【摘要】 <正> 1 引言 B样条曲面是几何造型中一种用途广泛的方法,在实际应用中,大量问题需要我们研究曲面的凸性与连续性,它们都归结为求曲面在任意点处关于任意方向的各阶导数的求值问题. 给定（m+M）×（n十N）个空间点f_ij及两个非减节点向量{u_i;0≤i≤2m+M}和{v_j;0≤j≤2n+N},则定义在[u_m,u_m+M]×[v_n,v_n+N]上的m×n次B条曲面为 f（u,v）=（sum from i=0 to m+M-1）（sum from j=0 to n+N-1）(f_ijN_i^m（u）N_jⁿ（v）, （1）其中N_i^m（u）和N_jⁿ（v）为定义在前两节点向量上的规范B样条基函数,它们可以按严格形式递推地定义为下式更多还原

【Abstract】 By means of a description of all directional derivatives of a B-spline patch, an efficient e-valuation algorithm for all derivatives is presented, which is more effective than de Boor algorithm in storage and multiplication and division numbers, and is stable.更多还原