Delaunay stability via perturbations

نویسندگان

  • Jean-Daniel Boissonnat
  • Ramsay Dyer
  • Arijit Ghosh
چکیده

We present an algorithm that takes as input a finite point set in R, and performs a perturbation that guarantees that the Delaunay triangulation of the resulting perturbed point set has quantifiable stability with respect to the metric and the point positions. There is also a guarantee on the quality of the simplices: they cannot be too flat. The algorithm provides an alternative tool to the weighting or refinement methods to remove poorly shaped simplices in Delaunay triangulations of arbitrary dimension, but in addition it provides a guarantee of stability for the resulting triangulation. Key-words: Delaunay triangulation, stability, algorithm ∗ Indian Statistical Institute, ACM Unit, Kolkata, India Stabilité de la triangulation de Delaunay vis à vis de perturbations Résumé : On présente un algorithme qui prend en entrée un ensemble fini de points de l’espace euclidien et les perturbent de façon à garantir que la triangulation de Delaunay des points perturbés est stable de manière quantifiable vis à vis de perturbations de la métrique ou de la position des points. L’algorithme offre également une garantie sur la qualité des simplexes : ils ne peuvent pas être trop plats. L’algorithme propose une alternative simple aux techniques de pondération ou de raffinement qui permettent d’éliminer les simplexes plats des triangulations de Delaunay de dimension arbitraire, et fournit en plus une garantie sur la stabilité de la triangulation construite. Mots-clés : triangulation de Delaunay, stabilité, algorithme Delaunay stability 3

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عنوان ژورنال:
  • Int. J. Comput. Geometry Appl.

دوره 24  شماره 

صفحات  -

تاریخ انتشار 2014