B样条的p-nary细分

有关B样条曲线曲面的binary细分技巧及其应用的研究已经获得了许多成果,建立在B样条binary细分基础上的binary细分法收敛性连续性分析的生成多项式法就是其中之一。该文研究了B样条曲线的p-nary细分问题,给出并证明了B样条基函数的p尺度细分方程中细分系数的计算公式及其性质,讨论了用p-nary细分生成非有理及有理B样条曲线的细分规则。采用该文的方法可方便而快速地在计算机上绘制有理B样条曲线。文章的结果可用于对一般p-nary曲线细分法收敛性及连续性的分析。

P-nary Subdivision for B-splines

There have been a lot of results about the subdivision techniques of B-splines and its application,which make it a fast and effective way to generate B-splines with binary subdivision schemes.The binary subdivision schemes of B-splines are prototypes for general binary subdivision schemes and make it possible to analyze the convergence of a binary subdivision scheme to a limit curve/surface and the smoothness of this limit by using the method of generating polynomial.In this paper we study the p-nary subdivision process for B-splines.Discrete convolution and generating polynomial are introduced to get the subdivision coefficients.The properties of the subdivision coefficients are discussed.Finally the subdivision formulae for rational and non-rational B-spline curves are given and proved.