New Proper Reparameterization of Plane Rational Bézier Curves  

作　　者：Zhen-Fei Wang Xiao-Diao Chen Jun-Hai Yong 王振飞;陈小雕;雍俊海(School of Computer,Hangzhou Dianzi University,Hangzhou 310018,China;Haihe Laboratory of Information Technology Application Innovation,Tianjin 300480,China;School of Software,Tsinghua University,Beijing 100084,China)

机构地区：[1]School of Computer,Hangzhou Dianzi University,Hangzhou 310018,China [2]Haihe Laboratory of Information Technology Application Innovation,Tianjin 300480,China [3]School of Software,Tsinghua University,Beijing 100084,China

出　　处：《Journal of Computer Science & Technology》2024年第5期1193-1206,共14页计算机科学技术学报（英文版）

基　　金：supported by the National Natural Science Foundation of China under Grant Nos.61972120 and 62021002 and the Haihe Lab of ITAI Project(22HHXCJC00006);supported by the National Key Research and Development Program of China under Grant Nos.2020YFB1708900 and TC190A4DA/3.

摘　　要：Coincidence detection of two curves or two surfaces has wide application in computer-aided design(CAD)and computer-aided geometric design(CAGD).Proper reparameterization is the most complicated part in the detection.This paper presents and proves the efficient and necessary coincidence condition for two rational Bézier curves in a new way.It also proposes an effective and efficient proper reparameterization method,Algorithm 1,for detecting a rational Bézier curve which can be degenerated into a new one of a lower degree.A numerical proper reparameterization method,Algorithm 2,and examples are also presented.Algorithm 1 is up to ten times faster than other prevailing methods,and Algorithm 2 is twice as fast and half as close as other prevailing methods.New CAD systems using Algorithm 1 and Algorithm 2 will hold accuracy and little computation time.

关 键 词：rational Bézier curve coincidence condition control polygon DEGENERATION proper reparameterization 

分 类 号：TP39[自动化与计算机技术—计算机应用技术]