带参数的三重两步插值细分方法
Parameterized Ternary Two-Step Interpolatory Subdivision Scheme
摘要: 两步插值细分格式是一种新型式的细分格式，它具有在偶数次加细时插值控制网格的特点。这种特点使得它在计算机辅助几何设计中具有潜在的吸引力。本文给出了一种新的三重两步插值曲线细分格式。证明了通过调节参数其极限曲线可以达到 C 2 连续。其次，本文还分析了该细分格式的Hӧlder指数，并且给出了其基函数图像。数值实例表明，该两步插值细分方法可以使极限曲线较好的接近初始控制多边形并保证插值，该方法是合理有效的。
Abstract: The two-step interpolatory subdivision scheme is a novel type of subdivision method characterized by interpolating the control mesh at even refinement steps. Such a feature renders it potentially attractive in computer-aided geometric design (CAGD). In this paper, we propose a new ternary two-step interpolatory curve subdivision scheme. It is proved that the limit curve may attain C 2 -continuity by adjusting parameters. Furthermore, the Hölder exponent of the scheme is analyzed, and the graph of the basic limit function is provided. Numerical examples demonstrate that the proposed two-step interpolatory subdivision method yields limit curves that closely approximate the initial control polygon while ensuring interpolation, thus verifying the method’s reasonableness and effectiveness.
文章引用：钟明月, 亓万锋. 带参数的三重两步插值细分方法[J]. 应用数学进展, 2025, 14(11): 13-21. https://doi.org/10.12677/aam.2025.1411456

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