{"page":"311 - 336","article_type":"original","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."}],"language":[{"iso":"eng"}],"volume":4,"publist_id":"2038","publisher":"Springer","main_file_link":[{"open_access":"1","url":"https://link.springer.com/article/10.1007/BF02187733"}],"year":"1989","_id":"4081","date_created":"2018-12-11T12:06:50Z","oa_version":"Published Version","publication":"Discrete & Computational Geometry","month":"12","title":"The upper envelope of piecewise linear functions: Algorithms and applications","oa":1,"day":"01","citation":{"ista":"Edelsbrunner H, Guibas L, Sharir M. 1989. The upper envelope of piecewise linear functions: Algorithms and applications. Discrete & Computational Geometry. 4(1), 311–336.","ama":"Edelsbrunner H, Guibas L, Sharir M. The upper envelope of piecewise linear functions: Algorithms and applications. Discrete & Computational Geometry. 1989;4(1):311-336. doi:10.1007/BF02187733","short":"H. Edelsbrunner, L. Guibas, M. Sharir, Discrete & Computational Geometry 4 (1989) 311–336.","apa":"Edelsbrunner, H., Guibas, L., & Sharir, M. (1989). The upper envelope of piecewise linear functions: Algorithms and applications. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/BF02187733","chicago":"Edelsbrunner, Herbert, Leonidas Guibas, and Micha Sharir. “The Upper Envelope of Piecewise Linear Functions: Algorithms and Applications.” Discrete & Computational Geometry. Springer, 1989. https://doi.org/10.1007/BF02187733.","mla":"Edelsbrunner, Herbert, et al. “The Upper Envelope of Piecewise Linear Functions: Algorithms and Applications.” Discrete & Computational Geometry, vol. 4, no. 1, Springer, 1989, pp. 311–36, doi:10.1007/BF02187733.","ieee":"H. Edelsbrunner, L. Guibas, and M. Sharir, “The upper envelope of piecewise linear functions: Algorithms and applications,” Discrete & Computational Geometry, vol. 4, no. 1. Springer, pp. 311–336, 1989."},"type":"journal_article","date_updated":"2022-02-10T15:53:48Z","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","article_processing_charge":"No","status":"public","issue":"1","publication_status":"published","extern":"1","date_published":"1989-12-01T00:00:00Z","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.","doi":"10.1007/BF02187733","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"intvolume":" 4","quality_controlled":"1","author":[{"first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"first_name":"Leonidas","last_name":"Guibas","full_name":"Guibas, Leonidas"},{"last_name":"Sharir","full_name":"Sharir, Micha","first_name":"Micha"}]}