Discrete & Computational Geometry

, Volume 13, Issue 3–4, pp 415–440

The union of balls and its dual shape

  • H. Edelsbrunner

DOI: 10.1007/BF02574053

Cite this article as:
Edelsbrunner, H. Discrete Comput Geom (1995) 13: 415. doi:10.1007/BF02574053


Efficient algorithms are described for computing topological, combinatorial, and metric properties of the union of finitely many spherical balls in ℝd. These algorithms are based on a simplicial complex dual to a decomposition of the union of balls using Voronoi cells, and on short inclusion-exclusion formulas derived from this complex. The algorithms are most relevant in ℝ3 where unions of finitely many balls are commonly used as models of molecules.

Copyright information

© Springer-Verlag New York Inc. 1995

Authors and Affiliations

  • H. Edelsbrunner
    • 1
  1. 1.Department of Computer ScienceUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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