GRASS GIS manual: v.voronoi

Note: A new GRASS GIS stable version has been released: GRASS GIS 7.4, available here.
Updated manual page: here

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
NOTES
EXAMPLE
REFERENCES
SEE ALSO
AUTHORS

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: