Plotting 3D image form a data in NumPy-array

Question

I have a data file in NumPy array, I would like to view the 3D-image. I am sharing an example, where I can view 2D image of size (100, 100), this is a slice in xy-plane at z = 0.

import numpy as np
from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
X, Y, Z = np.mgrid[-10:10:100j, -10:10:100j, -10:10:100j]
T = np.sin(X*Y*Z)/(X*Y*Z)
T=T[:,:,0]
im = plt.imshow(T, cmap='hot')
plt.colorbar(im, orientation='vertical')
plt.show()

How can I view a 3D image of the data T of shape (100, 100, 100)?

Answer 1

I think the main problem is, that you do have 4 informations for each point, so you are actually interessted in a 4-dimensional object. Plotting this is always difficult (maybe even impossible). I suggest one of the following solutions:

1. You change the question to: I'm not interessted in all combinations of x,y,z, but only the ones, where z = f(x,y)

2. You change the accuracy of you plot a bit, saying that you don't need 100 levels of z, but only maybe 5, then you simply make 5 of the plots you already have.

In case you want to use the first method, then there are several submethods:

A. Plot the 2-dim surface f(x,y)=z and color it with T B. Use any technic that is used to plot complex functions, for more info see here.

The plot given by method 1.A (which I think is the best solution) with z=x^2+y^2 yields:

I used this programm:

import numpy as np
from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import matplotlib as mpl
X, Y = np.mgrid[-10:10:100j, -10:10:100j]
Z = (X**2+Y**2)/10 #definition of f
T = np.sin(X*Y*Z)
norm = mpl.colors.Normalize(vmin=np.amin(T), vmax=np.amax(T))
T = mpl.cm.hot(T) #change T to colors
fig = plt.figure()
ax = fig.gca(projection='3d')
surf = ax.plot_surface(X, Y, Z, facecolors=T, linewidth=0,
       cstride = 1, rstride = 1)
plt.show()

The second method gives something like:

With the code:

norm = mpl.colors.Normalize(vmin=-1, vmax=1)
X, Y= np.mgrid[-10:10:101j, -10:10:101j]
fig = plt.figure()
ax = fig.gca(projection='3d')
for i in np.linspace(-1,1,5):
    Z = np.zeros(X.shape)+i
    T = np.sin(X*Y*Z)
    T = mpl.cm.hot(T)
    ax.plot_surface(X, Y, Z, facecolors=T, linewidth=0, alpha = 0.5, cstride 
        = 10, rstride = 10)

plt.show()

Note: I changed the function to T = sin(X*Y*Z) because dividing by X*Y*Zmakes the functions behavior bad, as you divide two number very close to 0.