Spack

Spack

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Code available_ on Github, and documentation_ at Read the Docs.

.. _Code available: https://github.com/wackywendell/spack

.. _documentation: https://pyspack.readthedocs.org

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 <http://www.numpy.org/>_ at a minimum, which you will probably want to have installed before installing this. Optionally, you may want vapory <https://github.com/Zulko/vapory>_ and povray <http://povray.org/>_ are required for making pretty pictures, and Voronoi tessellations are provided by tess <https://tess.readthedocs.org>_. The optional dependencies can be installed at any time, at which point the associated methods (:meth:~.Packing.scene and :meth:~.Packing.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

.. _github: https://www.github.com/wackywendell/tess

Example Usage

Make a :class:~spack.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.

.. image:: example-packing.png :align: center :alt: .. image:: docs/example-packing.png :align: center :alt:

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) # doctest: +SKIP

And this is the output:

.. image:: example-packing.gif :align: center :alt: .. image:: docs/example-packing.gif :align: center :alt:

There are a few other methods for things like finding the backbone of the packing (:meth:~.Packing.backbone), the adjacency matrix (:meth:~.Packing.neighbors), or getting the Voronoi tessellation (:meth:~.Packing.tess, requires tess_). See the :doc:api for more details.

.. _tess: https://tess.readthedocs.org