | CGAL::Apollonius_graph_hierarchy_2< Gt, Agds >
| We provide an alternative to the class `Apollonius_graph_2<Gt,Agds>` for the dynamic construction of the Apollonius graph. More...
class | CGAL::Apollonius_graph_hierarchy_vertex_base_2< Agvb >
| The class `Apollonius_graph_hierarchy_vertex_base_2` provides a model for the `ApolloniusGraphHierarchyVertexBase_2` concept, which is the vertex base required by the `Apollonius_graph_hierarchy_2<Gt,Agds>` class. More...
class | CGAL::Apollonius_graph_traits_2< K, Method_tag >
| The class `Apollonius_graph_traits_2` provides a model for the `ApolloniusGraphTraits_2` concept. More...
class | CGAL::Apollonius_graph_vertex_base_2< Gt, StoreHidden >
| The class `Apollonius_graph_vertex_base_2` provides a model for the `ApolloniusGraphVertexBase_2` concept which is the vertex base required by the `ApolloniusGraphDataStructure_2` concept. More...
class | CGAL::Apollonius_site_2< K >
| The class `Apollonius_site_2` is a model for the concept `ApolloniusSite_2`. More...