Advances in Computational Mathematics

, Volume 41, Issue 6, pp 1079–1099 | Cite as

Numerical reconstruction of convex polytopes from directional moments

  • Mathieu Collowald
  • Annie Cuyt
  • Evelyne Hubert
  • Wen-Shin Lee
  • Oliver Salazar Celis
Article

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.

Keywords

Shape from moment Brion’s formula Directional moments Prony Generalized eigenvalues Interval interpolation 

Mathematics Subject Classification (2010)

44A60 41A63 65F35 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Mathieu Collowald
    • 1
    • 3
  • Annie Cuyt
    • 2
  • Evelyne Hubert
    • 3
  • Wen-Shin Lee
    • 2
  • Oliver Salazar Celis
    • 2
  1. 1.University Nice Sophia AntipolisNiceFrance
  2. 2.Department of Mathematics & Computer ScienceUniversiteit AntwerpenAntwerpenBelgium
  3. 3.GALAADInria Sophia AntipolisNiceFrance

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