CGAL 5.0 - 2D Apollonius Graphs (Delaunay Graphs of Disks)
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.
(f,i)is replaced by two edges by means of inserting a vertex
von the edge. The faces \( f_1\) and \( f_2\) are created. Right to left: the faces \( f_1\) and \( f_2\) are destroyed. The vertex
vis deleted and its two adjacent edges are merged.
We only describe the additional requirements with respect to the
|Vertex_handle||insert_degree_2 (Face_handle f, int i)|
|Inserts a degree two vertex and two faces adjacent to it that have two common edges. More...|
|void||remove_degree_2 (Vertex_handle v)|
|Removes a degree 2 vertex and the two faces adjacent to it. More...|
Inserts a degree two vertex and two faces adjacent to it that have two common edges.
The edge defined by the face handle
f and the integer
i is duplicated. It returns a handle to the vertex created.
Removes a degree 2 vertex and the two faces adjacent to it.
The two edges of the star of
v that are not incident to it are collapsed.
vmust be equal to 2.