任意三角形控制网格的二元四次箱样条曲面算法

二元三方向剖分是方向最少的三角剖分,建立在其上的二元三向箱样条在工程曲面造型等领域有着极为广 泛的应用。规范的二元三向四次箱样条曲面计算仅针对网格中点的价数均为6的情形,从规范的算法出发,提出 了一种任意价数控制点的情形下的曲面计算算法,并对算法进行了较为详细的分析。分析及试验结果表明,按该 算法生成的曲面有较好的整体光顺特性,各面片间是C1连续的,而对某一个三角面片内部则是C2连续的。由于 本算法适用于任意的三角形控制网格,因此在CAD／CAGD等曲面造型中有很高的实用价值。

Surface algorithm based-on bivariate quartic box-spline for arbitrary triangular control meshes

Bivariate 3-directional subdivision is a triangulation with least direction. Box spline built on it is widely applied in the engineering of surface modeling. The normal algorithm of bivariate 3-directional spline surface is only for normal control meshes in which every point has valence 6. A surface algorithm based-on bivariate 3-directional quartic box-spline for arbitrary triangular control meshes is proposed. Next, the analyses of its properties, especially continuity, are presented in detail. Finally, two examples are given. The results show that surfaces got by this algorithm hold a better smoothness. Two adjacent patches have continuity of C1 and the inner of any one patch C2. Clearly, the algorithm can be applied to arbitrary triangular control meshes, so it is very practically valuable for surface modeling in CAD/CAGD.