任意三角剖分下的C^1-有理样条函数及基函数

Classes of basis of C^1-rational splines over triangulation

采用结点基的方法，结合研究多元多项式样条函数的光滑余因子方法的思想，解决了任意三角剖分下的Ｃ１－有理样条函数的存在性，并得到了任意三角剖分下具有最少自由度的Ｃ１－有理样条函数类．构造了具有３次代数精度的有理插值算子及其相应的全部Ｃ１－广义楔函数的简便的显示表达式。

The aim of this paper is to investigate the construction of C1-rational spline function classes which have the minimal dimension of freedom over any triangulation by means of the generalized wedge function method. The rational interpolation operator having degree of precision at least 3 and its equivalent representation are presented. Meanwhile, the authors give out the explicit expressions of all C1-generalized wedge functions on any triangulation.