Contour plot projection not showing properly in matplotlib 3d plotting

[Pushpa (Puspendu Rana)]

I am currently attempting to plot a contour map that shows the position of a random walker moving in a three-dimensional space on the xy, xz, and yz planes. While I have been able to successfully plot the contour map in the xy plane, I have encountered issues while plotting it in the xz and yz planes. Specifically, the distribution of the map appears strange and is not centred around the zero line as expected.
I am using Jupyter Notebook with Python to generate these plots. I have included the code snippet and the current plot for reference. Could you please suggest a solution for this issue? Additionally, if the problem is resolved, please provide an updated plot.

import numpy as np
import matplotlib.pyplot as plt
from matplotlib import cm

stepsize = 0.5
num_steps = 250
num_trials = 10**3

final_path = []

for _ in range(num_trials+1):
    pos = np.array([0.0,0.0,0.0])
    for _ in range(num_steps+1):
        pos= pos+  np.random.normal(0,0.5,3)
    final_path.append(list(pos))

final_path = np.array(final_path)

x = final_path[:,0]
y = final_path[:,1]
z = final_path[:,2]

fig = plt.figure(figsize = (15,12)) 
ax = fig.add_subplot(projection = '3d', computed_zorder = False)
ax.scatter(x,y,z, c = 'blue', s = 40, zorder = 2)
# ax.plot(x, y, z, 'k-',  linewidth=0.5, zorder = 2)

ax.scatter(x,y, zs = min(z), zdir = 'z', color = 'black',s = 8, zorder = 1)
ax.scatter(x,z, zs = max(y), zdir = 'y', color = 'black',s = 8, zorder = 1)
ax.scatter(y,z, zs = min(x), zdir = 'x', color = 'black',s = 8, zorder = 1)

counts_xy, xedges, yedges = np.histogram2d(x, y, bins=25)
x_grid_xy, y_grid_xy = np.meshgrid(np.linspace(min(x), max(x), 25), np.linspace(min(y), max(y), 25))

counts_xz, xedges, zedges = np.histogram2d(x, z, bins=25)
x_grid_xz, z_grid_xz = np.meshgrid(np.linspace(min(x), max(x), 25), np.linspace(min(z), max(z), 25))

counts_yz, yedges, zedges = np.histogram2d(y, z, bins=25)
y_grid_yz, z_grid_yz = np.meshgrid(np.linspace(min(y), max(y), 25), np.linspace(min(z), max(z), 25))

ax.contourf(x_grid_xy, y_grid_xy, counts_xy.T, zdir='z', offset=min(z), levels = 25, cmap='Reds', zorder=0)
ax.contourf(x_grid_xz, z_grid_xz, counts_xz.T, zdir='y', offset=max(y), levels = 25, cmap='Greens', zorder=0)
ax.contourf(y_grid_yz, z_grid_yz, counts_yz.T, zdir='x', offset=min(x), levels = 25, cmap='Blues', zorder=0)

ax.set_xlim(min(x),max(x))
ax.set_ylim(min(y),max(y))
ax.set_zlim(min(z),max(z))
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
ax.set_title('Walker\'s Position in 3D Space')

plt.show()

[catherine-toolan]

Aware that this is quite old but fixing this helped me understand how this projection works better. All that needs to change is the order of the ‘axes’ given. I say ‘axes’ in quotations because it’s a bit of a strange one; think of the ax.contourf(x_grid_xy, y_grid_xy, counts_xy.T, zdir=‘z’, offset=min(z), levels = 25, cmap=‘Reds’, zorder=0) line just flattening what a ax.contourf(x_grid_xy, y_grid_xy, counts_xy.T) plot would look like down to the xy plane. Thinking of it that way, it makes sense that the xz and yz projections look odd, as you’re taking the distributions and plotting them the same way again, and flattening them to the other axis (as if you were looking straight at the xz plane for example). To fix this, just swap around the order, so that the contourf plots would be covering the plane that you want to project them onto.

i.e. it should be:

ax.contourf(x_grid_xy, y_grid_xy, counts_xy.T, zdir=‘z’, offset=min(z), levels = 25, cmap=‘Reds’, zorder=0)ax.contourf(x_grid_xz, counts_xz.T, z_grid_xz, zdir=‘y’, offset=max(y), levels = 25, cmap=‘Greens’, zorder=0)ax.contourf(counts_yz.T, z_grid_yz, y_grid_yz, zdir=‘x’, offset=min(x), levels = 25, cmap=‘Blues’, zorder=0)

Hopefully the explanation makes sense, and sorry for the formatting! (haven’t posted here before!)