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The upper envelope of piecewise linear functions: Algorithms and applications

Discrete & Computational Geometry volume 4, pages 311–336 (1989)Cite this article

Abstract

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.

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Authors and Affiliations

  1. Department of Computer Science, University of Illinois at Urbana-Champaign, 61801, Urbana, IL, USA

    Herbert Edelsbrunner

  2. Computer Science Department, Stanford University, 94305, Stanford, CA, USA

    Leonidas J. Guibas

  3. DEC Systems Research Center, 94301, Palo Alto, CA, USA

    Leonidas J. Guibas

  4. Courant Institute of Mathematical Sciences, New York University, 10012, New York, NY, USA

    Micha Sharir

  5. School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel

    Micha Sharir

Authors
  1. Herbert Edelsbrunner
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  2. Leonidas J. Guibas
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  3. Micha Sharir
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Additional information

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.

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Edelsbrunner, H., Guibas, L.J. & Sharir, M. The upper envelope of piecewise linear functions: Algorithms and applications. Discrete Comput Geom 4, 311–336 (1989). https://doi.org/10.1007/BF02187733

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  • DOI: https://doi.org/10.1007/BF02187733

Keywords

  • Line Segment
  • Convex Hull
  • Voronoi Diagram
  • Piecewise Linear Function
  • Combinatorial Complexity