python绘制3D立方体

Question

我想画一个平行六面体.实际上我从绘制多维数据集的python脚本开始:

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

points = np.array([[-1, -1, -1],
                  [1, -1, -1 ],
                  [1, 1, -1],
                  [-1, 1, -1],
                  [-1, -1, 1],
                  [1, -1, 1 ],
                  [1, 1, 1],
                  [-1, 1, 1]])


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

r = [-1,1]

X, Y = np.meshgrid(r, r)

ax.plot_surface(X,Y,1, alpha=0.5)
ax.plot_surface(X,Y,-1, alpha=0.5)
ax.plot_surface(X,-1,Y, alpha=0.5)
ax.plot_surface(X,1,Y, alpha=0.5)
ax.plot_surface(1,X,Y, alpha=0.5)
ax.plot_surface(-1,X,Y, alpha=0.5)

ax.scatter3D(points[:, 0], points[:, 1], points[:, 2])

ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')

plt.show()

为了获得平行六面体,我将点矩阵乘以下面的矩阵:

P = 

[[2.06498904e-01  -6.30755443e-07   1.07477548e-03]

 [1.61535574e-06   1.18897198e-01   7.85307721e-06]

 [7.08353661e-02   4.48415767e-06   2.05395893e-01]]

如:

Z = np.zeros((8,3))

for i in range(8):

   Z[i,:] = np.dot(points[i,:],P)

Z = 10.0*Z

我的想法是表示如下:

ax.scatter3D(Z[:, 0], Z[:, 1], Z[:, 2])

ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')

plt.show()

这就是我得到的:

然后我如何将表面放在这些不同的点上以形成平行六面体(在上面的立方体的方式)？

Answer 1

使用3D PolyCollection绘制曲面(示例)

import numpy as np
from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits.mplot3d.art3d import Poly3DCollection, Line3DCollection
import matplotlib.pyplot as plt

points = np.array([[-1, -1, -1],
                  [1, -1, -1 ],
                  [1, 1, -1],
                  [-1, 1, -1],
                  [-1, -1, 1],
                  [1, -1, 1 ],
                  [1, 1, 1],
                  [-1, 1, 1]])

P = [[2.06498904e-01 , -6.30755443e-07 ,  1.07477548e-03],
 [1.61535574e-06 ,  1.18897198e-01 ,  7.85307721e-06],
 [7.08353661e-02 ,  4.48415767e-06 ,  2.05395893e-01]]

Z = np.zeros((8,3))
for i in range(8): Z[i,:] = np.dot(points[i,:],P)
Z = 10.0*Z

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

r = [-1,1]

X, Y = np.meshgrid(r, r)
# plot vertices
ax.scatter3D(Z[:, 0], Z[:, 1], Z[:, 2])

# list of sides' polygons of figure
verts = [[Z[0],Z[1],Z[2],Z[3]],
 [Z[4],Z[5],Z[6],Z[7]], 
 [Z[0],Z[1],Z[5],Z[4]], 
 [Z[2],Z[3],Z[7],Z[6]], 
 [Z[1],Z[2],Z[6],Z[5]],
 [Z[4],Z[7],Z[3],Z[0]]]

# plot sides
ax.add_collection3d(Poly3DCollection(verts, 
 facecolors='cyan', linewidths=1, edgecolors='r', alpha=.25))

ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')

plt.show()

Answer 2

鉴于此问题的标题是“ python draw 3D cube”，这是我在搜索该问题时发现的文章。

对于那些和我一样的人，他们只想绘制一个立方体，我创建了以下函数，该函数需要一个立方体的四个点，首先是一个角，然后是该角的三个相邻点。

然后绘制立方体。

该功能如下：

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits.mplot3d.art3d import Poly3DCollection, Line3DCollection

def plot_cube(cube_definition):
    cube_definition_array = [
        np.array(list(item))
        for item in cube_definition
    ]

    points = []
    points += cube_definition_array
    vectors = [
        cube_definition_array[1] - cube_definition_array[0],
        cube_definition_array[2] - cube_definition_array[0],
        cube_definition_array[3] - cube_definition_array[0]
    ]

    points += [cube_definition_array[0] + vectors[0] + vectors[1]]
    points += [cube_definition_array[0] + vectors[0] + vectors[2]]
    points += [cube_definition_array[0] + vectors[1] + vectors[2]]
    points += [cube_definition_array[0] + vectors[0] + vectors[1] + vectors[2]]

    points = np.array(points)

    edges = [
        [points[0], points[3], points[5], points[1]],
        [points[1], points[5], points[7], points[4]],
        [points[4], points[2], points[6], points[7]],
        [points[2], points[6], points[3], points[0]],
        [points[0], points[2], points[4], points[1]],
        [points[3], points[6], points[7], points[5]]
    ]

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

    faces = Poly3DCollection(edges, linewidths=1, edgecolors='k')
    faces.set_facecolor((0,0,1,0.1))

    ax.add_collection3d(faces)

    # Plot the points themselves to force the scaling of the axes
    ax.scatter(points[:,0], points[:,1], points[:,2], s=0)

    ax.set_aspect('equal')


cube_definition = [
    (0,0,0), (0,1,0), (1,0,0), (0,0,1)
]
plot_cube(cube_definition)

给出结果：