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Mesh Parameterization with Generalized Discrete Conformal Maps

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Abstract

We introduce a new method to compute conformal parameterizations using a recent definition of discrete conformity, and establish a discrete version of the Riemann mapping theorem. Our algorithm can parameterize triangular, quadrangular and digital meshes. It can also be adapted to preserve metric properties. To demonstrate the efficiency of our method, many examples are shown in the experiment section.

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Acknowledgements

This work was partially supported by the ANR project KIDICO (ANR-2010-BLAN-0205-02).

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Authors and Affiliations

  1. LIMOS, Clermont-Université, Complexe des Cézeaux, 63172, Aubière, France

    Colin Cartade & Rémy Malgouyres

  2. IUFM, Université Lyon 1, Bât. Braconnier, 69622, Vileurbanne, France

    Christian Mercat

  3. ISIT, Clermont-Université, Complexe des Cézeaux, 63172, Aubière, France

    Chafik Samir

Authors
  1. Colin Cartade
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  2. Christian Mercat
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  3. Rémy Malgouyres
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  4. Chafik Samir
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Correspondence to Colin Cartade.

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Cartade, C., Mercat, C., Malgouyres, R. et al. Mesh Parameterization with Generalized Discrete Conformal Maps. J Math Imaging Vis 46, 1–11 (2013). https://doi.org/10.1007/s10851-012-0362-y

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  • DOI: https://doi.org/10.1007/s10851-012-0362-y

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