{"issue":"1","oa_version":"Published Version","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02187733","open_access":"1"}],"title":"The upper envelope of piecewise linear functions: Algorithms and applications","quality_controlled":"1","intvolume":"         4","language":[{"iso":"eng"}],"publist_id":"2038","date_published":"1989-12-01T00:00:00Z","publisher":"Springer","article_type":"original","year":"1989","day":"01","publication_status":"published","publication":"Discrete & Computational Geometry","abstract":[{"lang":"eng","text":"This paper studies applications of envelopes of piecewise linear functions to problems in computational geometry. Among these applications we find problems involving hidden line/surface elimination, motion planning, transversals of polytopes, and a new type of Voronoi diagram for clusters of points. All results are either combinatorial or computational in nature. They are based on the combinatorial analysis in two companion papers [PS] and [E2] and a divide-and-conquer algorithm for computing envelopes described in this paper."}],"author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Guibas, Leonidas","first_name":"Leonidas","last_name":"Guibas"},{"first_name":"Micha","full_name":"Sharir, Micha","last_name":"Sharir"}],"doi":"10.1007/BF02187733","_id":"4081","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"volume":4,"date_updated":"2022-02-10T15:53:48Z","type":"journal_article","extern":"1","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","oa":1,"page":"311 - 336","status":"public","citation":{"ieee":"H. Edelsbrunner, L. Guibas, and M. Sharir, “The upper envelope of piecewise linear functions: Algorithms and applications,” <i>Discrete &#38; Computational Geometry</i>, vol. 4, no. 1. Springer, pp. 311–336, 1989.","mla":"Edelsbrunner, Herbert, et al. “The Upper Envelope of Piecewise Linear Functions: Algorithms and Applications.” <i>Discrete &#38; Computational Geometry</i>, vol. 4, no. 1, Springer, 1989, pp. 311–36, doi:<a href=\"https://doi.org/10.1007/BF02187733\">10.1007/BF02187733</a>.","ama":"Edelsbrunner H, Guibas L, Sharir M. The upper envelope of piecewise linear functions: Algorithms and applications. <i>Discrete &#38; Computational Geometry</i>. 1989;4(1):311-336. doi:<a href=\"https://doi.org/10.1007/BF02187733\">10.1007/BF02187733</a>","short":"H. Edelsbrunner, L. Guibas, M. Sharir, Discrete &#38; Computational Geometry 4 (1989) 311–336.","apa":"Edelsbrunner, H., Guibas, L., &#38; Sharir, M. (1989). The upper envelope of piecewise linear functions: Algorithms and applications. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/BF02187733\">https://doi.org/10.1007/BF02187733</a>","chicago":"Edelsbrunner, Herbert, Leonidas Guibas, and Micha Sharir. “The Upper Envelope of Piecewise Linear Functions: Algorithms and Applications.” <i>Discrete &#38; Computational Geometry</i>. Springer, 1989. <a href=\"https://doi.org/10.1007/BF02187733\">https://doi.org/10.1007/BF02187733</a>.","ista":"Edelsbrunner H, Guibas L, Sharir M. 1989. The upper envelope of piecewise linear functions: Algorithms and applications. Discrete &#38; Computational Geometry. 4(1), 311–336."},"date_created":"2018-12-11T12:06:50Z","month":"12","article_processing_charge":"No","acknowledgement":"Work on this paper by the first author has been supported by Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862. Work by the third author has been supported by the Office of Naval Research Grant N00014-82-K-0381, National Science Foundation Grant No. NSF-DCR-83-20085, by grants from the Digital Equipment Corporation and the IBM Corporation, and by a research grant from NCRD, the Israeli National Council for Research and Development."}