A new C2 rational interpolation based on function values and constrained control of the interpolant curves

Qi Duan, Liqiu Wang, E. H. Twizell

Research output: Journal article publicationJournal articleAcademic researchpeer-review

48 Citations (Scopus)

Abstract

In this paper a new method is developed to create a high-order smoothness interpolation using values of the function being interpolated. This is a kind of rational cubic interpolation with quadratic denominator. This rational spline not only belongs to C2 in the interpolating interval, but could also be used to constrain the shape of the interpolant curve such as to force it to be in the given region, all because of the selectable parameters in the rational spline itself. The more important achievement mathematically of this method is that the uniqueness of the interpolating function for the given data would be replaced by the uniqueness of the interpolating curve for the given data and the selected parameters.

Original languageEnglish
Pages (from-to)311-322
Number of pages12
JournalApplied Mathematics and Computation
Volume161
Issue number1
DOIs
Publication statusPublished - 4 Feb 2005
Externally publishedYes

Keywords

  • Constrained interpolation
  • Curve design
  • Error estimation
  • Rational spline

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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