A Parameterized 7-Ary Five-Point Dual Interpolatorty Subdivision

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。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.