文章基本信息

标题：A nonlinear generalized subdivision scheme of arbitrary degree with a tension parameter
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作者：Zeze Zhang ; Hongchan Zheng ; Jie Zhou 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2020
卷号：2020
期号：1
页码：1-13
DOI：10.1186/s13662-020-03118-6
出版社：Hindawi Publishing Corporation
摘要：In this paper, a nonlinear generalized subdivision scheme of arbitrary degree with a tension parameter is presented, which refines 2D point-normal pairs. The construction of the scheme is built upon the stationary linear generalized subdivision scheme of arbitrary degree with a tension parameter, by replacing the weighted binary arithmetic average in the linear scheme with the circle average. For such a nonlinear scheme, we investigate its smoothness and get that it can reach $C^{1}$ with suitable choices of the tension parameter when degree $m\geq 3$ . Besides, the nonlinear scheme can reconstruct the circle and the selection of parameters and initial normal vectors can effectively control the shape of the limit curves.
关键词：Linear and nonlinear subdivision schemes ; Circle average ; Convergence analysis ; Smoothness analysis ; Tension parameter