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v.voronoi(1) Grass User's Manual v.voronoi(1)

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

-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

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

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 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.

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

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

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

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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© 2003-2018 GRASS Development Team, GRASS GIS 7.4.3 Reference Manual
GRASS 7.4.3

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