Morphing Planar Graph Drawings with Bent Edges

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.