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  2.3 Fortune's algorithm



Up to now, we have met all fundamental parts of Fortune's method and so we can think about an implementation. However, let us say just a word about termination condition. When all points are behind the scanning line and all events have been handled, Voronoi diagram is not fully constructed yet. We have to construct the remaining half-lines. For this purpose, the whole diagram is surrounded by a box (Figure 6) on which border all half-edges terminate.

Figure 6: Completely defined computer represented Voronoi diagram does not contain any half-edges

The following algorithm summaries the consideration done up to now and shows the core of the Fortune's method.

VORONOI_DIAGRAM(P)
Input:  A set P of point sites in the plane
Output:  The Voronoi diagram Vor(P) given inside a bounding box
in a doubly-connected edge list structure 
{ 
  Initialize the event tree Q with all point events
  while Q is not empty do
  { 
    Consider the event with largest y-coordinate in Q 
    if the event is a point event, occurring at site pi 
    then HANDLE_POINT_EVENT(pi)
    else HANDLE_CIRCLE_EVENT() 
    Remove the event from Q 
  } 
  Put Voronoi diagram into a box
}