一类具有保凸性质的四点二重细分格式  

A new four-point binary subdivision scheme with convexity preservation

作　　者：王燕 李志明[2] 朱洪[3] WANG Yan;LI Zhiming;ZHU Hong(School of Mathematics and Statistics,Hefei Normal University,Hefei Anhui 230601,China;School of Computer and Information,Hefei University of Technology,Hefei Anhui 230009,China;Department of Basic Courses,Anhui Sanlian University,Hefei Anhui 230601,China)

机构地区：[1]合肥师范学院数学与统计学院,安徽合肥230601 [2]合肥工业大学计算机与信息学院,安徽合肥230009 [3]安徽三联学院基础部,安徽合肥230601

出　　处：《阜阳师范大学学报（自然科学版）》2024年第2期1-6,共6页Journal of Fuyang Normal University:Natural Science

基　　金：国家自然科学基金青年科学基金项目(12101173);安徽省高等学校自然科学研究重点项目(KJ2020A0119);安徽省高校优秀青年人才支持计划重点项目(gxyqZD2022072)。

摘　　要：细分曲线曲面造型方法是一种简单、易操作的几何造型方法。为了进一步丰富曲线曲面造型的理论方法,通过二次融合的方式,提出了一类新型的带参数的四点二重逼近细分格式。当参数取特殊值时,构造的细分格式包含一些已有的逼近细分格式,比如三次B样条细分格式、四次B样条细分格式和五次B样条细分格式,还可以生成一些新的逼近细分格式。利用生成多项式的方法证明了该细分格式的收敛性和连续性,并且给出了相应的参数的取值范围。同时证明了当参数在特定范围内取值时,生成的极限曲线具有保凸性。最后通过一些数值实例证明了参数对极限曲线的影响,通过调节参数,该细分格式可以满足不同几何造型的需要,说明了所构造的细分格式是有效的。Subdivision method has become a powerful tool to create curves and surfaces geometric modeling because of its efficiency and simplicity.In order to enrich the methods of curve and surface modeling,a new four-point binary approximating subdivision scheme with a parameter is proposed through quadratic combination.By choice of appropriate parameters,some existing subdivision schemes such as the cubic B-spline scheme,the quartic B-spline scheme and the quintic B-spline scheme can be obtained,as well as some new approximating subdivision schemes.It is shown that the result curves are different continuity with different parameters.The range of the parameter for the property of convexity preservation of the limiting curves is also provided.Experimental results demonstrate the efficiency and flexibility of the scheme.

关 键 词：二重细分 B样条细分 收敛性 连续性 保凸性 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]