Spack¶
Code available on Github, and documentation at Read the Docs.
A 2D or 3D sphere packing analysis package¶
This package exists to enable fast, simple, and easy analysis of packings of spheres (3D) and disks (2D). It was developed for use in a Granular Materials lab, so some of the methods reflect that.
Installation¶
This library requires numpy at a minimum, which you will probably want to have installed
before installing this. Optionally, you may want vapory and povray are required for making pretty pictures, and Voronoi tessellations are provided by tess. The optional dependencies can be installed at any time, at which point the associated methods (scene() and tess()) will work.
To install, use pip (or easy_install):
pip install --user spack
Or to install from Github:
pip install --user git+git://github.com/wackywendell/spack@master
Example Usage¶
Make a Packing:
>>> from spack import Packing
>>> from numpy import array, pi
>>> L = 2.0066668050219723
>>> diameters = array([ 0.96, 0.97, 0.98, 0.99, 1. , 1.01, 1.02, 1.03, 1.04])
>>> locs = array([[ 1.40776762, 1.26647724, 0.73389219],
... [ 0.58704249, 2.11399 , 1.52956579],
... [ 1.75917911, 0.54290089, 1.27577478],
... [ 2.13750384, 0.87508242, 0.21938647],
... [ 1.07283961, 0.87692084, 1.9060841 ],
... [ 0.09550267, 1.94404465, 0.56463369],
... [ 1.07636871, 2.1942971 , 0.63752152],
... [ 0.49922725, 1.20002224, 1.13360082],
... [-0.27724757, 1.62152603, 1.67262247]])
>>> pack = Packing(locs, diameters, L=L)
How many contacts are in my packing?
>>> pack.contacts()
Contacts(Nc=25, stable=25, floaters=0)
>>> # 25 contacts found
>>> # 25 contacts required for stability (for a packing of 9 particles)
>>> # 0 floaters
What are its highest resonant frequencies?
>>> freqs = pack.DM_freqs()
>>> for f in reversed(sorted(freqs)[-4:]):
... print('{:.4f}'.format(f))
0.7018
0.6717
0.6416
0.6375
What does it look like? (requires vapory package and povray program)
>>> size = 400
>>> sc = pack.scene(rot=pi/4, camera_dist=2, cmap='autumn')
>>> sc.render('example-packing.png', width=size, height=size, antialiasing=0.0001)
Colors indicate diameter, with floaters drawn in gray.
Let’s look at all sides, using moviepy:
>>> from moviepy.editor import VideoClip
>>> import moviepy.editor as mpy
>>>
>>> duration = 10
>>> def make_frame(t):
... return (
... pack.scene(rot=(t/duration + .125)*2.*pi,
... camera_dist=2, cmap='autumn', bgcolor=[1,1,1])
... .render(width=size, height=size, antialiasing=0.001)
... )
>>> vc = VideoClip(make_frame, duration=duration)
>>>
>>> vc.write_gif("example-packing.gif",fps=24)
And this is the output:
There are a few other methods for things like finding the backbone of the packing (backbone()), the adjacency matrix (neighbors()), or getting the Voronoi tessellation (tess(), requires tess). See the Reference for more details.