Meeting C1-Continuity Bézier Triangular Patches with a Common Corner

We propose a new concept named mixed directional derivative,and then construct C1-continuity surfaces consisting of some degree four triangular patches which have degree four boundary curves also. Compared with the method proposed by Loop,in which twisting compatibility condition has been introduced ,the new method can obtain such good surfaces,their degree is two less than Loop’s surface,and their form can be locally adjusted.