Parallel-Redrawing Mechanisms, Pseudo-Triangulations and Kinetic Planar Graphs
Streinu, Ileana (2006) Parallel-Redrawing Mechanisms, Pseudo-Triangulations and Kinetic Planar Graphs. In: Graph Drawing 13th International Symposium, GD 2005, September 12-14, 2005, Limerick, Ireland , pp. 421-433 (Official URL: http://dx.doi.org/10.1007/11618058_38).
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We study parallel redrawing graphs: graphs embedded on moving point sets in such a way that edges maintain their slopes all throughout the motion. The configuration space of such a graph is of an oriented-projective nature, and its combinatorial structure relates to rigidity theoretic parameters of the graph. A special type of kinetic structure emerges, whose events can be analyzed combinatorially. Of particular interest are those planar graph s which maintain non-crossing edges throughout the motion. Our main result is that they are (essentially) pseudo-triangulation mechanisms. These kinetic graph structures have potential applications in morphing of more complex shapes than just simple polygons.
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