python - 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 diamond shaped when viewed in the two other dimensions.

def make_sphere(arr, x_pos, y_pos, z_pos, radius=10, size=256, plot=False):

    val = 255            
    for r in range(radius):
        y, x = np.ogrid[-x_pos:n-x_pos, -y_pos:size-y_pos]
        mask = x*x + y*y <= r*r 
        top_half = arr[z_pos+r]
        top_half[mask] = val #+ np.random.randint(val)
        arr[z_pos+r] = top_half

    for r in range(radius, 0, -1):
        y, x = np.ogrid[-x_pos:size-x_pos, -y_pos:size-y_pos]
        mask = x*x + y*y <= r*r 
        bottom_half = arr[z_pos+r]
        bottom_half[mask] = val#+ np.random.randint(val)
        arr[z_pos+2*radius-r] = bottom_half

    if plot:
        for i in range(2*radius):
            if arr[z_pos+i].max() != 0:
                print(z_pos+i)
                plt.imshow(arr[z_pos+i])
                plt.show()

    return arr

Answer 1

EDIT: pymrt.geometry has been removed in favor of raster_geometry.

---

DISCLAIMER: I am the author of both pymrt and raster_geometry.

If you just need to have the sphere, you can use the pip-installable module pymrt, and particularly pymrt.geometry.sphere(), e.g:

import pymrt as mrt
import pymrt.geometry

arr = mrt.geometry.sphere(3, 1)

array([[[False, False, False],
        [False,  True, False],
        [False, False, False]],

        [[False,  True, False],
        [ True,  True,  True],
        [False,  True, False]],

        [[False, False, False],
        [False,  True, False],
        [False, False, False]]], dtype=bool)

internally, this is implemented as an n-dimensional superellipsoid generator, you can check its source code for details. Briefly, the (simplified) code would reads like this:

import numpy as np


def sphere(shape, radius, position):
    # assume shape and position are both a 3-tuple of int or float
    # the units are pixels / voxels (px for short)
    # radius is a int or float in px
    semisizes = (radius,) * 3

    # genereate the grid for the support points
    # centered at the position indicated by position
    grid = [slice(-x0, dim - x0) for x0, dim in zip(position, shape)]
    position = np.ogrid[grid]
    # calculate the distance of all points from `position` center
    # scaled by the radius
    arr = np.zeros(shape, dtype=float)
    for x_i, semisize in zip(position, semisizes):
        # this can be generalized for exponent != 2
        # in which case `(x_i / semisize)`
        # would become `np.abs(x_i / semisize)`
        arr += (x_i / semisize) ** 2

    # the inner part of the sphere will have distance below 1
    return arr <= 1.0

and testing it:

arr = sphere((256, 256, 256), 10, (127, 127, 127))
# this will save a sphere in a boolean array
# the shape of the containing array is: (256, 256, 256)
# the position of the center is: (127, 127, 127)
# if you want is 0 and 1 just use .astype(int)
# for plotting it is likely that you want that

# just for fun you can check that the volume is matching what expected
np.sum(arr)
# gives: 4169

4 / 3 * np.pi * 10 ** 3
# gives: 4188.790204786391
# (the two numbers do not match exactly because of the discretization error)

I am failing to get how your code exactly works, but to check that this is actually producing spheres (using your numbers) you could try:

import pymrt as mrt
import pymrt.geometry

arr = mrt.geometry.sphere(256, 10, 0.5)


# plot in 3D
import matplotlib.pyplot as plt
from skimage import measure

fig = plt.figure()
ax = fig.add_subplot(1, 1, 1, projection='3d')

verts, faces, normals, values = measure.marching_cubes(arr, 0.5, (2,) * 3)
ax.plot_trisurf(
    verts[:, 0], verts[:, 1], faces, verts[:, 2], cmap='Spectral',
    antialiased=False, linewidth=0.0)
plt.show()