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An axiomatic approach to scalar data interpolation on surfaces

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Abstract

We discuss possible algorithms for interpolating data given on a set of curves in a surface of ℝ 3. We propose a set of basic assumptions to be satisfied by the interpolation algorithms which lead to a set of models in terms of possibly degenerate elliptic partial differential equations. The Absolutely Minimizing Lipschitz Extension model (AMLE) is singled out and studied in more detail. We study the correctness of our numerical approach and we show experiments illustrating the interpolation of data on some simple test surfaces like the sphere and the torus.

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Authors and Affiliations

  1. Dept. de Tecnologia, University of Pompeu-Fabra, Passeig de Circumval.lació, 8, 08003, Barcelona, Spain

    V. Caselles & L. Igual

  2. Institut für Mathematik II, Freie Universität Berlin, Arnimallee 2-6, 14195, Berlin, Germany

    O. Sander

Authors
  1. V. Caselles
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  2. L. Igual
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  3. O. Sander
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Correspondence to V. Caselles.

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Caselles, V., Igual, L. & Sander, O. An axiomatic approach to scalar data interpolation on surfaces. Numer. Math. 102, 383–411 (2006). https://doi.org/10.1007/s00211-005-0656-8

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  • DOI: https://doi.org/10.1007/s00211-005-0656-8

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