Drawing 3-Polytopes with Good Vertex Resolution

  • André Schulz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5849)


We study the problem how to obtain a small drawing of a 3-polytope with Euclidean distance between any two points at least 1. The problem can be reduced to a one-dimensional problem, since it is sufficient to guarantee distinct integer x-coordinates. We develop an algorithm that yields an embedding with the desired property such that the polytope is contained in a 2(n − 2)×1 ×1 box. The constructed embedding can be scaled to a grid embedding whose x-coordinates are contained in [0,2(n − 2)]. Furthermore, the point set of the embedding has a small spread, which differs from the best possible spread only by a multiplicative constant.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • André Schulz
    • 1
  1. 1.Computer Science and Artificial Intelligence LaboratoryMITCambridgeUSA

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