Degree elevation operator and geometric construction of C-B-spline curves

作     者：ZHU Ping1,2*,WANG GuoZhao1 & YU JingJing1 1Institute of Computer Graphics and Image Processing,Zhejiang University,Hangzhou 310027,China 2Laboratory of Scientific Computing,Southeast University,Nanjing 211189,China 

作者机构：1. Institute of Computer Graphics and Image Processing Zhejiang University Hangzhou 310027 China2. Laboratory of Scientific Computing Southeast University Nanjing 211189 China 

出 版 物：《Science China(Information Sciences)》 (中国科学:信息科学(英文版))

年 卷 期：2010年第53卷第9期

页      面：1753-1764页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the the National Natural Science Foundation of China(Grant Nos.60773179,60970079,60933008) the National Youth Science Foundation of China(Grant No.60904070) 

主　　题：C-B-spline degree elevation operator bi-order C-B-spline geometric convergence geometric construction 

摘      要：Unlike a B ezier curve,a spline curve is hard to be obtained through geometric corner cutting on control polygons because the degree elevation operator is difficult to be obtained and geometric convergence is hard to be *** order to obtain geometric construction algorithm on C-B-splines,firstly we construct the degree elevation operator by using bi-order splines in this *** we can obtain a control polygon sequence by degree elevation based on the degree elevation operator derived from a C-B-spline ***,we prove that this polygon sequence will converge to initial C-B-spline *** geometric construction algorithm possesses strong geometric *** is also simple,stable and suitable for hardware to *** algorithm is important for CAD modeling systems,since many common engineering curves such as ellipse,helix,*** be represented explicitly by C-B-splines.