Morphing Planar Graphs in Spherical Space
Kobourov, Stephen G. and Landis, Matthew (2007) Morphing Planar Graphs in Spherical Space. In: Graph Drawing 14th International Symposium, GD 2006, September 18-20, 2006, Karlsruhe, Germany , pp. 306-317 (Official URL: http://dx.doi.org/10.1007/978-3-540-70904-6_30).
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We consider the problem of intersection-free planar graph morphing, and in particular, a generalization from Euclidean space to spherical space. We show that there exists a continuous and intersection-free morph between two sphere drawings of a maximally planar graph, provided that both sphere drawings have convex inscribed polytopes, where sphere drawings are the spherical equivalent of plane drawings: intersection-free geodesic-arc drawings. In addition, we describe a morphing algorithm along with its implementation. Movies of sample morphs can be found at http://www.cs.arizona.edu/~mlandis/smorph.
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