摘要
基于三维射影空间中点和平面间的对偶性,提出了计算机辅助设计五次样条上可展曲面的一种简单且有效的方法,通过采用该方法,可利用具有B啨zier和B样条基的控制平面设计可展曲面。基于将可展曲面作为平面单参数族包络面的思想,给出在B啨zier和B样条基下可展曲面的参数表示形式。讨论了所设计可展曲面的特点和几何构造,研究结果表明,所提出的设计方法具有现有曲线设计方法的特征,现有的对于曲线的一些几何构造技术可延伸到可展曲面的设计。
It order to overcome the difficulties in representation of developable surfaces utilizing traditional approaches, based the concept of duality between points and planes in 3D projective space, a direct explicit method of computer-aided design for developable surfaces was presented. In this manner, a developable surface was designed using control planes with Bézier and B-spline basis functions. Techniques for the geometric design of developable surfaces herein had all the characteristics of existing approaches for curves design. Meanwhile, the properties of Bézier and B-spline representation were discussed respectively,and the method of representing control planes according to its center point was given. It shows that some of the geometric construction algorithms that exist for curves can be also generalized to the design of developable surfaces. Furthermore, by the design method that a developable surface is an envelope surface, we give detail analysis of examples about using the same control planes to design developable surfaces. The algorithms were explained in detail, and the examples demonstrate efficiency of the method.
出处
《中国机械工程》
EI
CAS
CSCD
北大核心
2007年第12期1425-1429,共5页
China Mechanical Engineering
基金
国家自然科学基金资助项目(60672135)
关键词
可展曲面
对偶性
控制平面
几何构造
developable surface
duality
control plane
geometric construction
