一个五重七点对偶插值型细分  

A Five-Arity Seven-Point Dual Interpolatory Subdivision Scheme

作　　者：刘月 钟明月 薛靖儒 亓万锋[1] 

机构地区：[1]辽宁师范大学数学学院,辽宁 大连

出　　处：《应用数学进展》2025年第1期433-441,共9页Advances in Applied Mathematics

摘　　要：对偶插值型细分方法通过结合对偶型细分的拓扑特性与插值型细分的几何精确性,逐步成为细分领域的研究热点。该方法的关键在于生成的曲线或曲面既能保持初始控制多边形插值特性,又具备光滑性等特点。本文阐述了一种基于两个参数的五重七点对偶插值细分格式,针对该细分格式的多项式再生性和连续性开展了计算与讨论。为提升对偶插值型细分方法的灵活性和适用性提供了新思路。Dual interpolatory subdivision scheme, by combining the topological properties of dual subdivision with the geometric precision of interpolatory subdivision, has gradually become a research hotspot in the subdivision field. The key to this scheme lies in generating curves or surfaces that both preserve the interpolation characteristics of the initial control polygon and exhibit smoothness. This paper proposes a five-arity seven-point dual interpolatory subdivision scheme with two parameters, and analyzes its continuity and regeneration. This provides new ideas to enhance the flexibility and applicability of dual interpolatory subdivision schemes.

关 键 词：细分格式 再生性 连续性 

分 类 号：O17[理学—数学]