Pyplot: Plot a 3D figure in a 2D frame?

Question

In my current project, I want to plot a 3D shape with pyplot. This is relatively straightforward:

The complication comes from the fact that I would like the figure to display in a straight 2D figure similar to this example:

That is to say, remove the 3D axes and ticks, the gridlines, and wrap everything in a flat 2D border. Is it possible to do this with Pyplot? You can find my code to generate the two figures below:

import matplotlib.pyplot as plt
import numpy as np

plt.figure()

x   = np.asarray([0,1,1.5,0.5,0])
y   = np.asarray([0,0,0.5,0.5,0])

# Plot 2D projection of cube
plt.plot(x,y,color='k')
plt.plot(x,y+1,color='k')
plt.plot([0,0],[0,1],color='k')
plt.plot([1,1],[0,1],color='k')
plt.plot([1.5,1.5],[0.5,1.5],color='k')
plt.plot([0.5,0.5],[0.5,1.5],color='k')

plt.title("2D projection of cube")
plt.axis('equal')
plt.tick_params(left=False,
                bottom=False,
                labelleft=False,
                labelbottom=False)

# Now try the same thing in 3D
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

x   = np.asarray([0,1,1,0,0])
y   = np.asarray([0,0,1,1,0])

# Plot 2D projection of cube
ax.plot3D(x,y,np.zeros(5),color='k')
ax.plot3D(x,y,np.ones(5),color='k')
ax.plot3D([0,0],[0,0],[0,1],color='k')
ax.plot3D([0,0],[1,1],[0,1],color='k')
ax.plot3D([1,1],[0,0],[0,1],color='k')
ax.plot3D([1,1],[1,1],[0,1],color='k')

plt.title("3D projection of cube")

Answer 1

The following approach:

• describes a cube by 8 vertices and 12 edges
• the vertices start in an axis-aligned position
• the vertices are rotated around some arbitrary axis; using code from Rotating around a 3D vector
• the x and y positions of the rotated vertices are used to draw the cube (so, parallel projection of the rotated cube onto the xy plane)

import matplotlib.pyplot as plt
import numpy as np
import math

def rotation_matrix(axis, theta):
    """
    Return the rotation matrix associated with counterclockwise rotation about
    the given axis by theta radians.
    """
    axis = np.asarray(axis)
    axis = axis / math.sqrt(np.dot(axis, axis))
    a = math.cos(theta / 2.0)
    b, c, d = -axis * math.sin(theta / 2.0)
    aa, bb, cc, dd = a * a, b * b, c * c, d * d
    bc, ad, ac, ab, bd, cd = b * c, a * d, a * c, a * b, b * d, c * d
    return np.array([[aa + bb - cc - dd, 2 * (bc + ad), 2 * (bd - ac)],
                     [2 * (bc - ad), aa + cc - bb - dd, 2 * (cd + ab)],
                     [2 * (bd + ac), 2 * (cd - ab), aa + dd - bb - cc]])

x = np.array([0, 1, 1, 0, 0, 1, 1, 0])
y = np.array([0, 0, 1, 1, 0, 0, 1, 1])
z = np.array([0, 0, 0, 0, 1, 1, 1, 1])
# the 8 vertices of the cube
vertices = np.vstack([x, y, z])
# the 12 edges, each connecting two of the vertices
edges = [[0, 1], [1, 2], [2, 3], [3, 0], [4, 5], [5, 6], [6, 7], [7, 4], [0, 4], [1, 5], [2, 6], [3, 7]]

axis = [4, 3, 0]
theta = 20
rot_vertices = np.dot(rotation_matrix(axis, math.radians(theta)), vertices)
for v0, v1 in edges:
    plt.plot(rot_vertices[0, [v0, v1]], rot_vertices[1, [v0, v1]], color='black')

plt.title("2D projection of cube")
plt.axis('equal')
plt.xticks([])
plt.yticks([])
plt.show()