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Translating polygons in the plane

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STACS 85 (STACS 1985)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 182))

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Abstract

Let P = (p1,...,pn) and Q = (q1,...,qm) be two simple polygons with non-intersecting 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.

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Author information

Authors and Affiliations

  1. School of Computer Science, Carleton University, Colonel By Drive, K1S 5B6, Ottawa, Ontario, Canada

    Jörg-R. Sack

  2. School of Computer Science, McGill University, 805 Sherbrooke Street West, H3A 2K6, Montreal, Quebec, Canada

    Godfried T. Toussaint

Authors
  1. Jörg-R. Sack
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  2. Godfried T. Toussaint
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K. Mehlhorn

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© 1984 Springer-Verlag Berlin Heidelberg

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Sack, JR., Toussaint, G.T. (1984). Translating polygons in the plane. In: Mehlhorn, K. (eds) STACS 85. STACS 1985. Lecture Notes in Computer Science, vol 182. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0024019

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  • DOI: https://doi.org/10.1007/BFb0024019

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13912-6

  • Online ISBN: 978-3-540-39136-4

  • eBook Packages: Springer Book Archive

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