五点二重有理逼近细分算法

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英文篇名：A Five-point Binary Rational Approximating Subdivision Scheme 作者：朱洪 ; 王娟 ; 李宝萍 英文作者：ZHU Hong;WANG Juan;LI Baoping;Department of Basic Courses,Anhui Sanlian University; 关键词：细分法 ; 有理逼近 ; 连续性 ; 生成多项式 英文关键词：subdivision scheme;;rational approximation;;continuity;;generating polynomial 中文刊名：安庆师范大学学报(自然科学版) 英文刊名：Journal of Anqing Normal University(Natural Science Edition) 机构：安徽三联学院基础部; 出版日期：2019-08-23 11:07 出版单位：安庆师范大学学报(自然科学版) 年：2019 期：03 基金：安徽省高校自然科学研究重点项目(KJ2016A250);; 安徽三联学院校级自然科学研究重点项目(KJZD2017007) 语种：中文; 页：16-21 页数：6 CN：34-1328/N ISSN：1007-4260 分类号：TP391.72

摘要

在研究有理B样条曲线及五点二重逼近细分算法各自优点的基础上,提出了一种新的有理形式的五点二重逼近细分算法供工业造型设计使用。利用生成多项式的方法来分析该算法的一致收敛性和各阶连续性,得出该算法在参数范围内生成的极限曲线可达C~1～C~5连续,尤其是当ω=1/30时,可达C~7连续。具体数值算例表明,极限曲线在保持较高光滑性的同时,还非常地接近初始控制多边形,并且通过调整参数取值可以灵活地改变极限曲线的形状。
        A five-point binary rational approximating subdivision scheme with the parameter is constructed for industrial modeling design. The uniform convergence and continuity of the subdivision scheme are analyzed by generating polynomial method. It is shown that a family of limiting curves are continuous for certain range of the parameter and the limiting curves for.The numerical examples show that the subdivision curves are very close to the initial control polygon while maintaining high smoothness and the shape of the curves are adjustable can be flexibly changed by adjusting the parameter values.

引文

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