关于二元样条空间Sr（3r）（△*）的维数

On the Dimension of the Bivariate Splines Spaces

英文关键词:multivariate spline  HCT triangulation  B-net  super-spline

中文摘要:

      设△^*任何三角剖分△的ＨＣＴ细分的三角剖分．本文建立了定义于△^*上的二元样条函数空间S^r_（3r）（△^*）的维数公式．我们的证明方法同时给出了S^r_（3r）（△^*）的一组显示的基函数，并阐明基函数具有某种意义的局部最小支集

英文摘要:

      We establish the dimensional formula of the space of C^r bivariate piecewisepolynomials defined on a triangulation △^* which comes from an original triangulation △ of a connected polygonal domain with HCT subdivision for each triangle of △. Ourapproach is made by constructing a minimal determining set and an associated explicitbasis for the space S^r_（3r）（△^*）. The minimal determining set is defined well.