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COMPGEOM
2007
ACM

Embedding 3-polytopes on a small grid

8 years 8 months ago
Embedding 3-polytopes on a small grid
We show how to embed a 3-connected planar graph with n vertices as a 3-polytope with small integer coordinates. The coordinates are bounded by O(27.55n ). The crucial part is the construction of a plane embedding which supports an equilibrium stress. We have to guarantee that the size of the coordinates and the stresses are small. This is achieved by applying Tutte's spring embedding method carefully. Categories and Subject Descriptors F.2.2 [Nonnumerical Algorithms and Problems]: Geometrical problems and computations; G.2.2 [Graph Theory]: Graph algorithms General Terms Algorithms, Theory Keywords Spring embedding, equilibrium stress
Ares Ribó Mor, Günter Rote, Andr&eacut
Added 14 Aug 2010
Updated 14 Aug 2010
Type Conference
Year 2007
Where COMPGEOM
Authors Ares Ribó Mor, Günter Rote, André Schulz
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