language: en

A Perturbation Scheme for Spherical Arrangements with Application to Molecular Modeling

Dan Halperin
Tel Aviv University
Christian R. Shelton
Massachusetts Institute of Technology
July 31, 1997

Abstract We describe a software package for computing and manipulating the subdivision of a sphere by a collection of (not necessarily great) circles and for computing the boundary surface of the union of spheres. We present problems that arise in the implementation of the software and the solutions that we have found for them. At the core of the paper is a novel perturbation scheme to overcome degeneracies and precision problems in computing spherical arrangements while using floating point arithmetic. The scheme is relatively simple, it balances between the efficiency of computation and the magnitude of the perturbation, and it performs well in practice. We report and discuss experimental results. Our package is a major component in a larger package aimed to support geometric queries on molecular models; it is currently employed by chemists working in `rational drug design.' The spherical subdivisions are used to construct a geometric model of a molecule where each sphere represents an atom. We also give an overview of the molecular modeling package and detail additional features and implementation issues.

[This work has been supported in part by a grant from Pfizer Central Research. Dan Halperin has also been supported by an Alon Fellowship, by ESPRIT IV LTR Project No. 21957 (CGAL), and by the Hermann Minkowski]

- Minerva Center for Geometry at Tel Aviv University.
Department of Computer Science, Tel Aviv University,
Tel Aviv 69978, Israel.
E-mail: halperin@math.tau.ac.il.
Department of Computer Science, MIT,
Cambridge, MA 02139.
E-mail: cshelton@ai.mit.edu.

[Part of the work on this paper was carried out while Christian Shelton was at the Department of Computer Science, Stanford University]