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On Zlámal Minimum Angle Condition for the Longest-Edge n-Section Algorithm with n ≥ 4

  • Sergey KorotovEmail author
  • Ángel Plaza
  • José P. Suárez
  • Tania Moreno
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)

Abstract

In this note we analyse the classical longest-edge n-section algorithm applied to the simplicial partition in Rd, and prove that an infinite sequence of simplices violating the Zlámal minimum angle condition, often required in finite element analysis and computer graphics, is unavoidably produced if n ≥ 4. This result implies the fact that the number of different simplicial shapes produced by this version of n-section algorithms is always infinite for any n ≥ 4.

Notes

Acknowledgements

The authors are indebted to Jan Brandts for valuable comments on the work.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Sergey Korotov
    • 1
    Email author
  • Ángel Plaza
    • 2
  • José P. Suárez
    • 2
  • Tania Moreno
    • 3
  1. 1.Department of Computing, Mathematics and PhysicsWestern Norway University of Applied SciencesBergenNorway
  2. 2.Division of Mathematics, Graphics and Computation (MAGiC), IUMA, Information and Communication SystemsUniversity of Las Palmas de Gran CanariaLas Palmas, Canary IslandsSpain
  3. 3.Faculty of Mathematics and InformaticsUniversity of HolguínHolguínCuba

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