Translating polygons in the plane

Jӧrg R. Sack, Godfried Toussaint

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

    Abstract

    Let P = (p1,..,pn) and Q = (ql,..,qm) be two simple polygons with nonintersecting interiors in the plane specified by their cartesian coordinates in order. Given a direction d we can ask whether P can be translated an arbitrary distance in direction d without colliding with Q. It has been shown that this problem can be solved in time proportional to the number of vertices in P and Q. Here we present a new and efficient algorithm for determining all directions in which such movement is possible. In designing this algorithm a partitioning technique is developed which might find applications when solving other geometric problems. The algorithm utilizes several tools and concepts (e.g. convex hulls, point-location, weakly edge-visible polygons) from the area of computational geometry.

    Original languageEnglish (US)
    Title of host publicationSTACS 85 - 2nd Annual Symposium on Theoretical Aspects of Computer Science
    PublisherSpringer-Verlag
    Pages310-321
    Number of pages12
    ISBN (Print)9783540139126
    DOIs
    StatePublished - Jan 1 1985
    Event2nd Annual Symposium on Theoretical Aspects of Computer Science, STACS 1985 - Saarbrucken, Germany
    Duration: Jan 3 1985Jan 5 1985

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume182 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other2nd Annual Symposium on Theoretical Aspects of Computer Science, STACS 1985
    CountryGermany
    CitySaarbrucken
    Period1/3/851/5/85

    Fingerprint

    Polygon
    Computational geometry
    Point Location
    Simple Polygon
    Computational Geometry
    Cartesian
    Convex Hull
    Partitioning
    Interior
    Efficient Algorithms
    Directly proportional
    Arbitrary
    Concepts
    Movement

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    Sack, J. R., & Toussaint, G. (1985). Translating polygons in the plane. In STACS 85 - 2nd Annual Symposium on Theoretical Aspects of Computer Science (pp. 310-321). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 182 LNCS). Springer-Verlag. https://doi.org/10.1007/BFb0024019

    Translating polygons in the plane. / Sack, Jӧrg R.; Toussaint, Godfried.

    STACS 85 - 2nd Annual Symposium on Theoretical Aspects of Computer Science. Springer-Verlag, 1985. p. 310-321 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 182 LNCS).

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

    Sack, JR & Toussaint, G 1985, Translating polygons in the plane. in STACS 85 - 2nd Annual Symposium on Theoretical Aspects of Computer Science. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 182 LNCS, Springer-Verlag, pp. 310-321, 2nd Annual Symposium on Theoretical Aspects of Computer Science, STACS 1985, Saarbrucken, Germany, 1/3/85. https://doi.org/10.1007/BFb0024019
    Sack JR, Toussaint G. Translating polygons in the plane. In STACS 85 - 2nd Annual Symposium on Theoretical Aspects of Computer Science. Springer-Verlag. 1985. p. 310-321. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/BFb0024019
    Sack, Jӧrg R. ; Toussaint, Godfried. / Translating polygons in the plane. STACS 85 - 2nd Annual Symposium on Theoretical Aspects of Computer Science. Springer-Verlag, 1985. pp. 310-321 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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