C~1的四边形混合曲面片

对任意四边形，给出了在边界上插值已给定顶点的型值向量，一阶偏微商及各边中点法向微商的插值型的四边形曲面片Ｂｉ（ｕ，ｖ），曲面Ｂｉ（ｕ，ｖ）在边界上的Ｂéｚｉｅｒ控制点由顶点处的１２个条件唯一确定，内部的一些控制点可以由各边的法向微商确定，这样便可以求得Ｃ１插值于边ｅｉ（ｉ＝１，２，３，４）的曲面Ｂｉ（ｕ，ｖ）。引进混合函数，构造出混合曲面Ｐ（ｕ，ｖ），它分别在边ｅｉ（ｉ＝１，２，３，４）处Ｃ１插值于Ｂｉ（ｕ，ｖ）（ｉ＝１，２，３，４）。

C 1 Quadrilateral Blending Surface Patches

For arbitrary quadrilateral, the values of positions, first order derivatives at the every vertices of quadrilateral patches and normal derivatives at midpoints are given. The Bzier control point of boundary are determined only by 12 conditions at the vertices. But some inner control points are determined by n i(i =1,2,3,4), they are different. Hence we can get C 1 interpolating patch B i(u,v) at edges e i . Supposing blending function, blending surface P(u,v) can be constructed, and it C 1 interpolates B i(u,v) at edges e i(i =1,2,3,4).