The package can compute the sweep-plane volume function for a union of polytopes. A short paper about it can be found here

• ZIB-Report

The algorithm was also part of my master thesis and anyone who is interested in that, should contact me.

This package needs the python wrapper for ppl, which is called pplpy. Pplpy needs a specific version of gmpy2, see https://github.com/videlec/pplpy/issues/36, which has to be installed via pip install gmpy2==2.1.0a1 --no-binary ":all:" [--user] You can then install sweepvolume by invoking pip install /path/to/project

You might want to checkout pips -e option which allows a in development installation. Alternatively you can use the bash shell script setup.sh.

If you have installed the dependencies you can use the package as well but make sure that the toplevel directory is added to the PYTHONPATH. You can ensure that by using set_env to set up the environment that means source set_env

You can compute the sweep volume of a union of polytops for polytopes specified in a json by invoking

python sweepvolume/main.py --polytopesFile testing/test.json

Please take a look on the file testing/test.json for an example of the format in which the polytopes have to be specified. Polytopes in json should be given as lists of constraints whereby [a_1, ..., a_n, b] corresponds to the constraint a_1 x_1 + ... + a_n x_n + b <= 0.

This package contains a two-stage algorithm.

• In the first stage you create a cell decomposition object. Examples for that are to be found in testing/fixtures.py
• Afterwards you can call

from sweepvolume import sweep
s = Sweep(cell_decomposition.events, sweep_plane=None)

You can specify the direction of the sweep through the parameter sweep_plane. If no sweep-plane is given, a random one is chosen. After you created a sweep-object, you can calculate the volume up to the sweep-plane at the time lam

volume = s.calculate_volume(lam=None)

If no lam is given the volume of the whole union of polytopes is calculated.

The plotting code is very unorganized and dirty, since I did not have the time to clean up. You can plot your cell decomposition (if they're 2D or 3D) by

from sweepvolume.util import plot_polytopes_and_cut
plot_polytopes_and_cut(cell_decomposition)

sweepvolume is distributed under the terms of the GNU General Public License (GPL) published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version. See http://www.gnu.org/licenses/.