Drawing 3-Polytopes with Good Vertex Resolution
Schulz , André (2010) Drawing 3-Polytopes with Good Vertex Resolution. In: Graph Drawing 17th International Symposium, GD 2009, September 22-25, 2009, Chicago, IL, USA , pp. 33-44 (Official URL: http://dx.doi.org/10.1007/978-3-642-11805-0_6).
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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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