How can an almost arbitrary plane in a 3D dataset be plotted by matplotlib?

Question

There is an array containing 3D data of shape e.g. (64,64,64), how do you plot a plane given by a point and a normal (similar to hkl planes in crystallography), through this

Answer 1

For the reduced requirements, I prepared a simple example

import numpy as np
import pylab as plt

data = np.arange((64**3))
data.resize((64,64,64))

def get_slice(volume, orientation, index):
    orientation2slicefunc = {
        "x" : lambda ar:ar[index,:,:], 
        "y" : lambda ar:ar[:,index,:],  
        "z" : lambda ar:ar[:,:,index]
    }
    return orientation2slicefunc[orientation](volume)

plt.subplot(221)
plt.imshow(get_slice(data, "x", 10), vmin=0, vmax=64**3)

plt.subplot(222)
plt.imshow(get_slice(data, "x", 39), vmin=0, vmax=64**3)

plt.subplot(223)
plt.imshow(get_slice(data, "y", 15), vmin=0, vmax=64**3)
plt.subplot(224)
plt.imshow(get_slice(data, "z", 25), vmin=0, vmax=64**3)  

plt.show()  

This leads to the following plot:

The main trick is dictionary mapping orienations to lambda-methods, which saves us from writing annoying if-then-else-blocks. Of course you can decide to give different names, e.g., numbers, for the orientations.

Maybe this helps you.

Thorsten

P.S.: I didn't care about "IndexOutOfRange", for me it's o.k. to let this exception pop out since it is perfectly understandable in this context.