中文摘要：

以二元四次多项式在三角域和矩形域上的Bezier形式的Blossom为工具，给出了当给定一张三向四次箱样条曲面时，能与之C^0、C^1、C^2拼接的三边或矩形Bezier曲面的控制顶点所要满足的一个显式表示的充分条件。这一结果在使用三向四次箱样条曲面或Loop细分曲面造型，而又需要构造Bezier曲面与之拼接或补洞时，具有理论和实际应用价值。

英文摘要：

Using bivariate quartic polynomial＇ s Blossom over triangular and rectangular domains, when a 3-direction quartic box spline surface is given, in order to make triangular or rectangular B6zier surface to be C^0, C^1, C^2 connected with it , one kind of explicit sufficient condition of the B6zier surface＇ s control points which should be subjected is discussed. When geometric modeling with 3-direction quartic box spline surface or Loop subdivision surface, this conclusion is valuable for making Bdzier surface to be smooth connected with the modeling surface or to fill holes.