, Volume 13, Issue 1, pp 415-440

The union of balls and its dual shape

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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.

This work is supported by the National Science Foundation, under Grant ASC-9200301, and the Alan T. Waterman award, Grant CCR-9118874. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the author and do not necessarily reflect the view of the National Science Foundation.