Developable Bezier function surface  

作　　者：CHEN Dongren and WANG Guojin(State Key Laboratory of CAD&CG, Institute of Images and Graphics, Zhejiang University, Hangzhou 310027, China) 

出　　处：《Progress in Natural Science:Materials International》2002年第5期383-387,共5页自然科学进展·国际材料（英文版）

基　　金：Supported jointly by the National Natural Science Foundation of China (Grant No. 69973041); Natural Science Foundation of Zhejiang Province (Grant No.698025) ; the Foundation of State Key Basic Research 973 Item (Grant No.G1998030600).

摘　　要：Developable surface plays an important role in engineering practice. And Bezier function surfaces on the rectangular and triangular domains are common representation forms in a computer aided geometric design system. However, there are no studies about developable Bezier function surface up to now. General characterizations of developable Bezier function surfaces of arbitrary degree on the rectangular and triangular domains are presented. It is proved that a developable Bezier function surface of degree 2 on the triangular domain must be a parabolic cylinder. The construction methods of developable Bezier function surfaces of degree 3 on the triangular domain and of degree (2,2) on the rectangular domain are presented. The conclusions can be easily extended to bivariate polynomial function surface.Developable surface plays an important role in engineering domains are common representation forms in a computer aided geometric function surface up to now. General characterizations of developable function surface of degree 2 on the triangular domain must be a parabolic of degree 3 on the triangular domain and of degree (2,2) on the rectangular domain are presented. The conclusions can be easily extended to bivariate polynomial function surface.

关 键 词：triangular Bezier surface tensor product Bezier surface developable surface shift operator. 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]