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()