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International Conference on Foundations of Software Technology and Theoretical Computer Science

FSTTCS 1999: Foundations of Software Technology and Theoretical Computer Science pp 1–21Cite as

Recent Developments in the Theory of Arrangements of Surfaces

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1738))

Abstract

We review recent progress in the study of arrangements of surfaces in higher dimensions. This progress involves new and nearly tight bounds on the complexity of lower envelopes, single cells, zones, and other substructures in such arrangements, and the design of efficient algorithms (near optimal in the worst case) for constructing and manipulating these structures. We then present applications of the new results to a variety of problems in computational geometry and its applications, including motion planning, Voronoi diagrams, union of geometric objects, visibility, and geometric optimization.

Workon this paper has been supported by NSF Grant CCR-97-32101, by a grant from the U.S.-Israeli Binational Science Foundation, by the ESPRIT IV LTR project No. 21957 (CGAL), and by the Hermann Minkowski—MINERVA Center for Geometry at Tel Aviv University.

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Authors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, Tel Aviv, 69978, Israel

    Micha Sharir

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

    Micha Sharir

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  1. Micha Sharir
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Editors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology, Chennai, 600036, India

    C. Pandu Rangan

  2. Institute of Mathematical Sciences C.I.T. Campus, Chennai, 600113, India

    V. Raman  & R. Ramanujam  & 

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Sharir, M. (1999). Recent Developments in the Theory of Arrangements of Surfaces. In: Rangan, C.P., Raman, V., Ramanujam, R. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1999. Lecture Notes in Computer Science, vol 1738. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46691-6_1

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  • DOI: https://doi.org/10.1007/3-540-46691-6_1

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