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       v.voronoi   -  Creates  a Voronoi diagram constrained to the extents of the current region
       from an input vector map containing points or centroids.


       vector, geometry, triangulation, skeleton


       v.voronoi --help
       v.voronoi   [-aslt]   input=name     [layer=string]     output=name     [smoothness=float]
       [thin=float]   [--overwrite]  [--help]  [--verbose]  [--quiet]  [--ui]

           Create Voronoi diagram for input areas

           Extract skeletons for input areas

           Output tessellation as a graph (lines), not areas

           Do not create attribute table

           Allow output files to overwrite existing files

           Print usage summary

           Verbose module output

           Quiet module output

           Force launching GUI dialog

       input=name [required]
           Name of input vector map
           Or data source for direct OGR access

           Layer number or name (’-1’ for all layers)
           A  single  vector  map  can  be  connected  to  multiple  database tables. This number
           determines which table to use. When used with direct OGR  access  this  is  the  layer
           Default: -1

       output=name [required]
           Name for output vector map

           Factor for output smoothness
           Applies  to  input  areas  only.  Smaller values produce smoother output but can cause
           numerical instability.
           Default: 0.25

           Maximum dangle length of skeletons
           Applies only to skeleton extraction. Default = -1 will extract the center line.
           Default: -1


       v.voronoi creates a Voronoi diagram (Thiessen polygons) from points or centroids.

       The bounds of the output map are limited by the current region (see g.region).

       The -a flag can be used to create a Voronoi diagram for areas.

       The -s flag can be used to extract the center line of areas or  skeletons  of  areas  with
       thin  >=  0.  Smaller values for the thin option will preserve more detail, while negative
       values will extract only the center line.


       Voronoi diagrams may be used for  nearest-neighbor  flood  filling.   Give  the  centroids
       attributes (start with v.db.addcolumn), then optionally convert the result to a raster map

       The extraction of skeletons and center lines with the -s flag is a brute  force  approach.
       Faster  and more accurate algorithms to extract skeletons from areas exist but are not yet
       implemented. In the meantime, skeletons and  center  lines  can  be  simplified  with  the
       Douglas-Peucker algorithm: v.generalize method=douglas.


   Voronoi diagram for points
       This example uses the hospitals in the North Carolina dataset.
       g.region -p raster=elev_state_500m
       v.voronoi input=hospitals output=hospitals_voronoi
       Voronoi diagram for hospitals in North Carolina

   Voronoi diagram for areas
       This example uses urban areas in the North Carolina dataset.
       g.region -p n=162500 s=80000 w=727000 e=846000 res=500
       v.voronoi input=urbanarea output=urbanarea_voronoi -a
       Voronoi diagram for urban areas in North Carolina

   Skeletons and center lines of areas
       This example uses urban areas in the North Carolina dataset.
       g.region -p n=161000 s=135500 w=768500 e=805500 res=500
       v.voronoi input=urbanarea output=urbanarea_centerline -s
       v.voronoi input=urbanarea output=urbanarea_skeleton -s thin=2000
       Skeleton (blue) and center line (red) for urban areas in North Carolina


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


        g.region, v.delaunay, v.hull


       James Darrell McCauley, Purdue University
       GRASS 5 update, improvements: Andrea Aime, Modena, Italy
       GRASS 5.7 update: Radim Blazek
       Markus Metz

       Last changed: $Date: 2015-06-08 09:20:07 +0200 (Mon, 08 Jun 2015) $


       Available at: v.voronoi source code (history)

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