CGAL 4.7 - 2D Segment Delaunay Graphs
SegmentDelaunayGraphDataStructure_2 Concept Reference

## Definition

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.

The join and split operations. Left to right: The vertex v is split into $$v_1$$ and $$v_2$$. The faces $$f$$ and $$g$$ are inserted after $$f_1$$ and $$f_2$$, respectively, in the counter-clockwise sense. The vertices $$v_1$$, $$v_2$$ and the faces $$f$$ and $$g$$ are returned as a boost tuple in that order. Right to left: The edge (f,i) is collapsed, and thus the vertices $$v_1$$ and $$v_2$$ are joined. The vertex v is returned.

We only describe the additional requirements with respect to the ApolloniusGraphDataStructure_2 concept.

Refines:
ApolloniusGraphDataStructure_2
Has Models:
CGAL::Triangulation_data_structure_2<Vb,Fb>
TriangulationDataStructure_2
ApolloniusGraphDataStructure_2
SegmentDelaunayGraphVertexBase_2
TriangulationFaceBase_2

## Modification

Vertex_handle join_vertices (Face_handle f, int i)
Joins the vertices that are endpoints of the edge (f,i). More...

boost::tuples::tuple
< Vertex_handle, Vertex_handle,
Face_handle, Face_handle
split_vertex (Vertex_handle v, Face_handle f1, Face_handle f2)
Splits the vertex v into two vertices v1 and v2. More...

## Member Function Documentation

 Vertex_handle SegmentDelaunayGraphDataStructure_2::join_vertices ( Face_handle f, int i )

Joins the vertices that are endpoints of the edge (f,i).

It returns a vertex handle to common vertex.

 boost::tuples::tuple SegmentDelaunayGraphDataStructure_2::split_vertex ( Vertex_handle v, Face_handle f1, Face_handle f2 )

Splits the vertex v into two vertices v1 and v2.

The common faces f and g of v1 and v2 are created after (in the counter-clockwise sense) the faces f1 and f2. The 4-tuple (v1,v2,f,g) is returned (see Fig. figsdgdssplitjoin).