用Python中的体素制成的椭球

问题描述

我需要用python中的体素制作一个椭圆体，但我仍然不完全了解如何定义该图的边界。我已经看到了一些使用布尔操作定义体素的示例，但我无法使其按照我想要的方式工作。任何帮助将不胜感激。

这是我一直在尝试的：

import matplotlib.pyplot as plt
import numpy as np
from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits.mplot3d.art3d import poly3DCollection

fig = plt.figure()
ax = fig.add_subplot(111,projection='3d')

# the angles and radius
u = np.linspace(0,2 * np.pi,100)
v = np.linspace(0,np.pi,100)
radius = 4

# equations for the shell of the ellipsoid
X = 3*radius*np.sin(v)*np.cos(u)
Y = 2*radius*np.sin(v)*np.sin(u)
Z = radius*np.cos(v)


x,y,z = np.indices((10,10,10))
voxels = (x <= X) | (y <= Y) | (z <= Z)
ax.voxels(voxels)

plt.show()

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-12-f0d9033151c5> in <module>
     14 
     15 x,10))
---> 16 voxels = (x <= X) | (y <= Y) | (z <= Z)
     17 ax.voxels(voxels)
     18 

ValueError: operands Could not be broadcast together with shapes (10,10) (100,)

解决方法

您可以使用meshgrid在均匀间隔的网格上过滤到椭圆体内的点，然后对这些点应用布尔掩码：

import matplotlib.pyplot as plt
import numpy as np
from mpl_toolkits.mplot3d import Axes3D

fig = plt.figure()
ax = fig.add_subplot(111,projection='3d')

# grid points in spherical coord:
N = 40
R = 1
x,y,z = np.meshgrid(np.linspace(-R,R,N),np.linspace(-R,N))

# filter points outside ellipsoid interior:
mask = (2*x)**2 + (3*y)**2 + z**2 <= R**2
x = x[mask]
y = y[mask]
z = z[mask]


# convert to cartesian for plotting:

ax.scatter3D(x,z)
ax.set_xlim(-1.2,1.2)
ax.set_ylim(-1.2,1.2)
ax.set_zlim(-1.2,1.2)
plt.show()