摘要
§1.引言众所周知,de Boor-Con递推公式及微分-差分公式对于一元B样条的理论和应用极为重要。在多元样条中是否存在类似的结果,已成为近年来的研究课题。本文从B网结构出发,讨论三向剖分下不同次数样条空间的B样条之间的递推关系,指出不能简单地把函数形式的de Boor-Con公式搬到这里,然而可以在B网意义下实现递推。
Two kinds of explicit recurrence algorithms for evaluating B-splines in three directions are presented in terms of B-net in this paper. These algorithms may be used to compute the B-net coefficients of B-splines in spaces S_(3v)^(2v-1)and S_(3v+1)~2v, only using the simplest B step function and piecewise linear function, respectively. The results are a generalization of the so called de Boor-Cox recurrence of B-splines in one dimension to the case of three directions in two dimensions. As an example of the recurrence, the B-net coefficients of B-spline is S_6~3 is given.
出处
《计算数学》
CSCD
北大核心
1990年第4期365-375,共11页
Mathematica Numerica Sinica
基金
国家自然科学基金
