## Abstract

Several different procedures are presented to produce smooth interpolating curves on the two-sphere S^{2}. The first class of methods is a combination of the pull back/push forward technique with unrolling data from S^{2} into a tangent plane, solving there the interpolation problem, and then wrapping the resulting interpolation curve back to the manifold. The second method results from converting a variational problem into a finite dimensional optimisation problem by a proper discretisation process. It turns out that the resulting curves look very similar. The main difference though is that the first approach gives closed form solutions to the interpolation problem, whereas the second method results in a finite number of points. These points then require further treatment, e.g. one could connect them by geodesic arcs, i.e. by great circle segments, to get an approximate solution to the variational problem. Although the result would not be smooth, it seems to be the best that one can get if the dicretisation process is combined with a sufficiently cheap interpolation procedure.

Original language | English |
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Title of host publication | Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 6403-6407 |

Number of pages | 5 |

ISBN (Print) | 1424401712, 9781424401710 |

DOIs | |

Publication status | Published - 2006 |

Event | 45th IEEE Conference on Decision and Control 2006, CDC - San Diego, CA, United States Duration: 13 Dec 2006 → 15 Dec 2006 |

### Publication series

Name | Proceedings of the IEEE Conference on Decision and Control |
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ISSN (Print) | 0743-1546 |

ISSN (Electronic) | 2576-2370 |

### Conference

Conference | 45th IEEE Conference on Decision and Control 2006, CDC |
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Country/Territory | United States |

City | San Diego, CA |

Period | 13/12/06 → 15/12/06 |

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