Question

considering I have a 3D histogram or for simplicity a 3D numpy array of shape (X,Y,Z)

import numpy as np
array = np.random.random((100,100,100))

What is the best way, using numpy or scipy to obtain array’s values’ indexes of which satisfy a sphere conditions?

(index_x**2 + index_y**2 + index_z**2) <= radius**2

Obvioulsy, in the later condition, the array center is (0, 0, 0). In general the condition will be

((index_x-center_x)**2 + (index_y-center_y)**2 +(index_z-center_z)**2) <= radius**2

The problem is easy to solve using simply a python loop, but I need that to be optimized.

many thanks for your help

Answer 1

Just for making @EOL nice approach more general, one can define a center within the shape of the array

array = np.random.random((100,100,100))
center = (30,10,25)
radius = 5.0
x, y, z = np.ogrid[-center[0]:array.shape[0]-center[0],-center[1] :array.shape[1]-center[1], -center[2]:array.shape[2]-center[2]]
indexes = numpy.transpose((x**2+y**2+z**2 <= radius**2).nonzero())