带参的非对称四重五点对偶插值型细分格式
A Parametric Asymmetric Quaternary Five-Point Dual Interpolatory Subdivision Scheme
摘要: 对偶插值型细分是几何建模领域的研究热点，现有相关格式多为对称掩模形式，本文提出一个带参非对称四重五点对偶插值型细分格式，构建含单参数的非对称掩模，可灵活调控极限曲线的光滑性。理论分析表明，该格式最高可达到C2连续，计算Hӧlder指数量化分数阶连续性；同时，通过数值实验可验证其插值性。
Abstract: Dual interpolatory subdivision schemes are a research hotspot in geometric modeling. Most existing related schemes adopt symmetric masks. This paper proposes a parametric asymmetric quaternary five-point dual interpolatory subdivision scheme with a single parameter, enabling flexible control over the smoothness of the limit curve. Theoretical analysis demonstrates that the scheme can achieve C2 continuity, and the Hölder exponent is computed to quantify the fractional-order continuity. Meanwhile, the dual interpolation property is verified through numerical experiments.
文章引用：王佳怡, 郝金双, 亓万锋. 带参的非对称四重五点对偶插值型细分格式[J]. 应用数学进展, 2026, 15(8): 180-192. https://doi.org/10.12677/aam.2026.158344

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