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Geometrical Treatment of Periodic Graphs with Coordinate System Using Axis-fiber and an Application to a Motion Planning

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3 Author(s)
Fu, N. ; Dept. of Comput. Sci., Univ. of Tokyo, Tokyo, Japan ; Hashikura, A. ; Imai, H.

Motivated by an application to nanotechnology, Voronoi diagrams on (ℓ1-embeddable) periodic graphs and a motion planning problem on those graphs have been investigated by Fu, Hashikura, Imai and Moriyama. In this paper, through the investigations on the coordinate system using geodesic fibers defined originally as invariants on periodic graphs by Eon, we show that a fast geometric algorithm for the motion planning problem is possible on periodic graphs with nice properties.

Published in:

Voronoi Diagrams in Science and Engineering (ISVD), 2012 Ninth International Symposium on

Date of Conference:

27-29 June 2012