How do I plot 3 contours in 3D in matplotlib

Question

I have 3 contours, generated by the following:

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from scipy import stats

mean0 = [ 3.1627717, 2.74815376]
cov0  = [[0.44675818, -0.04885433], [-0.04885433, 0.52484173]]
mean1 = [ 6.63373967, 6.82700035]
cov1  = [[ 0.46269969, 0.11528141], [0.11528141, 0.50237073]]
mean2 = [ 7.20726944, 2.61513787]
cov2  = [[ 0.38486096, -0.13042758], [-0.13042758, 0.40928813]]

x = np.linspace(0, 10, 100)
y = np.linspace(0, 10, 100)
X, Y = np.meshgrid(x, y)
Z0 = np.random.random((len(x),len(y)))
Z1 = np.random.random((len(x),len(y)))
Z2 = np.random.random((len(x),len(y)))

def pdf0(arg1,arg2):
    return (stats.multivariate_normal.pdf((arg1,arg2), mean0, cov0))
def pdf1(arg1,arg2):
    return (stats.multivariate_normal.pdf((arg1,arg2), mean1, cov1))
def pdf2(arg1,arg2):
    return (stats.multivariate_normal.pdf((arg1,arg2), mean2, cov2))


for i in range (0, len(x)):
    for j in range(0,len(y)):
        Z0[i,j] = pdf0(x[i],y[j])
        Z1[i,j] = pdf1(x[i],y[j])
        Z2[i,j] = pdf2(x[i],y[j])

Z0=Z0.T
Z1=Z1.T        
Z2=Z2.T

fig3 = plt.figure()
ax3 = fig3.add_subplot(111)
ax3.contour(X,Y,Z0)
ax3.contour(X,Y,Z1)
ax3.contour(X,Y,Z2)
plt.show()

Which, visually, is plotted as the following:

I am wishing to plot all of these in a 3D plot, but when I try do so with:

fig = plt.figure()
ax = fig.add_subplot(1, 1, 1, projection='3d')

# 3D plots for each contour.
surf1 = ax.plot_surface(X, Y, Z0, cmap=cm.coolwarm, linewidth=0, antialiased=False)
surf2 = ax.plot_surface(X, Y, Z1, cmap=cm.coolwarm, linewidth=0, antialiased=False)
surf3 = ax.plot_surface(X, Y, Z2, cmap=cm.coolwarm, linewidth=0, antialiased=False)

ax.contour(X, Y, Z0, zdir='z', offset=-0.5)
ax.contour(X, Y, Z1, zdir='z', offset=-0.5)
ax.contour(X, Y, Z2, zdir='z', offset=-0.5)

ax.set_zlim(-0.5, 0.31)

plt.show()

The resulting graph is this:

How can I get the other two 3D contours to show nicely?

As can be seen below in the for loop, arg1 and arg2 are the passed in values for each point in x and y, and mean and cov are the mean and covariance for that particular dataset — bluey31, Mar 17 '18 at 21:32

score 3 · Accepted Answer · answered Mar 17 '18 at 22:13

There is no general solution to this problem. Matplotlib cannot decide to show part of an object more in front than another part of it. See e.g. the FAQ, or other questions, like How to obscure a line behind a surface plot in matplotlib?

One may of course split up the object in several parts if necessary. Here, however, it seems sufficient to add the functions up.

surf1 = ax.plot_surface(X, Y, Z0+Z1+Z2, cmap=plt.cm.coolwarm, 
                                        linewidth=0, antialiased=False)
ax.contour(X, Y, Z0+Z1+Z2, zdir='z', offset=-0.5)

How do I plot 3 contours in 3D in matplotlib

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