二元样条的积分表示及分层三角剖分下二次样条空间的维数

An Integral Representation of Bivariate Splines and the Dimension of Quadratic Spline Spaces over Stratified Triangulation

本文通过引入一个积分协调条件，首次给出了二元样条的一个积分表示．文中还定义了平面单连通多边形区域的所谓分层三角剖分，并确定了此剖分下二次样条空间的维数．

In this paper, by introducing an integral conformality conditions, an integral rep- resentation of bivariate spline functions is given. Then, a new kind of so-called stratified triangulation of a simply connected planar polygonal region is introduced. Finally , the dimension of quadratic spline space associated with the stratified triangulation is determined.