Morphing Planar Graphs in Spherical Space

  • Stephen G. Kobourov
  • Matthew Landis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4372)

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://www.cs.arizona.edu/~mlandis/smorph.

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Stephen G. Kobourov
    • 1
  • Matthew Landis
    • 1
  1. 1.Department of Computer Science, University of Arizona 

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