一个含参数的七重五点对偶插值型细分
A Parameterized 7-Ary Five-Point Dual Interpolatorty Subdivision
摘要: 在细分技术领域，对偶插值细分作为一类新兴细分范式，展现出独特的构造机理与应用价值。与传统细分模式不同，其通过特殊拓扑规则实现极限曲线对原始控制网格的精确插值，突破了逐次插值的传统框架。本文提出一种参数化的七重五点对偶插值细分方案，系统分析了格式的连续性特征，保障生成曲线的平滑衔接性能；同时探究了其多项式再生属性，并通过计算极限函数的Hölder指数，评估该格式的正则性与光滑度水平。
Abstract: In the research of subdivision technology, the dual-type subdivision scheme, as a new-type subdivision scheme, has a unique construction method and application characteristics. Different from the traditional subdivision schemes, it adopts specific rules, and the limit curve precisely interpolates the original control mesh, breaking the conventional step-by-step interpolatory mode. This paper constructs a dual-type 7-ary five-point subdivision scheme with parameter adjustment function, analyzes the continuity of this scheme, and ensures that the generated curve can achieve a smooth transition effect. Meanwhile, it studies its polynomial reproduction property and calculates the Hölder exponent of the limit function to measure the regularity and smoothness of this scheme.
文章引用：薛靖儒, 王佳怡, 亓万锋. 一个含参数的七重五点对偶插值型细分[J]. 应用数学进展, 2025, 14(7): 235-243. https://doi.org/10.12677/aam.2025.147360

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