In this paper, a generalized algorithm to develop a class of approximating binary subdivision schemes is presented. The proposed algorithm is based on three-point approximating binary and four-point interpolating binary subdivision schemes. It contains a parameter which classifies members of the new class of subdivision schemes. A set of efficient properties, for instance, polynomial generation and reproduction, support, continuity, and Hölder continuity, is discussed. Moreover, applications of the proposed subdivision schemes are given in order to demonstrate their variety, flexibility, and visual performance.

中文翻译：

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二元细分方案类构造的近似插值细分方案统一框架

本文提出了一种通用的算法来开发一类近似的二进制细分方案。所提出的算法基于三点近似二进制和四点插值二进制细分方案。它包含一个参数，该参数对新细分方案类别的成员进行分类。讨论了一组有效的属性，例如多项式生成和再现，支持，连续性和Hölder连续性。此外，给出了建议的细分方案的应用，以证明其多样性，灵活性和视觉效果。