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Numerical reconstruction of convex polytopes from directional moments

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An Erratum to this article was published on 12 July 2016

Abstract

We reconstruct an n-dimensional convex polytope from the knowledge of its directional moments. The directional moments are related to the projection of the polytope vertices on a particular direction. To extract the vertex coordinates from the moment information we combine established numerical algorithms such as generalized eigenvalue computation and linear interval interpolation. Numerical illustrations are given for the reconstruction of 2-d and 3-d convex polytopes.

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Authors and Affiliations

  1. University Nice Sophia Antipolis, Nice, France

    Mathieu Collowald

  2. Department of Mathematics & Computer Science, Universiteit Antwerpen, Antwerpen, Belgium

    Annie Cuyt, Wen-Shin Lee & Oliver Salazar Celis

  3. GALAAD, Inria Sophia Antipolis, Nice, France

    Mathieu Collowald & Evelyne Hubert

Authors
  1. Mathieu Collowald
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  2. Annie Cuyt
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  3. Evelyne Hubert
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  4. Wen-Shin Lee
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  5. Oliver Salazar Celis
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Correspondence to Mathieu Collowald.

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Communicated by: Leslie Greengard

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Collowald, M., Cuyt, A., Hubert, E. et al. Numerical reconstruction of convex polytopes from directional moments. Adv Comput Math 41, 1079–1099 (2015). https://doi.org/10.1007/s10444-014-9401-0

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  • DOI: https://doi.org/10.1007/s10444-014-9401-0

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