NAME

       v.voronoi   -  Creates  a  Voronoi  diagram  in  current  region  from an input vector map
       containing points or centroids.

KEYWORDS

       vector, geometry, triangulation, skeleton

SYNOPSIS

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

   Flags:
       -a
           Create Voronoi diagram for input areas

       -s
           Extract skeletons for input areas

       -l
           Output tessellation as a graph (lines), not areas

       -t
           Do not create attribute table

       --overwrite
           Allow output files to overwrite existing files

       --help
           Print usage summary

       --verbose
           Verbose module output

       --quiet
           Quiet module output

       --ui
           Force launching GUI dialog

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

       layer=string
           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
           name.
           Default: -1

       output=name [required]
           Name for output vector map

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

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

DESCRIPTION

       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.

NOTES

       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
       with v.to.rast.

       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.

EXAMPLE

   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
       Result:
       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
       Result:
       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
       Result:
       Skeleton (blue) and center line (red) for urban areas in North Carolina

REFERENCES

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

SEE ALSO

        g.region, v.delaunay, v.hull

AUTHORS

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

       Last changed: $Date: 2015-05-22 17:06:44 +0200 (Fri, 22 May 2015) $

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