lattice_spheres

Generates a cubic packing of spheres in a specified lattice arrangement.

import matplotlib.pyplot as plt
import porespy as ps

[01:04:24] ERROR    PARDISO solver not installed, run `pip install pypardiso`. Otherwise,          _workspace.py:56
                    simulations will be slow. Apple M chips not supported.                                         

import inspect
b = inspect.signature(ps.generators.lattice_spheres)
print(b)

(shape: List, r: int = 5, spacing: int = None, offset: int = None, smooth: bool = True, lattice: Literal['sc', 'tri', 'fcc', 'bcc'] = 'sc')

radius

Controls the size of the spheres.

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

shape = [200, 200]
r=10
im1 = ps.generators.lattice_spheres(shape=shape, r=r)
ax[0].imshow(im1, interpolation='none')
ax[0].axis(False)
ax[0].set_title(f'radius = {r}')

r= 20
im2 = ps.generators.lattice_spheres(shape=shape, r=r)
ax[1].imshow(im2, interpolation='none')
ax[1].axis(False)
ax[1].set_title(f'radius = {r}');

spacing

The center-to-center spacing between the spheres. If this value is less than the sphere diamter then the spheres will overlap.

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

s = 35
im1 = ps.generators.lattice_spheres(shape=shape, r=r, spacing=s)
ax[0].imshow(im1, interpolation='none')
ax[0].axis(False)
ax[0].set_title(f'spacing = {s}')


s = 50
im2 = ps.generators.lattice_spheres(shape=shape, r=r, spacing=s)
ax[1].imshow(im2, interpolation='none')
ax[1].axis(False)
ax[1].set_title(f'spacing = {s}');

offset

Controls how far away from the edge the first sphere is located. The default is the sphere radius but it can be more or less depending on the desired effect:

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

o = 0
im1 = ps.generators.lattice_spheres(shape=shape, r=r, spacing=s, offset=o)
ax[0].imshow(im1, interpolation='none')
ax[0].axis(False)
ax[0].set_title(f'offset = {o}')

o = 25
im2 = ps.generators.lattice_spheres(shape=shape, r=r, spacing=s, offset=o)
ax[1].imshow(im2, interpolation='none')
ax[1].axis(False)
ax[1].set_title(f'offset = {o}');

lattice

Controls the arrange of spheres. In 2D the options are simple cubic (‘sc’) and triangular (‘tri’). Note that the offset and spacing apply to the outer spheres when lattice='tri'.

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

L='sc'
r = 10
im1 = ps.generators.lattice_spheres(shape=shape, r=r, spacing=s, offset=o, lattice=L)

ax[0].imshow(im1, interpolation='none')
ax[0].axis(False)
ax[0].set_title(f'lattice = {L}')

L='tri'
im2 = ps.generators.lattice_spheres(shape=shape, r=r, spacing=s, offset=o, lattice=L)

ax[1].imshow(im2, interpolation='none')
ax[1].axis(False)
ax[1].set_title(f'lattice = {L}');

In 3D the options are simple cubic (‘sc’), face centered cubic (‘fcc’), and body centered cubic (‘bcc’). It’s more difficult to visualize in 3D but PoreSpy has a basic function called “show_3D” that works if the image is small:

fig, ax = plt.subplots(1, 3, figsize=[9, 3])

r = 10
s = 25
shape = [100, 100, 100]
L = 'sc'
im1 = ps.generators.lattice_spheres(shape=shape, r=r, spacing=s, offset=o, lattice=L)
ax[0].imshow(ps.visualization.show_3D(im1))
ax[0].axis(False)
ax[0].set_title(f'lattice = {L}')

L = 'fcc'
im2 = ps.generators.lattice_spheres(shape=shape, r=r, spacing=s, offset=o, lattice=L)
ax[1].imshow(ps.visualization.show_3D(im2))
ax[1].axis(False)
ax[1].set_title(f'lattice = {L}');

L = 'bcc'
im3 = ps.generators.lattice_spheres(shape=shape, r=r, spacing=s, offset=o, lattice=L)
ax[2].imshow(ps.visualization.show_3D(im3))
ax[2].axis(False)
ax[2].set_title(f'lattice = {L}');