{"article_processing_charge":"No","date_created":"2018-12-11T12:06:31Z","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.","doi":"10.1007/BF02574053","publication_status":"published","author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"}],"page":"415 - 440","date_updated":"2022-06-27T08:14:48Z","month":"12","issue":"1","extern":"1","oa":1,"title":"The union of balls and its dual shape","publist_id":"2095","day":"01","date_published":"1995-12-01T00:00:00Z","status":"public","volume":13,"intvolume":"        13","type":"journal_article","year":"1995","quality_controlled":"1","abstract":[{"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.","lang":"eng"}],"_id":"4028","citation":{"ista":"Edelsbrunner H. 1995. The union of balls and its dual shape. Discrete &#38; Computational Geometry. 13(1), 415–440.","chicago":"Edelsbrunner, Herbert. “The Union of Balls and Its Dual Shape.” <i>Discrete &#38; Computational Geometry</i>. Springer, 1995. <a href=\"https://doi.org/10.1007/BF02574053\">https://doi.org/10.1007/BF02574053</a>.","short":"H. Edelsbrunner, Discrete &#38; Computational Geometry 13 (1995) 415–440.","mla":"Edelsbrunner, Herbert. “The Union of Balls and Its Dual Shape.” <i>Discrete &#38; Computational Geometry</i>, vol. 13, no. 1, Springer, 1995, pp. 415–40, doi:<a href=\"https://doi.org/10.1007/BF02574053\">10.1007/BF02574053</a>.","ieee":"H. Edelsbrunner, “The union of balls and its dual shape,” <i>Discrete &#38; Computational Geometry</i>, vol. 13, no. 1. Springer, pp. 415–440, 1995.","apa":"Edelsbrunner, H. (1995). The union of balls and its dual shape. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/BF02574053\">https://doi.org/10.1007/BF02574053</a>","ama":"Edelsbrunner H. The union of balls and its dual shape. <i>Discrete &#38; Computational Geometry</i>. 1995;13(1):415-440. doi:<a href=\"https://doi.org/10.1007/BF02574053\">10.1007/BF02574053</a>"},"publisher":"Springer","oa_version":"Published Version","scopus_import":"1","publication_identifier":{"issn":["0179-5376"]},"language":[{"iso":"eng"}],"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publication":"Discrete & Computational Geometry","main_file_link":[{"open_access":"1","url":"https://link.springer.com/article/10.1007/BF02574053"}],"article_type":"original"}