High accuracy Hermite approximation for space curves in Rd

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16 Citations (Scopus)

Abstract

In this article, it is shown that a space curve in Rd can be approximated by a piecewise polynomial curve of degree m with order (m + 1) + ⌊ (m + 1) / (2 d - 1) ⌋ rather than m + 1. Moreover, we show that the optimal order (m + 1) + ⌊ (m - 1) / (d - 1) ⌋ is possible for a particular set of curves of nonzero measure. Analogous results were shown to be true for Taylor polynomial interpolation in [A. Rababah, High order approximation method for curves, Comput. Aided Geom. Design 12 (1995) 89-102].

Original languageEnglish
Pages (from-to)920-931
Number of pages12
JournalJournal of Mathematical Analysis and Applications
Volume325
Issue number2
DOIs
Publication statusPublished - Jan 15 2007
Externally publishedYes

Keywords

  • Approximation order
  • Computer aided geometric design
  • Hermite approximation
  • High accuracy
  • Space curves

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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