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Drawing 3-Polytopes with Good Vertex Resolution

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

Abstract

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.

Keywords

Planar Graph Laplace Matrix Equilibrium Stress Boundary Vertex Interior 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 2010

Authors and Affiliations

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

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