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

The library is able to generate ordered list of coordinates, you just need to make use of the index lists provided:

import numpy as np
from scipy.spatial import Voronoi

...

ids = np.array(my_points_list)
vor = Voronoi(points)
polygons = {}
for id, region_index in enumerate(vor.point_region):
    points = []
    for vertex_index in vor.regions[region_index]:
        if vertex_index != -1:  # the library uses this for infinity
            points.append(list(vor.vertices[vertex_index]))
    points.append(points[0])
    polygons[id]=points

each polygon in the polygons dictionary can be exported to geojson or brought into shapely and I was able to render them properly in QGIS

Answer 2

As others have said, it is because you have to rebuild the polygons from the resulting points correctly based on indexes. Although you have the solution, I thought I should mention there is also another pypi supported tesselation package called Pytess (Disclaimer: I am the package maintainer) where the voronoi function returns the voronoi polygons fully built for you.

Answer 3

The function you implemented (order_vertices() ), cannot work in your case, because it simply takes a already ordered sequence of coordinates, which builds a rectangle, and inverts the direction of the polygon (and maybe works only with rectangles...). But you have a not ordered sequence of coordinates

Generally speaking, you can not build a polygon from a arbitrary sequence of not ordered vertices because there is no a unique solution for concave polygons, as showed in this example: https://stackoverflow.com/a/7408711/4313133

However, if you are sure that your polygons are always convex, you can build a convex hull with this code: https://stackoverflow.com/a/15945375/4313133 (tested right now, it worked for me)

Probably you can build the convex hull with scipy as well, but I dint test it: scipy.spatial.ConvexHull

Answer 4

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)))