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# Approximating geodesics on point set surfaces

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Type of Publication: | Contribution to a conference collection |

URI (citable link): | http://nbn-resolving.de/urn:nbn:de:bsz:352-229957 |

Author: | Ruggeri, Mauro Roberto; Darom, Tal; Saupe, Dietmar; Kiryati, Nahum |

Year of publication: | 2006 |

Conference: | Eurographics/IEEE VGTC Symposium, Jul 29, 2006 - Jul 30, 2006, Boston, Massachusetts, USA |

Published in: | Point-based graphics 2006 [SPBG '06] : Eurographics/IEEE VGTC Symposium proceedings / Botsch, Mario et al. (ed.). - Aire-la-Ville : Eurographics Association, 2006. - pp. 85-94. - ISBN 3-905673-32-0 |

DOI (citable link): | https://dx.doi.org/10.2312/SPBG/SPBG06/085-093 |

Summary: |
We present a technique for computing piecewise linear approximations of geodesics on point set surfaces by minimizing an energy function defined for piecewise linear path. The function considers path length, closeness to the
surface for the nodes of the piecewise linear path and for the intermediate line segments. Our method is robust with respect to noise and outliers. In order to avoid local minima, a good initial piecewise linear approximation of a geodesic is provided by Dijkstra’s algorithm that is applied to a proximity graph constructed over the point set. As the proximity graph we use a sphere-of-influence weighted graph extended for surfel sets. The convergence of our method has been studied and compared to results of other methods by running experiments on surfaces whose geodesics can be computed analytically. Our method is presented and optimized for surfel-based representations but it has been implemented also for MLS surfaces. Moreover, it can also be applied to other surface representations, e.g., triangle meshes, radial-basis functions, etc. |

Subject (DDC): | 004 Computer Science |

Link to License: | In Copyright |

Bibliography of Konstanz: | Yes |

Checksum:
MD5:953769a443cbe1e56c90670e75c70630

RUGGERI, Mauro Roberto, Tal DAROM, Dietmar SAUPE, Nahum KIRYATI, 2006. Approximating geodesics on point set surfaces. Eurographics/IEEE VGTC Symposium. Boston, Massachusetts, USA, Jul 29, 2006 - Jul 30, 2006. In: BOTSCH, Mario, ed. and others. Point-based graphics 2006 [SPBG '06] : Eurographics/IEEE VGTC Symposium proceedings. Aire-la-Ville:Eurographics Association, pp. 85-94. ISBN 3-905673-32-0. Available under: doi: 10.2312/SPBG/SPBG06/085-093

@inproceedings{Ruggeri2006Appro-22995, title={Approximating geodesics on point set surfaces}, year={2006}, doi={10.2312/SPBG/SPBG06/085-093}, isbn={3-905673-32-0}, address={Aire-la-Ville}, publisher={Eurographics Association}, booktitle={Point-based graphics 2006 [SPBG '06] : Eurographics/IEEE VGTC Symposium proceedings}, pages={85--94}, editor={Botsch, Mario}, author={Ruggeri, Mauro Roberto and Darom, Tal and Saupe, Dietmar and Kiryati, Nahum} }

Ruggeri_229957.pdf | 331 |