lattice_spheres#

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

import matplotlib.pyplot as plt
import porespy as ps
import inspect
b = inspect.signature(ps.generators.lattice_spheres)
print(b)
(shape: List[int], r: int, spacing: int = None, offset: int = None, smooth: bool = True, lattice: str = '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}');
../../../_images/d84b50a36c4c9b4a2a9dbaade8197e1e7096d7444191bb70418ebd19077659c6.png

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}');
../../../_images/43d0848efc5ccd31092e710ed42870411e6a1c4564fcce2a3a1f684ec6c12fb5.png

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}');
../../../_images/3f4762a4fffd28196758ae0fa673e5222908594705fb1cb9ae265ba40ff64ac3.png

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}');
../../../_images/451e6bf0dc9af51f6bfb84f892552894bd2fc1ae594186e97f22d15aa882cf7f.png

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}');
../../../_images/33ead5b4a78d3fb1f1396a64aed83549378f9920ab737cc7d4ddda927665c999.png