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Visibility and intersectin problems in plane geometry

Published: 01 June 1985 Publication History
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  • Abstract

    We develop new data structures for solving various visibility and intersection problems about a simple polygon P on n vertices. Among our results are a simple Ο(n log n) algorithm for computing the illuminated subpolygon of P from a luminous side, and an Ο(log n) algorithm for determining which side of P is first hit by a bullet fired from a point in a certain direction. The latter method requires preprocessing on P which takes time Ο(n log n) and space Ο(n). Our main new tool in attacking these problems is geometric duality on the two-sided plane.

    References

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    [1] Chazelle, B. A theorem on polygon cutting with applications , Proc. 23rd Annual FOCS Symp., 339-349, 1982.
    [2]
    [2] Chazelle, B. Computing on a free tree via complexity preserving mappings, Proc. 25th Annual FOCS Symp., 358- 368, 1984.
    [3]
    [3] Chazelle, B., and Guibas, L.J., Fractional Cascading: A data structuring technique with geometric applications, Efficient Algorithms workshop, Oberwalfach, W. Germany, 1984. To appear in the Proceedings of the 1985 ICALP, Nafplion, Greece.
    [4]
    [4] El Gindy, H.A. An efficient algorithm for computing the weak visibility polygon from an edge in simple polygons, unpublished manuscript, McGill University, 1984.
    [5]
    [5] Guibas, L., Ramshaw, L., and Stolfi, J. A kinetic framework for computational geometry, Proc. 24th Annual FOCS Symp., pp. 100-111, 1983.
    [6]
    [6] Lee, D.T., and Lin, A., Computing the visibility polygon from an edge, unpublished manuscript, Northwestern Univ., 1984.
    [7]
    [7] Edelsbrunner, H., Guibas, L., and Stolfi, J., Optimal point location in monotone subdivisions. DEC/SRC Technical Report #2, 1984.

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    cover image ACM Conferences
    SCG '85: Proceedings of the first annual symposium on Computational geometry
    June 1985
    322 pages
    ISBN:0897911636
    DOI:10.1145/323233
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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    New York, NY, United States

    Publication History

    Published: 01 June 1985

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    • (2023)A Sub-quadratic Time Algorithm for Computing the Beacon Kernel of Simple PolygonsComputing and Combinatorics10.1007/978-3-031-49193-1_6(69-81)Online publication date: 9-Dec-2023
    • (2014)On the Performance of Triangulation-Based Multiple Shooting Method for 2D Geometric Shortest Path ProblemsTransactions on Large-Scale Data- and Knowledge-Centered Systems XVI10.1007/978-3-662-45947-8_4(45-56)Online publication date: 17-Dec-2014
    • (2010)Finding the minimum-distance schedule for a boundary searcher with a flashlightProceedings of the 9th Latin American conference on Theoretical Informatics10.1007/978-3-642-12200-2_9(84-95)Online publication date: 19-Apr-2010
    • (2008)Query point visibility computation in polygons with holesComputational Geometry: Theory and Applications10.1016/j.comgeo.2007.02.00539:2(78-90)Online publication date: 1-Feb-2008
    • (2006)Where to Build a Door2006 IEEE/RSJ International Conference on Intelligent Robots and Systems10.1109/IROS.2006.281873(4084-4090)Online publication date: Oct-2006
    • (2005)Efficient computation of query point visibility in polygons with holesProceedings of the twenty-first annual symposium on Computational geometry10.1145/1064092.1064140(314-320)Online publication date: 6-Jun-2005
    • (2005)The visibility diagram: A data structure for visibility problems and motion planningSWAT 9010.1007/3-540-52846-6_81(97-110)Online publication date: 8-Jun-2005
    • (2005)Upper envelope onion peelingSWAT 9010.1007/3-540-52846-6_105(368-379)Online publication date: 8-Jun-2005
    • (2005)An optimal algorithm for the boundary of a cell in a union of raysGeometry and Robotics10.1007/3-540-51683-2_34(247-274)Online publication date: 31-May-2005
    • (2005)Computing the kernel of a point set in a polygonAlgorithms and Data Structures10.1007/3-540-51542-9_12(135-146)Online publication date: 26-May-2005
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