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