均匀样条上可展面的计算机辅助设计  

Computer-aided design of uniformly developable surfaces

作　　者：周敏[1] 彭国华[2] 叶正麟[2] 杨俊清[1] 

机构地区：[1]西安航空技术高等专科学校,陕西西安710077 [2]西北工业大学数学与信息科学系,陕西西安710072

出　　处：《陕西师范大学学报（自然科学版）》2002年第2期11-14,共4页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目 (10 0 710 6 0 )

摘　　要：将Bodduluri和Ravani对三次均匀样条上可展面的研究结论进行了推广 ,提出了任意次均匀样条上可展面的设计方法 ,讨论了所设计可展面的特点和几何构造 ,并以不同的以中心点表示控制平面的方式对曲面的设计进行了实例分析 ,分析表明设计结果良好 .Using the concept of duality between points and planes in 3D projective space, the paper presents a direct explicit representation for developable surfaces utilizing control planes. In this manner, a developable surface is designed using control planes with Bezier and B spline basis functions. Techniques for the geometric design of developable surfaces in this paper have all the characteristics of existing methods for curves design. Some of the geometric constructions that exist for curves are also generalized to the design of developable surfaces. The paper also proves that representation control planes according to its centre point and the distance to the centre point from the origin may display range of control planes by its centre point. This allows a designer to control planes directly in designing a surface and displaying the trajectory of the generating plane.

关 键 词：均匀样条 可展面 计算机辅助设计 Bezier表示 B样条表示 对偶性 曲面设计 几何构造 

分 类 号：O18[理学—数学] TP391.72[理学—基础数学]