如何使用 matplotlib 或/和离线绘图可视化由 3D 顶点定义的多面体？

Question

我想可视化由 3 个形状 (8, 3) 的 numpy 数组定义的 3 个多面体。

我正在寻找类似的东西：

我的数据如下：

A = np.array([[0.92523719, 0.26843252, 0.77794309],
       [0.73156748, 0.27794309, 0.57476281],
       [0.62113842, 0.37886158, 0.87886158],
       [0.72205691, 0.07476281, 0.76843252],
       [0.57476281, 0.23156748, 0.72205691],
       [0.77794309, 0.42523719, 0.73156748],
       [0.87886158, 0.12113842, 0.62113842],
       [0.76843252, 0.22205691, 0.92523719]])

B = np.array([[0.23156748, 0.72205691, 0.57476281],
       [0.26843252, 0.77794309, 0.92523719],
       [0.12113842, 0.62113842, 0.87886158],
       [0.22205691, 0.92523719, 0.76843252],
       [0.27794309, 0.57476281, 0.73156748],
       [0.37886158, 0.87886158, 0.62113842],
       [0.07476281, 0.76843252, 0.72205691],
       [0.42523719, 0.73156748, 0.77794309]])

C = np.array([[0.73156748, 0.77794309, 0.42523719],
       [0.62113842, 0.87886158, 0.12113842],
       [0.77794309, 0.92523719, 0.26843252],
       [0.57476281, 0.73156748, 0.27794309],
       [0.87886158, 0.62113842, 0.37886158],
       [0.72205691, 0.57476281, 0.23156748],
       [0.76843252, 0.72205691, 0.07476281],
       [0.92523719, 0.76843252, 0.22205691]])

Answer 1

您似乎有 3D 点，但没有边缘或多边形信息。假设多面体是凸多面体，scipy.spatial可以ConvexHull找到凸包上的所有多边形。凸包由三角形组成，可以将其作为Poly3DCollection.

from mpl_toolkits.mplot3d.art3d import Poly3DCollection
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import pyplot as plt
import numpy as np
from scipy.spatial import ConvexHull

A = np.array([[0.92523719, 0.26843252, 0.77794309], [0.73156748, 0.27794309, 0.57476281], [0.62113842, 0.37886158, 0.87886158], [0.72205691, 0.07476281, 0.76843252], [0.57476281, 0.23156748, 0.72205691], [0.77794309, 0.42523719, 0.73156748], [0.87886158, 0.12113842, 0.62113842], [0.76843252, 0.22205691, 0.92523719]])
B = np.array([[0.23156748, 0.72205691, 0.57476281], [0.26843252, 0.77794309, 0.92523719], [0.12113842, 0.62113842, 0.87886158], [0.22205691, 0.92523719, 0.76843252], [0.27794309, 0.57476281, 0.73156748], [0.37886158, 0.87886158, 0.62113842], [0.07476281, 0.76843252, 0.72205691], [0.42523719, 0.73156748, 0.77794309]])
C = np.array([[0.73156748, 0.77794309, 0.42523719], [0.62113842, 0.87886158, 0.12113842], [0.77794309, 0.92523719, 0.26843252], [0.57476281, 0.73156748, 0.27794309], [0.87886158, 0.62113842, 0.37886158], [0.72205691, 0.57476281, 0.23156748], [0.76843252, 0.72205691, 0.07476281], [0.92523719, 0.76843252, 0.22205691]])
fig = plt.figure()
ax = fig.add_subplot(111, projection="3d")
for cube, color in zip([A, B, C], ['r', 'g', 'b']):
    hull = ConvexHull(cube)
    # draw the polygons of the convex hull
    for s in hull.simplices:
        tri = Poly3DCollection([cube[s]])
        tri.set_color(color)
        tri.set_alpha(0.5)
        ax.add_collection3d(tri)
    # draw the vertices
    ax.scatter(cube[:, 0], cube[:, 1], cube[:, 2], marker='o', color='purple')
plt.show()

假设每个三角形的最长边是立方体的面对角线，我们可以搜索两条最短边并将它们画成黑色：

from mpl_toolkits.mplot3d.art3d import Poly3DCollection
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import pyplot as plt
import numpy as np
from scipy.spatial import ConvexHull

A = np.array([[0.92523719, 0.26843252, 0.77794309], [0.73156748, 0.27794309, 0.57476281], [0.62113842, 0.37886158, 0.87886158], [0.72205691, 0.07476281, 0.76843252], [0.57476281, 0.23156748, 0.72205691], [0.77794309, 0.42523719, 0.73156748], [0.87886158, 0.12113842, 0.62113842], [0.76843252, 0.22205691, 0.92523719]])
B = np.array([[0.23156748, 0.72205691, 0.57476281], [0.26843252, 0.77794309, 0.92523719], [0.12113842, 0.62113842, 0.87886158], [0.22205691, 0.92523719, 0.76843252], [0.27794309, 0.57476281, 0.73156748], [0.37886158, 0.87886158, 0.62113842], [0.07476281, 0.76843252, 0.72205691], [0.42523719, 0.73156748, 0.77794309]])
C = np.array([[0.73156748, 0.77794309, 0.42523719], [0.62113842, 0.87886158, 0.12113842], [0.77794309, 0.92523719, 0.26843252], [0.57476281, 0.73156748, 0.27794309], [0.87886158, 0.62113842, 0.37886158], [0.72205691, 0.57476281, 0.23156748], [0.76843252, 0.72205691, 0.07476281], [0.92523719, 0.76843252, 0.22205691]])
fig = plt.figure()
ax = fig.add_subplot(111, projection="3d")
for cube, color in zip([A, B, C], ['r', 'g', 'b']):
    hull = ConvexHull(cube)
    # draw the polygons of the convex hull
    for s in hull.simplices:
        tri = Poly3DCollection([cube[s]])
        tri.set_color(color)
        tri.set_alpha(0.5)
        ax.add_collection3d(tri)
    # draw the vertices
    ax.scatter(cube[:, 0], cube[:, 1], cube[:, 2], marker='o', color='purple')
plt.show()