给定 XYZ 网格点，计算球体内部的体积

Question

我有一个由均匀分布的 xyz 笛卡尔点组成的大型 3D 网格（约 800,000 点），我想根据占据球体的点数找到球体内部的体积。我目前正在使用 scipy cKDTree 并使用 query_ball_point 检测原点（0,0,0）一定半径内的所有点来估计体积，但这个体积（grid_vol，下面）通常有很大不同（50% 错误或更大) 比真实体积 (sphere_vol)。

import numpy as np
from scipy import spatial
import math
#constants
xl = -3.15
xr =  1.75
yl = -2.0
yr =  2.0
zl = -1.15
zr = 3.9
spacing = 0.05
R = 3.5
cube = spacing ** 3  
#Create grid
x=np.arange(xl,xr,spacing)
y=np.arange(yl,yr,spacing)
z=np.arange(zl,zr,spacing)
x2,y2,z2=np.meshgrid(x,y,z,indexing='ij')
all_grid=np.array([x2.flatten(),y2.flatten(),z2.flatten()]).T
cube = spacing ** 3                  
point_tree = spatial.cKDTree(all_grid)                  # allgrid = evenly spaced rectangular grid
n_voxel = len(point_tree.query_ball_point((0,0,0), R))   # number of points in grid occupying sphere of radius R
grid_vol = n_voxel * cube                               # volume based on grid points
sphere_vol = 4 / 3 * math.pi * R ** 3                # vol of sphere w/ radius R to compare

在这种情况下：

grid_vol = 78.1275
sphere_vol = 179.5944

我想知道是否有一个已知的模块可以很好地用于从网格点测量球体的这种应用

Answer 1

嘿，guilian，我试过你的代码，据我所知，它工作得很好（由于近似值造成的一些错误，但不是一个大错误

import numpy as np
from scipy import spatial
#define constants
l=-1
r=1
spacing=0.05
R=0.5
cube = spacing ** 3  
#Create grid
x=np.arange(l,r,spacing)
y=np.arange(l,r,spacing)
z=np.arange(l,r,spacing)
x2,y2,z2=np.meshgrid(x,y,z,indexing='ij')
all_grid=np.array([x2.flatten(),y2.flatten(),z2.flatten()]).T
# your code            
point_tree = spatial.cKDTree(all_grid)
n_voxel = len(point_tree.query_ball_point((0,0,0), R))   # number of points in grid occupying sphere of radius R
grid_vol = n_voxel * cube                               # volume based on grid points
sphere_volume = 4 / 3 * np.pi * R ** 3
print(grid_vol) # 0.5185000000000001
print(sphere_volume) # 0.5235987755982988