TY - JOUR

T1 - A perturbation scheme for spherical arrangements with application to molecular modeling

AU - Halperin, Dan

AU - Shelton, Christian R.

N1 - Funding Information:
It has been found out and repeatedly rediscovered that there is a huge gap between geometric algorithms as they are described in most theoretical papers and their implementation in software. Two ¢: This work has been supported in part by a grant from Pfizer Central Research. Dan Halperin has also been supported in part by an Alon Fellowship, by ESPRIT IV LTR Project No. 21957 (CGAL), by the USA-Israel Binational Science Foundation, by The Israel Science Foundation founded by the Israel Academy of Sciences and Humanities, and by the Hermann Minkowski-Minerva Center for Geometry at Tel Aviv University. Part of the work on this paper was carried out while Christian Shelton was at the Department of Computer Science, Stanford University. * Corresponding author. E-mail: cshelton@ai.mit.edu. 1 E-mail: halperin@math.tau.ac.il.

PY - 1998/7

Y1 - 1998/7

N2 - 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. In one O(n) time pass through the data, it perturbs the inputs necessary to insure no potential degeneracies and then passes the perturbed inputs on to the geometric algorithm. 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.

AB - 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. In one O(n) time pass through the data, it perturbs the inputs necessary to insure no potential degeneracies and then passes the perturbed inputs on to the geometric algorithm. 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.

UR - http://www.scopus.com/inward/record.url?scp=0000231709&partnerID=8YFLogxK

U2 - 10.1016/S0925-7721(98)00014-5

DO - 10.1016/S0925-7721(98)00014-5

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AN - SCOPUS:0000231709

VL - 10

SP - 273

EP - 287

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

SN - 0925-7721

IS - 4

ER -