Morphing Planar Graphs in Spherical Space

Abstract

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://smorph.cs.arizona.edu