Discrete & Computational Geometry

, Volume 13, Issue 1, pp 415-440

The union of balls and its dual shape

  • H. EdelsbrunnerAffiliated withDepartment of Computer Science, University of Illinois at Urbana-Champaign

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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.