Determining sector visibility of a polygon

B. Bhattacharya, D. G. Kirkpatrick, Godfried Toussaint

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    We consider a generalization of notions of external visibility of simple polygons, namely weak external visibility, weak external visibility from a line and monotonicity, that we call sector visibility. Informally, sector visibility addresses the question of external visibility along rays (or sight lines) whose angles are restricted to a sector (wedge) of specified width u. This provides an interesting measure of the degree of external visibility of a polygon. Our framework also permits a unification and extension of a number of previously unrelated results. Finally, our results uncover a curious complexity discontinuity in this family of problems; algorithms are θ(n) when γ < φ or γ = 2φr, but require ω(n log n) time (at least), when φ < u < 2φ.

    Original languageEnglish (US)
    Title of host publicationProceedings of the 5th Annual Symposium on Computational Geometry, SCG 1989
    PublisherAssociation for Computing Machinery
    Pages247-254
    Number of pages8
    VolumePart F130124
    ISBN (Electronic)0897913183
    DOIs
    StatePublished - Jun 5 1989
    Event5th Annual Symposium on Computational Geometry, SCG 1989 - Saarbruchen, Germany
    Duration: Jun 5 1989Jun 7 1989

    Other

    Other5th Annual Symposium on Computational Geometry, SCG 1989
    CountryGermany
    CitySaarbruchen
    Period6/5/896/7/89

    Fingerprint

    Visibility
    Polygon
    Sector
    Simple Polygon
    Line
    Wedge
    Unification
    Monotonicity
    Half line
    Discontinuity
    Angle

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Geometry and Topology
    • Computational Mathematics

    Cite this

    Bhattacharya, B., Kirkpatrick, D. G., & Toussaint, G. (1989). Determining sector visibility of a polygon. In Proceedings of the 5th Annual Symposium on Computational Geometry, SCG 1989 (Vol. Part F130124, pp. 247-254). Association for Computing Machinery. https://doi.org/10.1145/73833.73860

    Determining sector visibility of a polygon. / Bhattacharya, B.; Kirkpatrick, D. G.; Toussaint, Godfried.

    Proceedings of the 5th Annual Symposium on Computational Geometry, SCG 1989. Vol. Part F130124 Association for Computing Machinery, 1989. p. 247-254.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Bhattacharya, B, Kirkpatrick, DG & Toussaint, G 1989, Determining sector visibility of a polygon. in Proceedings of the 5th Annual Symposium on Computational Geometry, SCG 1989. vol. Part F130124, Association for Computing Machinery, pp. 247-254, 5th Annual Symposium on Computational Geometry, SCG 1989, Saarbruchen, Germany, 6/5/89. https://doi.org/10.1145/73833.73860
    Bhattacharya B, Kirkpatrick DG, Toussaint G. Determining sector visibility of a polygon. In Proceedings of the 5th Annual Symposium on Computational Geometry, SCG 1989. Vol. Part F130124. Association for Computing Machinery. 1989. p. 247-254 https://doi.org/10.1145/73833.73860
    Bhattacharya, B. ; Kirkpatrick, D. G. ; Toussaint, Godfried. / Determining sector visibility of a polygon. Proceedings of the 5th Annual Symposium on Computational Geometry, SCG 1989. Vol. Part F130124 Association for Computing Machinery, 1989. pp. 247-254
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