### 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 language | English (US) |
---|---|

Title of host publication | Graph Drawing - 14th International Symposium, GD 2006, Revised Papers |

Pages | 306-317 |

Number of pages | 12 |

State | Published - Dec 1 2007 |

Event | 14th International Symposium on Graph Drawing, GD 2006 - Karlsruhe, Germany Duration: Sep 18 2006 → Sep 19 2006 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 4372 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 14th International Symposium on Graph Drawing, GD 2006 |
---|---|

Country | Germany |

City | Karlsruhe |

Period | 9/18/06 → 9/19/06 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

## Fingerprint Dive into the research topics of 'Morphing planar graphs in spherical space'. Together they form a unique fingerprint.

## 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).