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Connecting geodesics on smooth surfaces

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Abstract

In this paper, we present a novel method for computing multiple geodesic connections between two arbitrary points on a smooth surface. Our method is based on a homotopy approach that is able to capture the ambiguity of geodesic connections in the presence of positive Gaussian curvature that generates focal curves.

Contrary to previous approaches, we exploit focal curves to gain theoretical insights on the number of connecting geodesics and a practical algorithm for collecting these.

We consider our method as a contribution to the contemporary debate regarding the calculation of distances in general situations, applying continuous concepts of classical differential geometry which are not immediately transferable in purely discrete settings.

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Authors and Affiliations

  1. Welfenlab, Division of Computer Graphics, Leibniz University of Hannover, Hannover, Germany

    Hannes Thielhelm, Alexander Vais, Daniel Brandes & Franz-Erich Wolter

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  1. Hannes Thielhelm
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  2. Alexander Vais
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  3. Daniel Brandes
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  4. Franz-Erich Wolter
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Correspondence to Hannes Thielhelm.

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Thielhelm, H., Vais, A., Brandes, D. et al. Connecting geodesics on smooth surfaces. Vis Comput 28, 529–539 (2012). https://doi.org/10.1007/s00371-012-0681-4

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  • DOI: https://doi.org/10.1007/s00371-012-0681-4

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