A nonlinear generalized subdivision scheme of arbitrary degree with a tension parameter

Advances in Difference Equations

article

Zhang, Zeze¹  Zheng, Hongchan¹  Zhou, Jie²  Pan, Lulu¹ 

[1] School of Mathematics and Statistics, Northwestern Polytechnical University;School of Science, Xi’an Polytechnic University

关键词: Linear and nonlinear subdivision schemes;    Circle average;    Convergence analysis;    Smoothness analysis;    Tension parameter;   

DOI  :  10.1186/s13662-020-03118-6

学科分类：航空航天科学

来源: SpringerOpen

【 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.

【 授权许可】

CC BY