overlapping_spheres

Generates overlapping spheres by inserting random points then dilating them to the specified radius.

import matplotlib.pyplot as plt
import numpy as np
import porespy as ps

radius

Controls the size of the spheres:

fig, ax = plt.subplots(1, 2, figsize=[8, 4])

shape = [200, 200]
e = 0.6
r = 10
im1 = ps.generators.overlapping_spheres(shape=shape, r=r, porosity=e)
ax[0].imshow(im1)
ax[0].axis(False)
ax[0].set_title(f"radius = {r}")

r = 20
im2 = ps.generators.overlapping_spheres(shape=shape, r=r, porosity=e)
ax[1].imshow(im2)
ax[1].axis(False)
ax[1].set_title(f"radius = {r}");

porosity

The number of spheres added is adjusted by meet the requested porosity:

fig, ax = plt.subplots(1, 2, figsize=[8, 4])

r = 10
e = 0.8
im1 = ps.generators.overlapping_spheres(shape=shape, r=r, porosity=e)
ax[0].imshow(im1)
ax[0].axis(False)
ax[0].set_title(f"porosity = {e}")

e = 0.4
im2 = ps.generators.overlapping_spheres(shape=shape, r=r, porosity=e)
ax[1].imshow(im2)
ax[1].axis(False)
ax[1].set_title(f"porosity = {e}");

max_iter

Because the spheres overlap randomly, it’s not possible to match the desired porosity perfect so a trial and error approach is used. This parameters control the maximum number of iterations used to match the desired porosity within the specified tolerance.

fig, ax = plt.subplots(1, 2, figsize=[8, 4])
print("target porosity =", e)

np.random.seed(0)
mi = 1
im1 = ps.generators.overlapping_spheres(shape=shape, r=r, porosity=e, maxiter=mi)
ax[0].imshow(im1)
ax[0].axis(False)
ax[0].set_title(f"maxiter = {mi}")
print("porosity = ", ps.metrics.porosity(im1))

np.random.seed(0)
mi = 10
im2 = ps.generators.overlapping_spheres(shape=shape, r=r, porosity=e, maxiter=mi)
ax[1].imshow(im2)
ax[1].axis(False)
ax[1].set_title(f"maxiter = {mi}")
print("porosity = ", ps.metrics.porosity(im2))

target porosity = 0.4
porosity =  0.26175
porosity =  0.406125

tol

Tolerance for porosity relative to input value. If requesting a porosity of 0.5, then tol=0.1 will halt the iteration once the porosity is within 10% of the desired value, so between 0.45 and 0.55. Note that the procedure may also stop early if maxiter is reached first.

fig, ax = plt.subplots(1, 2, figsize=[8, 4])
print("target porosity =", e)

np.random.seed(0)
t = 1e-2
mi = 100
im1 = ps.generators.overlapping_spheres(shape=shape, r=r, porosity=e, maxiter=mi, tol=t)
ax[0].imshow(im1)
ax[0].axis(False)
ax[0].set_title(f"tol = {t}")
print("porosity = ", ps.metrics.porosity(im1))

np.random.seed(0)
t = 1e-4
im2 = ps.generators.overlapping_spheres(shape=shape, r=r, porosity=e, maxiter=mi, tol=t)
ax[1].imshow(im2)
ax[1].axis(False)
ax[1].set_title(f"tol = {t}")
print("porosity = ", ps.metrics.porosity(im2))

target porosity = 0.4
porosity =  0.406125

porosity =  0.400225