Subdivision of Uniform ωB-Spline Curves and Two Proofs of Its C^(k-2)-Continuity  

作　　者：Jing Tang Mei-e Fang Guozhao Wang 

机构地区：[1]School of Computer Sciences and Educational Softwares,Guangzhou University,Guangzhou,China [2]Department of Mathematics,Zhejiang University,Hangzhou,China

出　　处：《Computer Modeling in Engineering & Sciences》2018年第5期263-280,共18页工程与科学中的计算机建模（英文）

基　　金：the National Natural Science Foundation of China(61772164,61761136010);the Natural Science Foundation of Zhejiang Province(LY17F020025).

摘　　要：ωB-splines have many optimal properties and can reproduce plentiful commonly-used analytical curves.In this paper,we further propose a non-stationary subdivision method of hierarchically and efficiently generatingωB-spline curves of arbitrary order ofωB-spline curves and prove its C^k?2-continuity by two kinds of methods.The first method directly prove that the sequence of control polygons of subdivision of order k converges to a C^k?2-continuousωB-spline curve of order k.The second one is based on the theories upon subdivision masks and asymptotic equivalence etc.,which is more convenient to be further extended to the case of surface subdivision.And the problem of approximation order of this non-stationary subdivision scheme is also discussed.Then a uniform ωB-spline curve has both perfect mathematical representation and efficient generation method,which will benefit the application ofωB-splines.

关 键 词：ωB-spline SUBDIVISION C^(k-2)-continuity asymptotic equivalence approximation order 

分 类 号：O17[理学—数学]