Parametric 3D Surface Plot with color depending on (x,y,z)

Question

I want to plot a quantity which is given on a parametric surface in 3d space (for example the temperature distribution on a sphere). I can plot a parametric 3D plot of the sphere (as a function of the two parameters phi and theta ) but I don't know how to make the colors of the polygons making up the sphere depend on the parameters theta and phi (normally, the color of a polygon is simply determined by the z-Position of the polygon).

Here's a basic example which plots a torus with colormap:

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

angle = np.linspace(0, 2 * np.pi, 32)
theta, phi = np.meshgrid(angle, angle)
r, R = .25, 1.
X = (R + r * np.cos(phi)) * np.cos(theta)
Y = (R + r * np.cos(phi)) * np.sin(theta)
Z = r * np.sin(phi)

# Display the mesh
fig = plt.figure()
ax = fig.gca(projection = '3d')
ax.set_xlim3d(-1, 1)
ax.set_ylim3d(-1, 1)
ax.set_zlim3d(-1, 1)
ax.plot_surface(X, Y, Z, rstride = 1, cstride = 1,cmap="hot")
plt.show()

However, the colors of the files are given by the z position of the tile, I want the color to be given by a function f(x,y) .

Does anyone know how I can achieve this dependency in Matplotlib?

Thanks very much!

Answer 1

Ok, if anyone else is looking for a solution to this problem here's a possible solution:

The colors of the individual faces making up the surface plot can be set using the keyword argument facecolors . The following code will use the function X**2+Y**2 for coloring the faces of the parametric surface:

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

# Generate torus mesh
angle = np.linspace(0, 2 * np.pi, 32)
theta, phi = np.meshgrid(angle, angle)
r, R = .25, 1.
X = (R + r * np.cos(phi)) * np.cos(theta)
Y = (R + r * np.cos(phi)) * np.sin(theta)
Z = r * np.sin(phi)

colorfunction=(X**2+Y**2)
norm=colors.Normalize(colorfunction.min(),colorfunction.max())

# Display the mesh
fig = plt.figure()
ax = fig.gca(projection = '3d')
ax.set_xlim3d(-1, 1)
ax.set_ylim3d(-1, 1)
ax.set_zlim3d(-1, 1)
ax.plot_surface(X, Y, Z, rstride = 1, cstride = 1, facecolors=cm.jet(norm(colorfunction)))
plt.show()