Taiwanese Journal of Mathematics

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

Zeze Zhang, Hongchan Zheng, Weijie Song, and Baoxing Zhang

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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

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

First available in Project Euclid: 24 March 2020

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Primary: 65D17: Computer aided design (modeling of curves and surfaces) [See also 68U07] 26A18: Iteration [See also 37Bxx, 37Cxx, 37Exx, 39B12, 47H10, 54H25] 39B12: Iteration theory, iterative and composite equations [See also 26A18, 30D05, 37-XX]

ternary non-stationary subdivision combined scheme convergence exponential polynomial generation/reproduction approximation order


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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