On the Optimal Triangulation of Convex Hypersurfaces, Whose Vertices Lie in Ambient Space

M. H.M.J. Wintraecken*, G. Vegter

*Corresponding author for this work

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Abstract

Let Σ be a strictly convex (hyper-)surface, Sm an optimal triangulation (piecewise linear in ambient space) of Σ whose m vertices lie on Σ and (Formula presented.) an optimal triangulation of Σ with m vertices. Here we use optimal in the sense of minimizing dH(Sm,Σ), where dH denotes the Hausdorff distance. In ‘Lagerungen in der Ebene, auf der Kugel und im Raum’ Fejes Tóth conjectured that the leading term in the asymptotic development of dH(Sm,Σ) in m is twice that of (Formula presented.). This statement is proven.

Original languageEnglish
Pages (from-to)345-353
Number of pages9
JournalMathematics in computer science
Volume9
Issue number3
DOIs
Publication statusPublished - 1-Oct-2015

Keywords

  • Asymptotic approximations
  • Best approximation
  • Triangulation

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