Volume of Voronoi cell (python)

Question

I'm using Scipy 0.13.0 in Python 2.7 to calculate a set of Voronoi cells in 3d. I need to get the volume of each cell for (de)weighting output of a proprietary simulation. Is there any simple way of doing this - surely it's a common problem or a common use of Voronoi cells but I can't find anything. The following code runs, and dumps everything that the scipy.spatial.Voronoi manual knows about.

from scipy.spatial import Voronoi
x=[0,1,0,1,0,1,0,1,0,1]
y=[0,0,1,1,2,2,3,3.5,4,4.5]
z=[0,0,0,0,0,1,1,1,1,1]
points=zip(x,y,z)
print points
vor=Voronoi(points)
print vor.regions
print vor.vertices
print vor.ridge_points
print vor.ridge_vertices
print vor.points
print vor.point_region

Answer 1

As was mentioned in comments, you can compute ConvexHull of each Voronoi cell. Since Voronoi cells are convex, you will get the proper volumes.

def voronoi_volumes(points):
    v = Voronoi(points)
    vol = np.zeros(v.npoints)
    for i, reg_num in enumerate(v.point_region):
        indices = v.regions[reg_num]
        if -1 in indices: # some regions can be opened
            vol[i] = np.inf
        else:
            vol[i] = ConvexHull(v.vertices[indices]).volume
    return vol

This method works in any dimensions