The Alpha Shapes software library
(Edelsbrunner; Ban, Brady, Cheng, Kettner, Koehl, Zomorodian)

The notion of alpha shapes is a fundamental concept in the geometric approach to questions in molecular biology. Similarly, the Alpha Shapes software forms the basis for a number of computational experiments and developments within this ITR effort. The restructuring, maintenance, and extension of this software is an ongoing project. The goal is to provide a general software platform that facilitates quick proofs of concepts and also in-depth computational experiments. We expect, however, that specialized applications eventually lead to spin-off software that gains efficiency by narrowing the focus. The ProShape software implemented by Patrice Koehl is one example in which the speed needed for large-scale molecular dynamics simulations is achieved by a meticulous re-implementation of a subset of the features we find in the Alpha Shapes software. To facilitate more such spin-off projects, we plan to modularize the current software and to provide functions through a C++ library.

There are various new developments of software that extend and complement the current Alpha Shapes software. Some of these developments are fairly mature, while others just started out but already show their potential.

  • Area and volume derivatives (Koehl). These are currently available in the new ProShape software but need to be imported into the standard Alpha Shapes software.
  • Triangulated skin surfaces (Cheng). These smooth surfaces supplement the dual complex representation, but the current implementation is too slow to be offered as part of the Alpha Shapes software set.
  • Linking number (Zomorodian). The software computes the linking numbers of all alpha complexes in the filtration computed by the Alpha Shapes software. It provides an interesting analysis facility for large molecules.
  • Topological persistence (Zomorodian). The software filters out topological noise and reports and displays topologically significant features of molecular structures.
  • Molecular interfaces (Ban). Using alpha complexes, pockets, and topological persistence, this software displays interfaces in protein complexes as crumbled sheets of paper.