一个六重五点对偶插值型细分
A Six-Arity Five-Point Dual Interpolation Subdivision Scheme
DOI: 10.12677/aam.2025.142058, PDF,   
作者: 何月, 薛靖儒, 钟明月, 亓万锋*：辽宁师范大学数学学院，辽宁 大连
关键词: 细分格式；多项式再生性；连续性；Subdivision Scheme； Polynomial Reproduction； Continuity
摘要: 在计算机辅助几何设计领域，细分方法凭借其简单高效的优点成为了一种强大的工具。随着不断的发展，许多学者通过不同方法构造了不同种类的细分，其中包括近些年新提出的对偶插值型细分。相较于之前提出的细分，对偶插值型细分具有更高的连续性和多项式再生性。文章提出了一种六重五点对偶插值型细分，利用生成多项式对该细分格式的连续性和多项式再生性进行了分析。
Abstract: In the field of computer-aided geometric design, subdivisions have become a powerful tool due to their simplicity and efficiency. With continuous development, many scholars have constructed various types of subdivision schemes through different methods, including the recently proposed dual interpolation subdivision schemes. Compared to previously proposed subdivision schemes, dual interpolation subdivision schemes offer higher continuity and polynomial reproduction. This paper presents a six-fold five-point dual interpolation subdivision scheme and analyzes the continuity and polynomial reproduction of this subdivision scheme using generating polynomials.
文章引用：何月, 薛靖儒, 钟明月, 亓万锋. 一个六重五点对偶插值型细分[J]. 应用数学进展, 2025, 14(2): 125-134. https://doi.org/10.12677/aam.2025.142058

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