## Taiwanese Journal of Mathematics

### A Non-stationary Combined Ternary 5-point Subdivision Scheme with $C^{4}$ Continuity

#### Abstract

In this paper, a family of non-stationary combined ternary $5$-point subdivision schemes with multiple variable parameters is proposed. The construction of the scheme is based on the generalized ternary subdivision scheme of order $4$, which is built upon refinement of a family of generalized B-splines, using the variable displacements. For such a non-stationary scheme, we study its smoothness and get that it can generate $C^{2}$ interpolating limit curves and $C^{4}$ approximating limit curves. Besides, we investigate the exponential polynomial generation/reproduction property and approximation order. It can generate/reproduce certain exponential polynomials with suitable choices of the variable parameters, and reach approximation order $5$.

#### Article information

Source
Taiwanese J. Math., Advance publication (2020), 23 pages.

Dates
First available in Project Euclid: 24 March 2020

https://projecteuclid.org/euclid.twjm/1585036818

Digital Object Identifier
doi:10.11650/tjm/200303

#### Citation

Zhang, Zeze; Zheng, Hongchan; Song, Weijie; Zhang, Baoxing. A Non-stationary Combined Ternary 5-point Subdivision Scheme with $C^{4}$ Continuity. Taiwanese J. Math., advance publication, 24 March 2020. doi:10.11650/tjm/200303. https://projecteuclid.org/euclid.twjm/1585036818

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