三角B样条上可展曲面的设计与形状调节  

Design for Adjustably Developable Surfaces Based on Triangle-B Spline

作　　者：周敏[1] 杨俊清[2,3] 叶正麟[1] 彭国华[1] 

机构地区：[1]西北工业大学理学院应用数学系 [2]西安航空技术高等专科学校计算机工程系 [3]西安电子科技大学计算机学院,西安710071

出　　处：《计算机工程与应用》2006年第28期43-45,共3页Computer Engineering and Applications

基　　金：陕西省自然科学基金资助项目(编号:2004A03);西北工业大学研究生创业种子基金资助项目(编号:z200571)

摘　　要：提出了计算机辅助设计可展曲面的新方法,利用该文的方法,可展曲面可用具有三角B样条基函数的控制平面来设计,这种设计方法具有现存曲线设计方法的特征。同时,通过引入形状控制参数,使生成的可展曲面在较大的范围内可进行调节和控制,增加了造型的自由度。该文的设计方法直接、简单、有效,不仅能克服传统方法在可展曲面设计方法上的缺陷,而且能方便地解决工程中经常遇到的可展曲面的形状难以调节和控制的问题。In this paper,using the important idea of duality between plane and point geometries,we propose a direct explicit and efficient method of computer-aided design for developable surfaces based on triangle-B spline.The developable surfaces are represented using control planes with appropriate basis functions.The shapes of developable surfaces can be adjusted using a control parameter.When adjusting parameter,a family of developable surfaces can be constructed,they can keep the characteristics of B spline surfaces.Meanwhile,we show that the techniques for the geometric design of developable surfaces in this paper have all the characteristics of existing approaches for curves design.The new algorithm can not only overcome the difficulties in representation of developable surfaces utilizing traditional approaches,but also resolve the problems in adjusting and controlling the shape of developable surfaces that often faced in Engineering.The algorithms are explained in detail,and demonstrated with the examples in the paper.We expect our methods can fill the gaps in research of developable surfaces.

关 键 词：可展曲面 对偶性 三角B-样条 控制平面 控制参数 细分 

分 类 号：TP391[自动化与计算机技术—计算机应用技术] O245[自动化与计算机技术—计算机科学与技术]