非对称对偶两步插值细分格式

Asymmetric Dual Two-Step Interpolatory Subdivision Scheme

摘要: 非对称对偶插值型细分是一类近年来受到关注的细分曲线构造方法，其通过引入非对称掩模，在保持插值特性的同时，在相同性质下，非对称具有更灵活的参数，在复杂几何建模与形状控制中具有更高的灵活性。本文提出并构建了一类非对称的五重五点对偶两步插值型细分格式，该格式细分两次可实现插值效果，进一步增强了形状调节的灵活性。文中分析了该格式的连续性、多项式再生性，并给出数值实例，以展示该格式在保持插值约束下调整曲线形态方面的灵活能力。

Abstract: Asymmetric dual interpolatory subdivision is a class of curve construction methods that have attracted increasing attention in recent years. By introducing asymmetric masks, these methods preserve the interpolatory property while offering more flexible parameters under the same constraints, thereby providing greater flexibility in complex geometric modeling and shape control. In this paper, we propose and construct a class of asymmetric five-point quinary dual interpolatory subdivision schemes, Two‑step subdivision of this scheme produces interpolation while improving shape‑adjustment flexibility. We analyze the continuity and polynomial reproducibility of the proposed scheme, and present numerical examples to demonstrate its capability of flexibly adjusting curve shapes while maintaining interpolatory constraints.