Journal of Graph Algorithms and Applications
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Morphing Planar Graph Drawings with Bent Edges
Anna Lubiw and Mark Petrick
Vol. 15, no. 2, pp. 205-227, 2011. Regular paper.
Abstract 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.
Submitted: May 2010.
Reviewed: October 2010.
Revised: October 2010.
Accepted: December 2010.
Final: February 2011.
Published: February 2011.
Communicated by Stephen G. Kobourov