NAME

       v.voronoi   -  Creates  a  Voronoi diagram constrained to the extents of the 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 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

       v.voronoi suffers from numerical instability, results can sometimes contain many artefacts. When creating
       Voronoi diagrams for areas or skeletons for areas, it is highly recommended to simplify the  areas  first
       with v.generalize.

       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

SOURCE CODE

       Available at: v.voronoi source code (history)

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       © 2003-2019 GRASS Development Team, GRASS GIS 7.8.2 Reference Manual