.TH VORONOI 7 .SH NAME voronoi - compute Voronoi diagram or Delaunay triangulation .SH SYNOPSIS .B voronoi [ .B -s -t -p ] .SH DESCRIPTION .I Voronoi reads the standard input 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. .PP If option .B -t is present, the Delaunay triangulation is produced. Each output line is a triple .I i j k, which are the indices of the three points in a Delaunay triangle. Points are numbered starting at 0. .PP If option .B -t is not present, the Voronoi diagram is produced. There are four output record types. .TP .I s a b indicates that an input point at coordinates .I a b was seen. .TP .I l a b c indicates a line with equation .I ax + by = c. .TP .I v a b indicates a vertex at .I a b. .TP .I e l v1 v2 indicates a Voronoi segment which is a subsegment of line number .I l with endpoints numbered .I v1 and .I v2. If .I v1 or .I v2 is -1, the line extends to infinity. .PP The other options are: .TP .B s The input is sorted by .I y coordinate (the second number in the pair). The first input line should be .I npoints xmin xmax ymin ymax. This describes the number of points and the range of the points. This line is used to determine internal hash table size; it need not be exact but performance suffers if it is grossly wrong. .TP .B p Produce output suitable for input to .I plot (1), rather than the forms described above. .PP On unsorted data uniformly distributed in the unit square, .I voronoi uses about .I 20n+140\(srn bytes of storage. On sorted data, .I voronoi uses about .I 160\(srn bytes. .SH AUTHOR Steve J. Fortune (1987) A Sweepline Algorithm for Voronoi Diagrams, Algorithmica 2, 153-174. .SH DIAGNOSTICS Insufficient memory. .SH BUGS The sort used by .I voronoi is much faster than .I sort (1). Also .I sort (1) does not correctly sort real data with embedded exponent fields. Very strange output results if .B -s is used on unsorted data. Binary input-output would probably halve execution time.
