【摘要】 通过改变k×h阶B样条曲面和NURBS(Non UniformRationalB spline)曲面的若干节点,分别产生一个B样条曲面族和NURBS曲面族,并指出:曲面族的包络是用相同控制顶点定义的(k -a)×(h -b)阶B样条曲面和NURBS曲面,其中a ,b分别是两个方向上所改变的节点的重数 对于B样条曲面来说,曲面族与其包络的任意阶相同偏微分之间只相差一个因子,文中所得结果可以作为计算机辅助设计系统中曲面造型和形状修改的理论参考更多还原

【Abstract】 Modifying some knots of a B-spline or NURBS surface of order k×h to generate a family of B-spline or NURBS surface is presented. We show that the envelope of the family is a B-spline or NURBS surface defined by the same control points, and its order is (k-a)×(h-b) , where a,b are the multiplicity of the modified knots. Moreover, any order partial derivatives of the B-spline surface and the family of B-spline surfaces differ only in a multiplier. The presented results can be served as a theoretical guidance for surface modeling and shape modifications in computer aided design today.更多还原