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    Reachability by paths of bounded curvature in a convex polygon

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    Type
    Article
    Authors
    Ahn, Heekap
    Cheong, Otfried
    Matoušek, Jiřǐ
    Vigneron, Antoine E. cc
    KAUST Department
    Visual Computing Center (VCC)
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Computer Science Program
    Geometric Algorithms Group
    Date
    2012-01
    Permanent link to this record
    http://hdl.handle.net/10754/562037
    
    Metadata
    Show full item record
    Abstract
    Let B be a point robot moving in the plane, whose path is constrained to forward motions with curvature at most 1, and let P be a convex polygon with n vertices. Given a starting configuration (a location and a direction of travel) for B inside P, we characterize the region of all points of P that can be reached by B, and show that it has complexity O(n). We give an O(n2) time algorithm to compute this region. We show that a point is reachable only if it can be reached by a path of type CCSCS, where C denotes a unit circle arc and S denotes a line segment. © 2011 Elsevier B.V.
    Citation
    Ahn, H.-K., Cheong, O., Matoušek, J., & Vigneron, A. (2012). Reachability by paths of bounded curvature in a convex polygon. Computational Geometry, 45(1-2), 21–32. doi:10.1016/j.comgeo.2011.07.003
    Sponsors
    Work by Cheong was supported by Mid-career Researcher Program through NRF grant funded by the MEST (No. R01-2008-000-11607-0). Work by Ahn was supported by the National IT Industry Promotion Agency (NIPA) under the program of Software Engineering Technologies Development.
    Publisher
    Elsevier BV
    Journal
    Computational Geometry
    DOI
    10.1016/j.comgeo.2011.07.003
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.comgeo.2011.07.003
    Scopus Count
    Collections
    Articles; Computer Science Program; Visual Computing Center (VCC); Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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