Geodesic
Morphing Planar Graph Drawings with Bent Edges
Journal of Graph Algorithms and Applications, Tome 15 (2011) no. 2, pp. 205-227.

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We give an algorithm to morph between two planar drawings of a graph, preserving planarity, but allowing edges to bend during the course of the morph. The morph is polynomial size and discrete: it uses a polynomial number of elementary steps, where each elementary step is a linear morph that moves each vertex along a straight line at uniform speed. Although there are previously-known planarity-preserving morphs that do not require edge bends, it is an open problem to find polynomial-size discrete morphs. We achieve polynomial size at the expense of edge bends.
DOI : 10.7155/jgaa.00223
Keywords: graph drawing, morphing, planar graph 
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Anna Lubiw; Mark Petrick. Morphing Planar Graph Drawings with Bent Edges. Journal of Graph Algorithms and Applications, Tome 15 (2011) no. 2, pp. 205-227. doi : 10.7155/jgaa.00223. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00223/

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