Discrete & Computational Geometry

, Volume 13, Issue 3–4, pp 415–440 | Cite as

The union of balls and its dual shape

  • H. Edelsbrunner


Efficient algorithms are described for computing topological, combinatorial, and metric properties of the union of finitely many spherical balls in ℝ d . 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.


Simplicial Complex Homology Group Voronoi Cell Convex Polyhedron Homotopy Equivalent 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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