simulate a torus in 3D

torus.py

import numpy as np
import matplotlib.pyplot as plt
import mrcfile

n = 64	# 3D map size in pixels
distance_ringcenter_to_boxcenter = n/2.0 * 0.5
radius_ring = distance_ringcenter_to_boxcenter * 0.1

def buildTorus(n, distance_ringcenter_to_boxcenter, radius_ring):
	# http://mathworld.wolfram.com/Torus.html
	m = np.zeros((n, n, n), dtype=float)

	z, y, x = np.mgrid[-n/2:n/2, -n/2:n/2, -n/2:n/2]
	x2 = x*x
	y2 = y*y
	z2 = z*z

	r2 = np.square(distance_ringcenter_to_boxcenter-np.sqrt(x2+y2))+z2

	m = np.exp( -r2/(radius_ring*radius_ring))
	return m

torus = buildTorus(n, distance_ringcenter_to_boxcenter, radius_ring)

with mrcfile.new('torus.mrc', overwrite=True) as mrc:
	mrc.set_data(torus.astype(np.float32))

plt.figure(0)
plt.imshow(torus[n/2,:,:])
plt.gray()
plt.show()