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

• Type: Conference
• Year: 2007
• Where: COMPGEOM
• Authors: Ares Ribó Mor, Günter Rote, André Schulz
• Keywords: 3-connected Planar Graph, COMPGEOM 2007, Discrete Geometry, Equilibrium Stress, Small Integer Coordinates