Colorized Voronoi diagram with Scipy, in 2D, including infinite regions

colorized_voronoi.py

import numpy as np
import matplotlib.pyplot as plt
from scipy.spatial import Voronoi

def voronoi_finite_polygons_2d(vor, radius=None):
    """
    Reconstruct infinite voronoi regions in a 2D diagram to finite
    regions.

    Parameters
    ----------
    vor : Voronoi
        Input diagram
    radius : float, optional
        Distance to 'points at infinity'.

    Returns
    -------
    regions : list of tuples
        Indices of vertices in each revised Voronoi regions.
    vertices : list of tuples
        Coordinates for revised Voronoi vertices. Same as coordinates
        of input vertices, with 'points at infinity' appended to the
        end.

    """

    if vor.points.shape[1] != 2:
        raise ValueError("Requires 2D input")

    new_regions = []
    new_vertices = vor.vertices.tolist()

    center = vor.points.mean(axis=0)
    if radius is None:
        radius = vor.points.ptp().max()*2

    # Construct a map containing all ridges for a given point
    all_ridges = {}
    for (p1, p2), (v1, v2) in zip(vor.ridge_points, vor.ridge_vertices):
        all_ridges.setdefault(p1, []).append((p2, v1, v2))
        all_ridges.setdefault(p2, []).append((p1, v1, v2))

    # Reconstruct infinite regions
    for p1, region in enumerate(vor.point_region):
        vertices = vor.regions[region]

        if all(v >= 0 for v in vertices):
            # finite region
            new_regions.append(vertices)
            continue

        # reconstruct a non-finite region
        ridges = all_ridges[p1]
        new_region = [v for v in vertices if v >= 0]

        for p2, v1, v2 in ridges:
            if v2 < 0:
                v1, v2 = v2, v1
            if v1 >= 0:
                # finite ridge: already in the region
                continue

            # Compute the missing endpoint of an infinite ridge

            t = vor.points[p2] - vor.points[p1] # tangent
            t /= np.linalg.norm(t)
            n = np.array([-t[1], t[0]])  # normal

            midpoint = vor.points[[p1, p2]].mean(axis=0)
            direction = np.sign(np.dot(midpoint - center, n)) * n
            far_point = vor.vertices[v2] + direction * radius

            new_region.append(len(new_vertices))
            new_vertices.append(far_point.tolist())

        # sort region counterclockwise
        vs = np.asarray([new_vertices[v] for v in new_region])
        c = vs.mean(axis=0)
        angles = np.arctan2(vs[:,1] - c[1], vs[:,0] - c[0])
        new_region = np.array(new_region)[np.argsort(angles)]

        # finish
        new_regions.append(new_region.tolist())

    return new_regions, np.asarray(new_vertices)

# make up data points
np.random.seed(1234)
points = np.random.rand(15, 2)

# compute Voronoi tesselation
vor = Voronoi(points)

# plot
regions, vertices = voronoi_finite_polygons_2d(vor)
print "--"
print regions
print "--"
print vertices

# colorize
for region in regions:
    polygon = vertices[region]
    plt.fill(*zip(*polygon), alpha=0.4)

plt.plot(points[:,0], points[:,1], 'ko')
plt.axis('equal')
plt.xlim(vor.min_bound[0] - 0.1, vor.max_bound[0] + 0.1)
plt.ylim(vor.min_bound[1] - 0.1, vor.max_bound[1] + 0.1)

plt.savefig('voro.png')
plt.show()

and edge_project is a function projecting points back on the boundary of shape using numerical gradient

def edge_project(pts, fd, h0=1.0):
    """
    project points back on the boundary (where fd=0) using numerical gradient

    note : you should specify h0 according to your actual mesh size
    """
    deps = sqrt(np.finfo(float).eps)*h0
    d = fd(pts)
    dgradx = (fd(pts + [deps, 0]) - d) / deps
    dgrady = (fd(pts + [0, deps]) - d) / deps
    dgrad2 = dgradx**2 + dgrady**2
    dgrad2[dgrad2 == 0] = 1.
    # calculate gradient vector (minus)
    pgrad = np.vstack([d*dgradx/dgrad2, d*dgrady/dgrad2]).T
    return pgrad

The procedure voronoi_finite_polygons_2d creates remote points, but it creates duplicate remote points.
For example:

35 [-0.60794158 -0.24345993]
36 [-3.41872139 -0.21721891]
37 [-3.41872139 -0.21721891]
38 [-0.99550093 0.83040914]

p36 and p37 are the same.

p37 belongs to polygon 8:
8 [37, 11, 1, 5, 7, 38]

p36 belongs to polygon 6:
6 [11, 36, 35, 9, 10]

Because they also share p11, in reality polygon 6 & 8 are adjacent. However, this point is missed and this influences the coloring !
Would it be possible to run the procedure with a parameter to "merge" common points together ?

I agree with @geertn444, the code generates duplicate points.