Packing Fraction

This app calculates the packing fraction of a 2D box containing circles via the equation

Packing Fraction = (Number of circles x Area of one circle) / Total area of the box

The packing fraction is calulated via a monte carlo method where a given number of sample circles are randomly generated within the box and removed if overlapping an existing circle.

Prerequisites

In order to run the app you will require the following to be installed.

• pipenv = 2023.2.18
• python = 3.8.15

Running the app

Firstly, start the virtual env:

pipenv shell

and install the dependencies (see Pipfile)

pipenv install

Then run the app

• Serial app: The serial app can be treated like any other python module, i.e. in a python script you can run

  from serial_app import main
  main(width=100, height=100, radius=1, num_of_samples=1000)

• Parallel app: The parallel app must be ran slightly differently in order to allow parallelisation.

  mpiexec -np <number_of_processors> python -m mpi4py parallel_app.py
  

  Therefore, to alter the inputs into the parallel app, update the call to main in parallel_app.py

Outputs

The program should output two graphs. One graph displays the circles within the box (coordinates.png) and the other the packing fraction vs the number of samples used (PF_vs_samples.png).

Tests

To run the tests, first activate the virtual env

pipenv shell

then, run the tests

python -m unittest