Visibility queries and maintenance in simple polygons

Boris Aronov, L. J. Guibas, M. Teichmann, L. Zhang

    Research output: Contribution to journalArticle

    Abstract

    In this paper we explore some novel aspects of visibility for stationary and moving points inside a simple polygon P. We provide a mechanism for expressing the visibility polygon from a point as the disjoint union of logarithmically many canonical pieces using a quadratic-space data structure. This allows us to report visibility polygons in time proportional to their size, but without the cubic space overhead of earlier methods. The same canonical decomposition can be used to determine visibility within a frustum, or to compute various attributes of the visibility polygon efficiently. By exploring the connection between visibility polygons and shortest-path trees, we obtain a kinetic algorithm that can track the visibility polygon as the viewpoint moves along polygonal paths inside P, at a polylogarithmic cost per combinatorial change in the visibility or in the flight plan of the point. The combination of the static and kinetic algorithms leads to a new static algorithm in which we can trade off space for increased overhead in the query time. As another application, we obtain an algorithm which computes the weak visibility polygon from a query segment inside P in output-sensitive time.

    Original languageEnglish (US)
    Pages (from-to)461-483
    Number of pages23
    JournalDiscrete and Computational Geometry
    Volume27
    Issue number4
    DOIs
    StatePublished - 2002

    Fingerprint

    Simple Polygon
    Visibility
    Maintenance
    Query
    Polygon
    Kinetics
    Shortest Path Tree
    Truncated cone or frustum
    Canonical Decomposition
    Data structures
    Data Structures
    Disjoint
    Union
    Trade-offs
    Directly proportional
    Attribute
    Decomposition
    Path
    Output

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computational Theory and Mathematics
    • Discrete Mathematics and Combinatorics
    • Geometry and Topology

    Cite this

    Visibility queries and maintenance in simple polygons. / Aronov, Boris; Guibas, L. J.; Teichmann, M.; Zhang, L.

    In: Discrete and Computational Geometry, Vol. 27, No. 4, 2002, p. 461-483.

    Research output: Contribution to journalArticle

    Aronov, B, Guibas, LJ, Teichmann, M & Zhang, L 2002, 'Visibility queries and maintenance in simple polygons', Discrete and Computational Geometry, vol. 27, no. 4, pp. 461-483. https://doi.org/10.1007/s00454-001-0089-9
    Aronov, Boris ; Guibas, L. J. ; Teichmann, M. ; Zhang, L. / Visibility queries and maintenance in simple polygons. In: Discrete and Computational Geometry. 2002 ; Vol. 27, No. 4. pp. 461-483.
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