Approximating geodesics on point set surfaces

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RUGGERI, Mauro Roberto, Tal DAROM, Dietmar SAUPE, Nahum KIRYATI, 2006. Approximating geodesics on point set surfaces. Eurographics/IEEE VGTC Symposium. Boston, Massachusetts, USA, 29. Jul 2006 - 30. Jul 2006. In: BOTSCH, Mario, ed. and others. Point-based graphics 2006 [SPBG '06] : Eurographics/IEEE VGTC Symposium proceedings. Eurographics/IEEE VGTC Symposium. Boston, Massachusetts, USA, 29. Jul 2006 - 30. Jul 2006. 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} }

Darom, Tal Darom, Tal Point-based graphics 2006 [SPBG '06] : Eurographics/IEEE VGTC Symposium proceedings, Boston, Massachusetts, USA, July 29 - 30, 2006 / papers chaire Mario Botsch ... . - Aire-la-Ville : Eurographics Association, 2006. - S. 85-94. - ISBN 3-905673-32-0 Ruggeri, Mauro Roberto 2006 Kiryati, Nahum Approximating geodesics on point set surfaces 2013-07-25T09:57:29Z Saupe, Dietmar deposit-license Ruggeri, Mauro Roberto eng 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<br />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. Kiryati, Nahum Saupe, Dietmar 2013-07-25T09:57:29Z

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