我想计算（封闭的）Voronoi单元的体积。有一些点对应于不重叠的球心，并且在半径为100、高度为100的圆柱体内具有50%的填充分数。这些点可以被找到here。
使用spicy.spatial可以很容易地生成Voronoi单元格。当区域中包含-1时，意味着它是开放的，因此我无法真正计算单元格的体积（可以吗？），因此将其设置为0。否则，使用ConvexHull，可以计算多面体的体积。这是通过以下脚本完成的：

from scipy.spatial import Voronoi, ConvexHull
import numpy as np

# These geometrical values were verified

radius_spheres = 6
radius_cylinder = 100
height_cylinder = 100

# Read positions file

points = np.genfromtxt('test_pos.txt', delimiter=',')
number_spheres = points.shape[0]

# Calculate total volume of the spheres

volume_spheres_total = 4/3*np.pi*radius_spheres**3 * number_spheres

# Calculate real cylinder volume

volume_cylinder = np.pi*(radius_cylinder**2)*height_cylinder

# Calculate Voronoi cells volumes

v = Voronoi(points)
volume_Voronoi = np.zeros(v.npoints)
for idx, i_region in enumerate(v.point_region):
    # Open cells are removed from the calculation of the total volume
    if -1 not in v.regions[i_region]:
        volume_Voronoi[idx] = ConvexHull(v.vertices[v.regions[i_region]]).volume

volume_Voronoi_total = sum(volume_Voronoi)

# Analyze distribution of Voronoi volume values

counts, values = np.histogram(volume_Voronoi, bins=np.logspace(np.log10(np.min(volume_Voronoi[volume_Voronoi!=0])), np.log10(np.max(volume_Voronoi)), 10))

# Calculate theorical and Voronoi packing fraction

packing_fraction_theoretical = volume_spheres_total/volume_cylinder
packing_fraction_Voronoi = volume_spheres_total/volume_Voronoi_total

通过这种实现，我希望Voronoi单元的总体积大致等于球体所在的圆柱体的体积。由于未考虑开放单元，因此该值甚至可能被低估。但是，当打印结果时，请使用：

# Summarize

print('Total volume of the spheres: {:.0f}\n'.format(volume_spheres_total))

print('Volume of the cylinder: {:.0f}'.format(volume_cylinder))
print('-> Theoretical packing fraction: {:.0f}%\n'.format(packing_fraction_theoretical*100))

print('Total volume of the (closed) Voronoi cells: {:.0f}'.format(volume_Voronoi_total))
print('Difference between Voronoi volume and cylinder volume: {:.0f}%'.format((volume_Voronoi_total-volume_cylinder)/volume_cylinder))
print('-> Voronoi packing fraction: {:.0f}%\n'.format(packing_fraction_Voronoi*100))

print('Volumes distribution:')
for i in range(len(values)-1):
    if counts[i]!=0:
        print('\t{} Voronoi cell volumes are between {:.2E} and {:.2E}'.format(counts[i], values[i], values[i+1]))

我获得了以下信息：

Total volume of the spheres: 1570696

Volume of the cylinder: 3141593
-> Theoretical packing fraction: 50%

Total volume of the (closed) Voronoi cells: 5547909930
Difference between Voronoi volume and cylinder volume: 1765%
-> Voronoi packing fraction: 0%

Volumes distribution:
    1181 Voronoi cell volumes are between 1.46E+03 and 7.47E+03
    136 Voronoi cell volumes are between 7.47E+03 and 3.82E+04
    96 Voronoi cell volumes are between 3.82E+04 and 1.95E+05
    63 Voronoi cell volumes are between 1.95E+05 and 9.99E+05
    36 Voronoi cell volumes are between 9.99E+05 and 5.11E+06
    15 Voronoi cell volumes are between 5.11E+06 and 2.61E+07
    12 Voronoi cell volumes are between 2.61E+07 and 1.33E+08
    2 Voronoi cell volumes are between 1.33E+08 and 6.82E+08

我们可以看到总体积被Voronoi技术高估了很多。从分布来看，似乎有些细胞的体积很大，我真的不明白为什么。你能告诉我可能发生了什么或者需要改变什么吗？

• 谢谢-谢谢