Documentation of the pw85 library

This library implements the “contact function” defined by Perram and Wertheim (J. Comp. Phys. 58(3), 409–416, DOI:10.1016/0021-9991(85)90171-8) for two ellipsoids. Given two ellipsoids, this function returns the square of the common factor by which both ellipsoids must be scaled (their centers being fixed) in order to be tangentially in contact.

This library is released under a BSD 3-Clause License.

A PDF version of this documentation can be dowloaded here.

Contents

• Overview
  • Introduction
  • The contact function of Perram and Wertheim [PW85]
  • Features of the overlap test
  • Implementation
  • Extensions
  • Acknowledgements
• Installation
  • Installing the C++ library
  • Installing the Python bindings
  • Building the documentation
• Tutorial
  • Python tutorial
  • C++ tutorial
• Theory
  • Mathematical representation of ellipsoids
  • The contact function of two ellipsoids
  • Geometric interpretation
• Implementation of the function f
  • Implementation #1: using Cholesky decompositions
  • Implementation #2: using rational functions
  • Comparison of the two implementations
• Optimization of the function f
• Testing the implementation of the contact function
• The C++ API
  • Representation of vectors and matrices
  • API
• The python API