v.voronoi(1grass) GRASS GIS User's Manual v.voronoi(1grass)
NAME
v.voronoi - Creates a Voronoi diagram constrained to the extents of
the current region from an input vector map containing points or cen-
troids.
KEYWORDS
vector, geometry, triangulation, skeleton
SYNOPSIS
v.voronoi
v.voronoi --help
v.voronoi [-aslt] input=name [layer=string] output=name [smooth-
ness=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 skele-
tons of areas with thin >= 0. Smaller values for the thin option will
preserve more detail, while negative values will extract only the cen-
ter 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 mean-
time, skeletons and center lines can be simplified with the Dou-
glas-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)
Accessed: unknown
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GRASS 7.8.7 v.voronoi(1grass)
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