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。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.
对偶插值型细分方法通过结合对偶型细分的拓扑特性与插值型细分的几何精确性,逐步成为细分领域的研究热点。该方法的关键在于生成的曲线或曲面既能保持初始控制多边形插值特性,又具备光滑性等特点。本文阐述了一种基于两个参数的五重七点对偶插值细分格式,针对该细分格式的多项式再生性和连续性开展了计算与讨论。为提升对偶插值型细分方法的灵活性和适用性提供了新思路。Dual interpolatory subdivision scheme, by combining the topological properties of dual subdivision with the geometric precision of interpolatory subdivision, has gradually become a research hotspot in the subdivision field. The key to this scheme lies in generating curves or surfaces that both preserve the interpolation characteristics of the initial control polygon and exhibit smoothness. This paper proposes a five-arity seven-point dual interpolatory subdivision scheme with two parameters, and analyzes its continuity and regeneration. This provides new ideas to enhance the flexibility and applicability of dual interpolatory subdivision schemes.
