Rocky Mountain Journal of Mathematics

Nonstationary interpolatory subdivision schemes reproducing high-order exponential polynomials

Jie Zhou, Hongchan Zheng, Zhaohong Li, and Weijie Song

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Abstract

We present a family of nonstationary interpolatory subdivision schemes which reproduces high-order exponential polynomials. First, by extending the classical $\fbox {D-D}$ interpolatory schemes, we present the explicit expression of the symbols that identify a family of the nonstationary interpolatory subdivision schemes. These schemes can allow reproduction of more exponential polynomials, and represent exactly circular shapes, parts of conics which are important analytical shapes in geometric modeling. Furthermore, a rigorous analysis regarding the smoothness of the new nonstationary interpolatory schemes is provided. Next, based on the recursive formulas of the symbols, a repeated local operation is proposed for rapidly computing new points from the old points. Finally, two examples are presented to illustrate the performance of the new schemes.

Article information

Source
Rocky Mountain J. Math., Volume 49, Number 7 (2019), 2429-2457.

Dates
First available in Project Euclid: 8 December 2019

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1575774145

Digital Object Identifier
doi:10.1216/RMJ-2019-49-7-2429

Mathematical Reviews number (MathSciNet)
MR4039977

Zentralblatt MATH identifier
07152872

Keywords
nonstationary interpolatory subdivision schemes high-order exponential polynomials explicit expression repeated local algorithm D-D interpolatory schemes

Citation

Zhou, Jie; Zheng, Hongchan; Li, Zhaohong; Song, Weijie. Nonstationary interpolatory subdivision schemes reproducing high-order exponential polynomials. Rocky Mountain J. Math. 49 (2019), no. 7, 2429--2457. doi:10.1216/RMJ-2019-49-7-2429. https://projecteuclid.org/euclid.rmjm/1575774145


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