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voronoi - compute Voronoi diagram or Delaunay triangulation

voronoi [-t -p -d]  [filename]

Voronoi reads from filename (or standard input if no filename given) for a set 
of points in the plane and writes either the Voronoi diagram or the Delaunay 
triangulation to the standard output.  Each input line should consist of two 
real numbers, separated by white space.

If option -t is present, the Delaunay triangulation is produced. 
Each output line is a triple i j k, which are the indices of the three points
in a Delaunay triangle. Points are numbered starting at 0.

If option -t is not present, the Voronoi diagram is produced.  
There are four output record types.

s a b      indicates that an input point at coordinates a b was seen.
l a b c    indicates a line with equation ax + by = c.
v a b      indicates a vertex at a b.
e l v1 v2  indicates a Voronoi segment which is a subsegment of line number l
           with endpoints numbered v1 and v2.  If v1 or v2 is -1, the line 
           extends to infinity.

Other options include:

d    Print debugging info

p    Produce output suitable for input to plot (1), rather than the forms 
     described above.

On unsorted data uniformly distributed in the unit square, voronoi uses about 
20n+140 bytes of storage.

AUTHOR
Steve J. Fortune (1987) A Sweepline Algorithm for Voronoi Diagrams,
Algorithmica 2, 153-174.
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