How to generate a sphere in 3D Numpy array

Question

Given a 3D numpy array of shape (256, 256, 256), how would I make a solid sphere shape inside? The code below generates a series of increasing and decreasing circles but is

Answer 1

Nice question. My answer to a similar question would be applicable here also.

You can try the following code. In the below mentioned code AA is the matrix that you want.

import numpy as np
from copy import deepcopy

''' size : size of original 3D numpy matrix A.
    radius : radius of circle inside A which will be filled with ones. 
'''
size, radius = 5, 2

''' A : numpy.ndarray of shape size*size*size. '''
A = np.zeros((size,size, size)) 

''' AA : copy of A (you don't want the original copy of A to be overwritten.) '''
AA = deepcopy(A) 

''' (x0, y0, z0) : coordinates of center of circle inside A. '''
x0, y0, z0 = int(np.floor(A.shape[0]/2)), \
        int(np.floor(A.shape[1]/2)), int(np.floor(A.shape[2]/2))


for x in range(x0-radius, x0+radius+1):
    for y in range(y0-radius, y0+radius+1):
        for z in range(z0-radius, z0+radius+1):
            ''' deb: measures how far a coordinate in A is far from the center. 
                    deb>=0: inside the sphere.
                    deb<0: outside the sphere.'''   
            deb = radius - abs(x0-x) - abs(y0-y) - abs(z0-z) 
            if (deb)>=0: AA[x,y,z] = 1

Following is an example of the output for size=5 and radius=2 (a sphere of radius 2 pixels inside a numpy array of shape 5*5*5):

[[[0. 0. 0. 0. 0.]
  [0. 0. 0. 0. 0.]
  [0. 0. 1. 0. 0.]
  [0. 0. 0. 0. 0.]
  [0. 0. 0. 0. 0.]]

 [[0. 0. 0. 0. 0.]
  [0. 0. 1. 0. 0.]
  [0. 1. 1. 1. 0.]
  [0. 0. 1. 0. 0.]
  [0. 0. 0. 0. 0.]]

 [[0. 0. 1. 0. 0.]
  [0. 1. 1. 1. 0.]
  [1. 1. 1. 1. 1.]
  [0. 1. 1. 1. 0.]
  [0. 0. 1. 0. 0.]]

 [[0. 0. 0. 0. 0.]
  [0. 0. 1. 0. 0.]
  [0. 1. 1. 1. 0.]
  [0. 0. 1. 0. 0.]
  [0. 0. 0. 0. 0.]]

 [[0. 0. 0. 0. 0.]
  [0. 0. 0. 0. 0.]
  [0. 0. 1. 0. 0.]
  [0. 0. 0. 0. 0.]
  [0. 0. 0. 0. 0.]]]

I haven't printed the output for the size and radius that you had asked for (size=32 and radius=4), as the output will be very long.