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
    VolumePart F129372
    ISBN (Electronic)0897917243
    DOIs
    StatePublished - Sep 1 1995
    Event11th Annual Symposium on Computational Geometry, SCG 1995 - Vancouver, Canada
    Duration: Jun 5 1995Jun 7 1995

    Other

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

    Fingerprint

    Visibility
    Polygon
    Half line
    Combinatorial Complexity
    Angle
    Simple Polygon
    Point Source
    Incidence

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Geometry and Topology
    • Computational Mathematics

    Cite this

    Aronov, B., Davis, A. R., Dey, T. K., Pal, S. P., & Prasad, D. C. (1995). Visibility with reflection. In Proceedings of the 11th Annual Symposium on Computational Geometry, SCG 1995 (Vol. Part F129372, pp. 316-325). Association for Computing Machinery. https://doi.org/10.1145/220279.220313

    Visibility with reflection. / Aronov, Boris; Davis, Alan R.; Dey, Tamal K.; Pal, Sudebkumar P.; Prasad, D. Chithra.

    Proceedings of the 11th Annual Symposium on Computational Geometry, SCG 1995. Vol. Part F129372 Association for Computing Machinery, 1995. p. 316-325.

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

    Aronov, B, Davis, AR, Dey, TK, Pal, SP & Prasad, DC 1995, Visibility with reflection. in Proceedings of the 11th Annual Symposium on Computational Geometry, SCG 1995. vol. Part F129372, Association for Computing Machinery, pp. 316-325, 11th Annual Symposium on Computational Geometry, SCG 1995, Vancouver, Canada, 6/5/95. https://doi.org/10.1145/220279.220313
    Aronov B, Davis AR, Dey TK, Pal SP, Prasad DC. Visibility with reflection. In Proceedings of the 11th Annual Symposium on Computational Geometry, SCG 1995. Vol. Part F129372. Association for Computing Machinery. 1995. p. 316-325 https://doi.org/10.1145/220279.220313
    Aronov, Boris ; Davis, Alan R. ; Dey, Tamal K. ; Pal, Sudebkumar P. ; Prasad, D. Chithra. / Visibility with reflection. Proceedings of the 11th Annual Symposium on Computational Geometry, SCG 1995. Vol. Part F129372 Association for Computing Machinery, 1995. pp. 316-325
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