Morphing planar graphs in spherical space

Stephen G. Kobourov, Matthew Landis

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

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.

Original languageEnglish (US)
Title of host publicationGraph Drawing - 14th International Symposium, GD 2006, Revised Papers
Pages306-317
Number of pages12
StatePublished - Dec 1 2007
Event14th International Symposium on Graph Drawing, GD 2006 - Karlsruhe, Germany
Duration: Sep 18 2006Sep 19 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4372 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other14th International Symposium on Graph Drawing, GD 2006
CountryGermany
CityKarlsruhe
Period9/18/069/19/06

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Kobourov, S. G., & Landis, M. (2007). Morphing planar graphs in spherical space. In Graph Drawing - 14th International Symposium, GD 2006, Revised Papers (pp. 306-317). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4372 LNCS).