# The union of balls and its dual shape

```@article{Edelsbrunner1993TheUO,
title={The union of balls and its dual shape},
author={Herbert Edelsbrunner},
journal={Discrete \& Computational Geometry},
year={1993},
volume={13},
pages={415-440}
}```
• H. Edelsbrunner
• Published 1 July 1993
• Mathematics
• Discrete & Computational Geometry
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.
425 Citations

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