Fractal Behavior of a Ternary 4-Point Rational Interpolation Subdivision Scheme

Mathematical and Computational Applications

Li, Zhiming¹  Tan, Jieqing²  Peng, Kaijun³ 

[1] Author to whom correspondence should be addressed;School of Computer and Information, Hefei University of Technology, Hefei 230009, China;School of Mathematics, Hefei University of Technology, Hefei 230009, China

关键词: subdivision scheme;    rational mask;    subdivision matrix;   

DOI  :  10.3390/mca23040065

学科分类：计算数学

来源: mdpi

【 摘 要 】

In this paper, a ternary 4-point rational interpolation subdivision scheme is presented, and the necessary and sufficient conditions of the continuity are analyzed. The generalization incorporates existing schemes as special cases: Hassan–Ivrissimtzis’s scheme, Siddiqi–Rehan’s scheme, and Siddiqi–Ahmad’s scheme. Furthermore, the fractal behavior of the scheme is investigated and analyzed, and the range of the parameter of the fractal curve is the neighborhood of the singular point of the rational scheme. When the fractal curve and surface are reconstructed, it is convenient for the selection of parameter values.

【 授权许可】

CC BY