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Proximity and Motion Planning on ℓ1-Rigid Planar Periodic Graphs

  • Norie Fu
  • Akihiro Hashikura
  • Hiroshi Imai
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8110)

Abstract

Motivated by an application to nanotechnology, Voronoi diagrams on periodic graphs with few orbits under translations and a motion planning problem on ℓ1-embeddable Archimedean tilings have been investigated by Fu, Hashikura, Imai and Moriyama. In this paper, through the investigations on the geodesic fibers defined originally as invariants on periodic graphs by Eon, we show fast geometric algorithms for Voronoi diagrams and the motion planning on ℓ1-rigid planar periodic graphs.

Keywords

Short Path Distance Function Motion Planning Voronoi Diagram Quotient Graph 
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 2013

Authors and Affiliations

  • Norie Fu
    • 1
  • Akihiro Hashikura
    • 1
  • Hiroshi Imai
    • 1
  1. 1.Department of Computer ScienceUniversity of TokyoJapan

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