--- _id: '4028' abstract: - lang: eng text: 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 R(3) where unions of finitely many balls are commonly used as models of molecules. acknowledgement: 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. article_processing_charge: No article_type: original author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 citation: ama: Edelsbrunner H. The union of balls and its dual shape. Discrete & Computational Geometry. 1995;13(1):415-440. doi:10.1007/BF02574053 apa: Edelsbrunner, H. (1995). The union of balls and its dual shape. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/BF02574053 chicago: Edelsbrunner, Herbert. “The Union of Balls and Its Dual Shape.” Discrete & Computational Geometry. Springer, 1995. https://doi.org/10.1007/BF02574053. ieee: H. Edelsbrunner, “The union of balls and its dual shape,” Discrete & Computational Geometry, vol. 13, no. 1. Springer, pp. 415–440, 1995. ista: Edelsbrunner H. 1995. The union of balls and its dual shape. Discrete & Computational Geometry. 13(1), 415–440. mla: Edelsbrunner, Herbert. “The Union of Balls and Its Dual Shape.” Discrete & Computational Geometry, vol. 13, no. 1, Springer, 1995, pp. 415–40, doi:10.1007/BF02574053. short: H. Edelsbrunner, Discrete & Computational Geometry 13 (1995) 415–440. date_created: 2018-12-11T12:06:31Z date_published: 1995-12-01T00:00:00Z date_updated: 2022-06-27T08:14:48Z day: '01' doi: 10.1007/BF02574053 extern: '1' intvolume: ' 13' issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://link.springer.com/article/10.1007/BF02574053 month: '12' oa: 1 oa_version: Published Version page: 415 - 440 publication: Discrete & Computational Geometry publication_identifier: issn: - 0179-5376 publication_status: published publisher: Springer publist_id: '2095' quality_controlled: '1' scopus_import: '1' status: public title: The union of balls and its dual shape type: journal_article user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17 volume: 13 year: '1995' ...