Adding legend to a surface plot

Question

I am trying to add legend to a surface plot but unable to do so. Here is the code.

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

def fun(x, y):
  return 0.063*x**2 + 0.0628*x*y - 0.15015876*x + 96.1659*y**2 - 74.05284306*y  +      14.319143466051


fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
x = y = np.arange(-1.0, 1.0, 0.05)
X, Y = np.meshgrid(x, y)
zs = np.array([fun(x,y) for x,y in zip(np.ravel(X), np.ravel(Y))])
Z = zs.reshape(X.shape)

ax.plot_surface(X, Y, Z)

ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
plt.plot(color='red',label='Lyapunov function on XY plane',linewidth=4)  # Adding legend

plt.show()

Kindly help. Thanks in advance.

Answer 1

It is not trivial to make a legend in a 3D axis. You can use the following hack:

import numpy as np
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import matplotlib as mpl
import random

def fun(x, y):
  return 0.063*x**2 + 0.0628*x*y - 0.15015876*x + 96.1659*y**2 - 74.05284306*y  +      14.319143466051


fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
x = y = np.arange(-1.0, 1.0, 0.05)
X, Y = np.meshgrid(x, y)
zs = np.array([fun(x,y) for x,y in zip(np.ravel(X), np.ravel(Y))])
Z = zs.reshape(X.shape)

ax.plot_surface(X, Y, Z)

ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
fake2Dline = mpl.lines.Line2D([0],[0], linestyle="none", c='b', marker = 'o')
ax.legend([fake2Dline], ['Lyapunov function on XY plane'], numpoints = 1)
plt.show()

I would say a title is more appropriate than a legend in this case.

Answer 2

According to this question, the issue is ongoing, and there is a relatively simple workaround. You can manually set the two missing attributes that would allow legend to automatically create the patch for you:

surf = ax.plot_surface(X, Y, Z, label='Lyapunov function on XY plane')
surf._edgecolors2d = surf._edgecolor3d
surf._facecolors2d = surf._facecolor3d

ax.legend()

The attribute names on the right hand side of the assignment are surf._edgecolors3d and surf.facecolors3d for matplotlib < v3.3.3.