## 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

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