给定任意拓扑控制多面体的分片光滑样条曲面拟合

张量积B样条曲面在CAD领域具有重要意义，但是普通张量积B样条曲面的控制顶点必须呈拓扑矩形阵列形式排列，不能满足任意拓扑控制网格的要求。本文基于双四次广义B样条基函数和G1连续条件，推导出线性混合矩阵。利用这些混合矩阵，非规则控制多面体中的控制顶点被转换成分片B样条曲面的控制顶点，相邻曲面片间满足G1连续条件。即利用混合矩阵，可以用与张量积B样条曲面相同的概念框架处理具有非四边界及多于或少于4个四边界面汇聚于一点的非规则控制多面体的曲面拟合。文中还包括应用实例以表明文中方法的正确性。

Smooth Piecewise Spline Surfaces over Arbitrary Control Polyhedron

Tensor-product B-spline surface is of great importance in computer-aided design. However, ordinary B-spline surface, whose control points must be in rectangular topology array, is not suitable for control polyhedron with arbitrary topology. Based on the generalized B-spline blending functions and G1 continuous conditions, the blending matrices are derived. By means of the blending matrices, the control vertexes in irregular control polyhedron are converted to control points of piecewise B-spline patches. The resulting patches are tangent continuous. That is, irregular meshes with non-quadrilateral cells and more or fewer than four cells meeting at a point can be input and treated in the same conceptual framework as tensor-product B-splines. Practical examples are included in the paper to verify the proposed method.