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Translating polygons in the plane

  • Jörg-R. Sack
  • Godfried T. Toussaint
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 182)

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.

Keywords

Computational Geometry Simple Polygon Convex Region Jordan Curve Theorem Reflex Vertex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Jörg-R. Sack
    • 1
  • Godfried T. Toussaint
    • 2
  1. 1.School of Computer ScienceCarleton UniversityOttawaCanada
  2. 2.School of Computer ScienceMcGill UniversityMontrealCanada

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