Basemap on the face of a matplotlib.mplot3d cube

Question

As the title suggests, I'm trying to plot a Basemap map on the z=0 surface of a matplotlib.mplot3d lineplot. I know the Axes3D object is capable of plotting on the z=0 surface (via Axes3D.plot, Axes3D.scatter, etc.), but I can't figure out how to do so with a Basemap object. Hopefully the code below shows what I need clearly enough. Any ideas would be much appreciated!

import matplotlib.pyplot as pp
from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits.basemap import Basemap

# make sample data for 3D lineplot
z = np.linspace(-2, 2, 100)
r = z**2 + 1
x = r * np.sin(theta)
y = r * np.cos(theta)

# make the 3D line plot
FIG = ct.pp.figure()
AX = Axes3D(FIG)
AX.plot(x, y, z, '-b')

# make the 2D basemap
### NEEDS TO SOMEHOW BE AT z=0 IN FIG
M = ct.Basemap(projection='stere', width=3700e3, height=2440e3,
               lon_0=-5.0, lat_0=71.0, lat_ts=71.0,
               area_thresh=100, resolution='c')
PATCHES = M.fillcontinents(lake_color='#888888', color='#282828')

Saw

Answer 1

Just add your map as a 3d collection to the Axes3D instance:

import numpy as np
import matplotlib.pyplot as pp
from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits.basemap import Basemap

theta = np.linspace(-4 * np.pi, 4 * np.pi, 100)
z = np.linspace(-500, 500, 100)
r = z**2 + 1
x = r * np.sin(theta)
y = r * np.cos(theta)

FIG = pp.figure()
AX = Axes3D(FIG)
AX.plot(x, y, z, '-b')

M = Basemap(projection='stere', width=3700e3, height=2440e3,
               lon_0=-5.0, lat_0=71.0, lat_ts=71.0,
               area_thresh=100, resolution='c')
AX.add_collection3d(M.drawcoastlines())
AX.grid(True)

pp.draw()
pp.show()

Clinker

Answer 2

AX.add_collection3d(M.drawcoastlines())

works but

PATCHES = M.fillcontinents(lake_color='#888888', color='#282828')

does not work.

As soon as you add color fill you get an error similar to: "AttributeError: 'Polygon' object has no attribute 'do_3d_projection'"

M.fillcontinents(lake_color='#888888', color='#282828')`

returns an array of Polygons, not one of the inputs required by add_collection(). collect.PatchCollection() does not seem to work either.

So what do you use to add `M.fillcontinents(lake_color='#888888', color='#282828') to a 3D plot?

Intermediate