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/81e2d06ae15acc3c1a02be95565cb3dde0dfe2345010c037a2c045e7577eb799.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/9291139a02d2ab7ead6fee309417e291eaf1d07e27f9a22600d9eb38e0a6e3dd.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/b19ec428befd273e87c147dc3721f7913f1b754a8db18c9954f1e29af3ae9537.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/44af1dc597939bd879b22bd5556e34f620ca7fc1e9f15ff8efe535a48c6ed5e3.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/e58a8d98e972375bca640dd6225eb1729a15811eee60577743a3665de4c5421f.png