I am trying to draw a parallelepiped. Actually I started from the python script drawing a cube as:
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()
In order to obtain a parallelepiped, I have multiplied the points matrix by the following matrix:
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]]
as:
Z = np.zeros((8,3))
for i in range(8):
Z[i,:] = np.dot(points[i,:],P)
Z = 10.0*Z
My idea is then to represent as follows:
ax.scatter3D(Z[:, 0], Z[:, 1], Z[:, 2])
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
plt.show()
And this is what I get:
How can I then put surfaces on these different points to form the parallelepiped (in the way of the cube above)?
Plot surfaces with 3D PolyCollection (example)
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()