python - 给定顶点 i 在 pylab 中绘制 3d 曲面

Question

我有 6 个点，它们都位于球体的表面，并且是八面体的顶点。我怎样才能在 3d 轴上探索球体内的这个八面体的表面？

我有以下代码，但它没有达到我的预期:

from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits.mplot3d.art3d import Poly3DCollection
import matplotlib.pyplot as plt

Points=[[ 0.17770898,  0.72315927,  0.66742804],
       [-0.65327074, -0.4196453 ,  0.63018661],
       [ 0.65382635,  0.42081934, -0.62882604],
       [-0.17907021, -0.72084723, -0.66956189],
       [-0.73452809,  0.5495376 , -0.39809158],
       [ 0.73451554, -0.55094017,  0.39617148]]

fig=plt.figure()
ax =fig.add_subplot(1, 1, 1, projection='3d', aspect=1)

ax.add_collection3d(Poly3DCollection([Points]))

u = np.linspace(0, np.pi, 30)
v = np.linspace(0, 2 * np.pi, 30)

x = np.outer(np.sin(u), np.sin(v))
y = np.outer(np.sin(u), np.cos(v))
z = np.outer(np.cos(u), np.ones_like(v))

ax.plot_wireframe(x, y, z, alpha=0.3)

plt.show()

感谢您的帮助。

Answer 1

补充一下 HYRY 的回答；一个体积是由几个多边形面的列表构建的，而每个面又是由一个点列表构建的。 (因此，如果面相邻，则每个点在列表列表中多次出现)。考虑以下片段，其中标记了点:

from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits.mplot3d.art3d import Poly3DCollection
import matplotlib.pyplot as plt
fig = plt.figure ()
ax = fig.add_subplot (1, 1, 1, projection = '3d', aspect = 1)

# octahedron
A = [ 0.17770898,  0.72315927,  0.66742804]
B = [-0.65327074, -0.4196453 ,  0.63018661]
C = [ 0.65382635,  0.42081934, -0.62882604]
D = [-0.17907021, -0.72084723, -0.66956189]
E = [-0.73452809,  0.5495376 , -0.39809158]
F = [ 0.73451554, -0.55094017,  0.39617148]
OCTO = [[E, A, B],
        [E, B, D],
        [E, D, C],
        [E, C, A],
        [F, A, B],
        [F, B, D],
        [F, D, C],
        [F, C, A],
]
ax.add_collection3d (Poly3DCollection (OCTO))

# sphere
u = np.linspace (0, np.pi, 30)
v = np.linspace (0, 2 * np.pi, 30)
x = np.outer (np.sin (u), np.sin (v))
y = np.outer (np.sin (u), np.cos (v))
z = np.outer (np.cos (u), np.ones_like (v))
ax.plot_wireframe (x, y, z, alpha = 0.3)

plt.show ()