如果我有细胞的坐标，如何找到 voronoi 细胞的种子？

Question

I want to calculate the distance between the vertex of the voronoi cell and the seed of that particular cell. However I have not been able to figure out how I can get the seed coordinate for that particular cell. I have given my code here which generates an array of cell coordinates. Could anyone tell me how I can find the corresponding seed for the particular cell?

import numpy as np
import freud
import matplotlib
import matplotlib.pyplot as plt
import freud.box
import matplotlib.pyplot as plt

points = np.array([
    [-2, 2, 0],
    [2, 4, 0],
    [-2, 3, 0],
    [3, 5, 0]])

box = freud.box.Box(10,12, is2D= True )
voro = freud.locality.Voronoi()
cells= voro.compute((box, points)).polytopes
print(cells)
plt.figure()
ax = plt.gca()
ax.scatter(points[:, 0], points[:, 1], c= 'k')
voro.plot(ax=ax)
plt.show()

The output of this code is the plot below and the print(cells) prints the coordinates of the cells vertices as show below.

[array([[-6.46875   , -1.40625   ,  0.        ],
       [-2.7       , -3.5       ,  0.        ],
       [-1.3       , -3.5       ,  0.        ],
       [ 2.26086957, -1.52173913,  0.        ],
       [ 0.25      ,  2.5       ,  0.        ],
       [-5.1       ,  2.5       ,  0.        ],
       [-5.25      ,  2.25      ,  0.        ]]), array([[ 0.25      ,  2.5       ,  0.        ],
       [ 2.26086957, -1.52173913,  0.        ],
       [ 3.53125   , -1.40625   ,  0.        ],
       [ 4.75      ,  2.25      ,  0.        ],
       [-1.16666667,  8.16666667,  0.        ]]), array([[-5.1       ,  2.5       ,  0.        ],
       [ 0.25      ,  2.5       ,  0.        ],
       [-1.16666667,  8.16666667,  0.        ],
       [-1.3       ,  8.5       ,  0.        ],
       [-2.7       ,  8.5       ,  0.        ]]), array([[ 4.75      ,  2.25      ,  0.        ],
       [ 4.9       ,  2.5       ,  0.        ],
       [ 7.3       ,  8.5       ,  0.        ],
       [ 3.53125   , 10.59375   ,  0.        ],
       [ 2.26086957, 10.47826087,  0.        ],
       [-1.3       ,  8.5       ,  0.        ],
       [-1.16666667,  8.16666667,  0.        ]])]

I want to calculate the vertex to seed distance for each of the cell as indicated by the lines in the figure.

Answer 1

Here is an example using scipy.spatial.Voronoi:

import numpy as np
import matplotlib
import matplotlib.pyplot as plt
from scipy.spatial import Voronoi, voronoi_plot_2d

points = np.array([
    [-2, 2],
    [2, 4],
    [1, 3],
    [-2, 3],
    [3, 5],
    [-1, 5],
    [2, 1]]
    )

vor = Voronoi(points)

print("Coordinates of point 2:")
print(vor.points[2])

print("Region for point 2:")
print(vor.point_region[2])

print("Vertices for region:")
print(vor.regions[vor.point_region[2]])

print("Coordinates of Voronoi vertices:")
print(vor.vertices[vor.regions[vor.point_region[2]]])

for vert in vor.vertices[vor.regions[vor.point_region[2]]]:
    distance = np.linalg.norm(vor.points[2]-vert)
    print("Distance between " + str(vor.points[2]) + " and " + str(vert) + " is " + str(distance))

fig = voronoi_plot_2d(vor)

plt.gca().set_aspect('equal')

plt.show()

Output running the code is:

Coordinates of point 2:
[1. 3.]
Region for point 2:
4
Vertices for region:
[6, 4, 2, 0, 5]
Coordinates of Voronoi vertices:
[[-0.5         3.5       ]
 [ 0.5         4.5       ]
 [ 2.5         2.5       ]
 [-0.07142857  1.21428571]
 [-0.5         2.5       ]]
Distance between [1. 3.] and [-0.5  3.5] is 1.5811388300841898
Distance between [1. 3.] and [0.5 4.5] is 1.5811388300841898
Distance between [1. 3.] and [2.5 2.5] is 1.5811388300841898
Distance between [1. 3.] and [-0.07142857  1.21428571] is 2.0824828195876073
Distance between [1. 3.] and [-0.5  2.5] is 1.5811388300841898

The Voronoi diagram produced contains a few data structures to traverse to associate the seed point with the Voronoi vertices of the cell. Specifically:

1. point_region converts the point (seed) index to the associated index in the regions array
2. regions contains a list of indices of the Voronoi vertices for a given cell
3. vertices contains the coordinates of the vertices of the Voronoi cells

In the code above, the Voronoi diagram shown below is computed and the distances between the seed point and vertices are computed for the Voronoi cell in the center of the diagram.