利用点和平面间的对偶性设计可展面  

Design of Developable Surfaces by Using Duality Between Plane and Point Geometries

作　　者：周敏[1] 彭国华[1] 叶正麟[1] 杨俊清[2] 

机构地区：[1]西北工业大学理学院,西安710072 [2]西安航空技术高等专科学校计算机工程系,西安710077

出　　处：《计算机辅助设计与图形学学报》2004年第10期1401-1406,共6页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金 (10 0 710 60 )资助

摘　　要：基于点和平面间的对偶性原理 ,提出了一种设计四次样条上可展面的方法 ,讨论了所设计可展面的特点和几何构造 ,并以中心点表示控制平面的方式对曲面的设计进行了较详细的实例分析 文中的设计方法直接、简单、有效 。Based on the idea of duality between plane and point geometries, we present an explicit representation for fourth degree developable surfaces In our scheme, a developable surface is designed by utilizing control planes with Bézier or B-spline basis functions In the paper, the properties and geometric construction algorithms for the developable surfaces designed are discussed, and furthermore, the method of representing control planes according to its center point is given It shows that the techniques for the geometric design of developable surfaces in this paper fully possess the characteristics of existing methods for curve design Our method provides a quite simple and intuitive way for designing developable surfaces

关 键 词：可展面 Bézier表示 B样条表示 对偶性 deCasteljau算法 G^2连续 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]