geopandas.GeoSeries.voronoi_polygons

GeoSeries.voronoi_polygons(tolerance=0.0, extend_to=None, only_edges=False)

Returns a GeoSeries consisting of objects representing the computed Voronoi diagram around the vertices of an input geometry.

All geometries within the GeoSeries are considered together within a single Voronoi diagram. The resulting geometries therefore do not necessarily map 1:1 to input geometries. Note that each vertex of a geometry is considered a site for the Voronoi diagram, so the diagram will be constructed around the vertices of each geometry.

Parameters:

tolerancefloat, default 0.0

Snap input vertices together if their distance is less than this value.

extend_toshapely.Geometry, default None

If set, the Voronoi diagram will be extended to cover the envelope of this geometry (unless this envelope is smaller than the input geometry).

only_edgesbool (optional, default False)

If set to True, the diagram will return LineStrings instead of Polygons.

See also

GeoSeries.delaunay_triangles

Delaunay triangulation around vertices

Notes

The order of polygons in the output currently does not correspond to the order of input vertices.

If you want to generate a Voronoi diagram for each geometry separately, use shapely.voronoi_polygons() instead.

Examples

The most common use case is to generate polygons representing the Voronoi diagram around a set of points:

>>> from shapely import LineString, MultiPoint, Point, Polygon
>>> s = geopandas.GeoSeries(
...     [
...         Point(1, 1),
...         Point(2, 2),
...         Point(1, 3),
...         Point(0, 2),
...     ]
... )
>>> s
0    POINT (1 1)
1    POINT (2 2)
2    POINT (1 3)
3    POINT (0 2)
dtype: geometry

By default, you get back a GeoSeries of polygons:

>>> s.voronoi_polygons()
0     POLYGON ((-2 5, 1 2, -2 -1, -2 5))
1        POLYGON ((4 5, 1 2, -2 5, 4 5))
2    POLYGON ((-2 -1, 1 2, 4 -1, -2 -1))
3       POLYGON ((4 -1, 1 2, 4 5, 4 -1))
dtype: geometry

If you set only_edges to True, you get back LineStrings representing the edges of the Voronoi diagram:

>>> s.voronoi_polygons(only_edges=True)
0     LINESTRING (-2 5, 1 2)
1    LINESTRING (1 2, -2 -1)
2      LINESTRING (4 5, 1 2)
3     LINESTRING (1 2, 4 -1)
dtype: geometry

You can also extend each diagram to a given geometry:

>>> limit = Polygon([(-10, -10), (0, 15), (15, 15), (15, 0)])
>>> s.voronoi_polygons(extend_to=limit)
0              POLYGON ((-10 13, 1 2, -10 -9, -10 13))
1    POLYGON ((15 15, 15 -10, 13 -10, 1 2, 14 15, 1...
2    POLYGON ((-10 -10, -10 -9, 1 2, 13 -10, -10 -10))
3       POLYGON ((-10 15, 14 15, 1 2, -10 13, -10 15))
dtype: geometry

The method supports any geometry type but keep in mind that the underlying algorithm is based on the vertices of the input geometries only and does not consider edge segments between vertices.

>>> s2 = geopandas.GeoSeries(
...     [
...         Polygon([(0, 0), (1, 1), (0, 1)]),
...         LineString([(1, 0), (2, 1), (1, 2)]),
...         MultiPoint([(2, 3), (2, 0), (3, 1)]),
...     ]
... )
>>> s2
0      POLYGON ((0 0, 1 1, 0 1, 0 0))
1          LINESTRING (1 0, 2 1, 1 2)
2    MULTIPOINT ((2 3), (2 0), (3 1))
dtype: geometry

>>> s2.voronoi_polygons()
0    POLYGON ((1.5 1.5, 1.5 0.5, 0.5 0.5, 0.5 1.5, ...
1    POLYGON ((1.5 0.5, 1.5 1.5, 2 2, 2.5 2, 2.5 0....
2    POLYGON ((-3 -3, -3 0.5, 0.5 0.5, 0.5 -3, -3 -3))
3    POLYGON ((0.5 -3, 0.5 0.5, 1.5 0.5, 1.5 -3, 0....
4     POLYGON ((-3 5, 0.5 1.5, 0.5 0.5, -3 0.5, -3 5))
5    POLYGON ((-3 6, -2 6, 2 2, 1.5 1.5, 0.5 1.5, -...
6    POLYGON ((1.5 -3, 1.5 0.5, 2.5 0.5, 6 -3, 1.5 ...
7       POLYGON ((6 6, 6 3.75, 2.5 2, 2 2, -2 6, 6 6))
8       POLYGON ((6 -3, 2.5 0.5, 2.5 2, 6 3.75, 6 -3))
dtype: geometry