From Voronoi tessellation to Shapely polygons

Question

from a set of points I built the Voronoi tessellation using scipy:

from scipy.spatial import Voronoi
vor = Voronoi(points)

Now I would like

Answer 1

If you're just after a collection of polygons you don't need to pre-order the point to build them.

The scipy.spatial.Voronoi object has a ridge_vertices attribute containing indices of vertices forming the lines of the Voronoi ridge. If the index is -1 then the ridge goes to infinity.

First start with some random points to build the Voronoi object.

import numpy as np
from scipy.spatial import Voronoi, voronoi_plot_2d
import shapely.geometry
import shapely.ops

points = np.random.random((10, 2))
vor = Voronoi(points)
voronoi_plot_2d(vor)

You can use this to build a collection of Shapely LineString objects.

lines = [
    shapely.geometry.LineString(vor.vertices[line])
    for line in vor.ridge_vertices
    if -1 not in line
]

The shapely.ops module has a polygonize that returns a generator for Shapely Polygon objects.

for poly in shapely.ops.polygonize(lines):
    #do something with each polygon

Or if you wanted a single polygon formed from the region enclosed by the Voronoi tesselation you can use the Shapely unary_union method:

shapely.ops.unary_union(list(shapely.ops.polygonize(lines)))