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

CGAL 4.8 - 2D Segment Delaunay Graphs

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2D Segment Delaunay Graphs Reference

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## Concepts
concept | SegmentDelaunayGraphDataStructure_2
| The concept `SegmentDelaunayGraphDataStructure_2` refines the concept `ApolloniusGraphDataStructure_2`. In addition it provides two methods for the merging of two vertices joined by an edge of the data structure, and the splitting of a vertex into two. The method that merges two vertices, called `join_vertices()` identifies the two vertices and deletes their common two faces. The method that splits a vertex, called `split_vertex()` introduces a new vertex that shares an edge and two faces with the old vertex (see figure below). Notice that the `join_vertices()` and `split_vertex()` operations are complementary, in the sense that one reverses the action of the other. More...
concept | SegmentDelaunayGraphHierarchyVertexBase_2
| The vertex of a segment Delaunay graph included in a segment Delaunay graph hierarchy has to provide some pointers to the corresponding vertices in the graphs of the next and preceeding levels. Therefore, the concept `SegmentDelaunayGraphHierarchyVertexBase_2` refines the concept `SegmentDelaunayGraphVertexBase_2`, by adding two vertex handles to the correponding vertices for the next and previous level graphs. More...
concept | SegmentDelaunayGraphSite_2
| The concept `SegmentDelaunayGraphSite_2` provides the requirements for the sites of a segment Delaunay graph. More...
concept | SegmentDelaunayGraphStorageSite_2
| The concept `SegmentDelaunayGraphStorageSite_2` provides the requirements for the storage sites of a segment Delaunay graph. The storage sites are sites that are used to store the information of a site in a more compact form (that uses less storage). This is achieved by storing handles to points instead of points. More...
concept | SegmentDelaunayGraphTraits_2
| The concept `SegmentDelaunayGraphTraits_2` provides the traits requirements for the `CGAL::Segment_Delaunay_graph_2<Gt,DS>` and `CGAL::Segment_Delaunay_graph_hierarchy_2<Gt,STag,DS>` classes. In particular, it provides a type `Site_2`, which must be a model of the concept `SegmentDelaunayGraphSite_2`. It also provides constructions for sites and several function object types for the predicates. More...
concept | SegmentDelaunayGraphVertexBase_2
| The concept `SegmentDelaunayGraphVertexBase_2` describes the requirements for the vertex base class of the `SegmentDelaunayGraphDataStructure_2` concept. A vertex stores a site of the segment Delaunay graph and provides access to one of its incident faces through a `Face_handle`. More...