Order of object in 3d plot - spiral - python-3.x

Question

I plotted a spiral and a line that should go through the spiral. I am not able to set that the line is behind the front part of the spiral and in front of the back part of the spiral. I tried to use zorder but the line is either whole in front of the spiral or whole behind the spiral. Thank you
Code:
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.pyplot as plt
mpl.rcParams['legend.fontsize'] = 10
fig = plt.figure()
ax = fig.gca(projection='3d')
theta = np.linspace(-4 * np.pi, 4 * np.pi, 100)
z = np.linspace(-2, 2, 100)
r = z**2 + 1
x = r * np.sin(theta)
y = r * np.cos(theta)
ax.plot(x, y, z, label='parametric curve')
ax.plot([-1,-1], # x
[2,2], # y
[-2, 2], c='red')
plt.show()
For instance, here. The red line is in front of the spiral. If I set zorder it could be behind the spiral. How to set the line goes properly throught the spiral?

Answer 1

Note that matplotlib isn't fully 3D. In order to get enough speed for complex plots, 3D is simulated drawing everything back to front, with each element drawn in its entirety on a specific depth. If you need full 3D, packages such as mayavi are worth investigating.
In order to get the red line inside the spiral, using matplotlib, the following approach can be used:
draw the spiral
draw the red line
draw the spiral again, but only the part that would be in front of the line
Note that such an approach only works if you don't rotate the view too much and you don't use transparency.
Now, to draw only a part of a curve, the standard way uses numpy's masked arrays. But these don't seem to be respected by the 3D plot. The alternative is to set unwanted points to NaN.
To better demonstrates the approach, the code below draws the red line much wider and uses green for the part of the spiral in front of the line. For the real thing, the spiral and the partial spiral would use the same colors.
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.gca(projection='3d')
theta = np.linspace(-4 * np.pi, 4 * np.pi, 100)
z = np.linspace(-2, 2, 100)
r = z**2 + 1
x = r * np.sin(theta)
y = r * np.cos(theta)
ax.plot(x, y, z, label='parametric curve') # the full spiral
ax.plot([-1,-1], # x
[2,2], # y
[-2, 2], c='red', lw=10)
ym = np.copy(y)
ym[y > 0] = np.NaN
ax.plot(x, ym, z, color='lime') # partial spiral
plt.show()