Visibility with reflection

Boris Aronov, Alan R. Davis, Tamal K. Dey, Sudebkumar P. Pal, D. Chithra Prasad

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

    Abstract

    We extend the concept of the polygon visible from a source point S in a simple polygon by considering visibility with two types of reflection, specular and diffuse. In specular reflection a light ray reflects from an edge of the polygon according to Snell's law: the angle of incidence equals the angle of reflection. In diffuse reflection a light ray reflects from an edge of the polygon in all inward directions. Several geometric and combinatorial properties of visibility polygons under these two types of reflection are revealed, when at most one reflection is permitted. We show that the visibility polygon Vs(S) under specular reflection may be non-simple, while the visibility polygon Vd(S) under diffuse reflection is always simple. We present a 9(n2) worst case bound on the combinatorial complexity of both Vs(S) and Vd(S) and describe simple 0(n2 log2 n) time algorithms for constructing the sets.

    Original languageEnglish (US)
    Title of host publicationProceedings of the 11th Annual Symposium on Computational Geometry, SCG 1995
    PublisherAssociation for Computing Machinery
    Pages316-325
    Number of pages10
    ISBN (Electronic)0897917243
    DOIs
    StatePublished - Sep 1 1995
    Event11th Annual Symposium on Computational Geometry, SCG 1995 - Vancouver, Canada
    Duration: Jun 5 1995Jun 7 1995

    Publication series

    NameProceedings of the Annual Symposium on Computational Geometry
    VolumePart F129372

    Other

    Other11th Annual Symposium on Computational Geometry, SCG 1995
    CountryCanada
    CityVancouver
    Period6/5/956/7/95

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Geometry and Topology
    • Computational Mathematics

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