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CGAL 4.8 - 2D Segment Delaunay Graphs

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2D Segment Delaunay Graphs Reference

##

Menelaos Karavelas
An algorithm for computing the dual of a Voronoi diagram of a set of segments under the Euclidean metric. It is a generalization of the standard Voronoi diagram for points. The algorithms provided are dynamic.

Introduced in: CGAL 3.1
Depends on: 2D Triangulation Data Structure
BibTeX: cgal:k-sdg2-16a
License: GPL
Windows Demo: 2D Segment Voronoi Diagram
Common Demo Dlls: dlls

CGAL provides the class `CGAL::Segment_Delaunay_graph_2<Gt,DS>` for computing the 2D Delaunay graph of segments and points. The two template parameters must be models of the `SegmentDelaunayGraphTraits_2` and `SegmentDelaunayGraphDataStructure_2` concepts. The first concept is related to the geometric objects and predicates associated with segment Delaunay graphs, whereas the second concept refers to the data structure used to represent the segment Delaunay graph, which is dual to the 2D Voronoi diagram of segments and points. The classes `CGAL::Segment_Delaunay_graph_traits_2<K,MTag>`, `CGAL::Segment_Delaunay_graph_traits_without_intersections_2<K,MTag>` `CGAL::Segment_Delaunay_graph_filtered_traits_2<K,MTag>` `CGAL::Segment_Delaunay_graph_filtered_traits_without_intersections_2<K,MTag>` are models of the `SegmentDelaunayGraphTraits_2` concept, whereas the class `CGAL::Triangulation_data_structure_2<Vb,Fb>` is a model of the `SegmentDelaunayGraphDataStructure_2` concept.

## Classified Reference Pages

## Concepts

- `SegmentDelaunayGraphSite_2`
- `SegmentDelaunayGraphStorageSite_2`
- `SegmentDelaunayGraphDataStructure_2`
- `SegmentDelaunayGraphVertexBase_2`
- `SegmentDelaunayGraphTraits_2`
- `SegmentDelaunayGraphHierarchyVertexBase_2`

## Classes

- `CGAL::Segment_Delaunay_graph_2<Gt,DS>`
- `CGAL::Segment_Delaunay_graph_site_2<K>`
- `CGAL::Segment_Delaunay_graph_storage_site_2<Gt>`
- `CGAL::Segment_Delaunay_graph_vertex_base_2<Gt,SSTag>`
- `CGAL::Segment_Delaunay_graph_traits_2<K,MTag>`
- `CGAL::Segment_Delaunay_graph_traits_without_intersections_2<K,MTag>`
- `CGAL::Segment_Delaunay_graph_filtered_traits_2<CK,CM,EK,EM,FK,FM>`
- `CGAL::Segment_Delaunay_graph_filtered_traits_without_intersections_2<CK,CM,EK,EM,FK,FM>`
- `CGAL::Segment_Delaunay_graph_hierarchy_2<Gt,STag,DS>`
- `CGAL::Segment_Delaunay_graph_hierarchy_vertex_base_2<Vbb>`

## Modules
| Concepts

## Classes
class | CGAL::Segment_Delaunay_graph_2< Gt, DS >
| The class `Segment_Delaunay_graph_2` represents the segment Delaunay graph (which is the dual graph of the 2D segment Voronoi diagram). More...
class | CGAL::Segment_Delaunay_graph_filtered_traits_2< CK, CM, EK, EM, FK, FM >
| The class `Segment_Delaunay_graph_filtered_traits_2` provides a model for the `SegmentDelaunayGraphTraits_2` concept. More...
class | CGAL::Segment_Delaunay_graph_filtered_traits_without_intersections_2< CK, CM, EK, EM, FK, FM >
| The class `Segment_Delaunay_graph_filtered_traits_without_intersections_2` provides a model for the `SegmentDelaunayGraphTraits_2` concept. More...
class | CGAL::Segment_Delaunay_graph_hierarchy_2< Gt, STag, DS >
| We provide an alternative to the class `Segment_Delaunay_graph_2<Gt,DS>` for the incremental construction of the segment Delaunay graph. More...
class | CGAL::Segment_Delaunay_graph_hierarchy_vertex_base_2< Vbb >
| The class `Segment_Delaunay_graph_hierarchy_vertex_base_2` provides a model for the `SegmentDelaunayGraphHierarchyVertexBase_2` concept, which is the vertex base required by the `Segment_Delaunay_graph_hierarchy_2<Gt,DS>` class. More...
class | CGAL::Segment_Delaunay_graph_site_2< K >
| The class `Segment_Delaunay_graph_site_2` is a model for the concept `SegmentDelaunayGraphSite_2`. More...
class | CGAL::Segment_Delaunay_graph_storage_site_2< Gt >
| The class `Segment_Delaunay_graph_storage_site_2` is a model for the concept `SegmentDelaunayGraphStorageSite_2`. More...
class | CGAL::Segment_Delaunay_graph_traits_2< K, MTag >
| The class `Segment_Delaunay_graph_traits_2` provides a model for the `SegmentDelaunayGraphTraits_2` concept. More...
class | CGAL::Segment_Delaunay_graph_traits_without_intersections_2< K, MTag >
| The class `Segment_Delaunay_graph_traits_without_intersections_2` provides a model for the `SegmentDelaunayGraphTraits_2` concept. More...
class | CGAL::Segment_Delaunay_graph_vertex_base_2< Gt, SSTag >
| The class `Segment_Delaunay_graph_vertex_base_2` provides a model for the `SegmentDelaunayGraphVertexBase_2` concept which is the vertex base required by the `SegmentDelaunayGraphDataStructure_2` concept. More...