Analysis of stationary subdivision schemes for curve design based on radial basis function interpolation

Yeon Ju Lee, Jungho Yoon

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

This paper provides a large family of interpolatory stationary subdivision schemes based on radial basis functions (RBFs) which are positive definite or conditionally positive definite. A radial basis function considered in this study has a tension parameter λ > 0 such that it provides design flexibility. We prove that for a sufficiently large λ ≥ λ0, the proposed 2 L-point (L ∈ N) scheme has the same smoothness as the well-known 2 L-point Deslauriers-Dubuc scheme, which is based on 2 L - 1 degree polynomial interpolation. Some numerical examples are presented to illustrate the performance of the new schemes, adapting subdivision rules on bounded intervals in a way of keeping the same smoothness and accuracy of the pre-existing schemes on R. We observe that, with proper tension parameters, the new scheme can alleviate undesirable artifacts near boundaries, which usually appear to interpolatory schemes with irregularly distributed control points.

Original languageEnglish
Pages (from-to)3851-3859
Number of pages9
JournalApplied Mathematics and Computation
Volume215
Issue number11
DOIs
StatePublished - 1 Feb 2010

Keywords

  • Gaussian
  • Interpolation
  • Inverse multiquadric
  • Multiquadric
  • Radial basis function
  • Smoothness
  • Stationary subdivision

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