合理展开封头曲面的研究  

Study on Reasonable Flattening of Head Surface

作　　者：郑鹏飞[1,2] 王波[2] 赵菊娣[1] 林大钧[1] 安琦[1] ZHENG Pengfei WANG Bo ZHAO Judi LIN Dajun AN Qi(School of Mechanical and Power Engineering,East China University of Science and Technology,Shanghai 200237, China School of Mechanical Information, Yiwu Industrial ＆ Commercial College, Yiwu 322000, China)

机构地区：[1]华东理工大学机械与动力工程学院,上海200237 [2]义乌工商职业技术学院机电信息学院,浙江义乌322000

出　　处：《东华大学学报（自然科学版）》2017年第4期597-602,共6页Journal of Donghua University(Natural Science)

摘　　要：根据测地线的短程性与线上各点测地曲率为零的几何特性,采用在不可展的封头曲面上构建由测地线与法截线交织成线网的方法来获得椭圆形封头和球形封头展开图的边界,并建立对应的数学模型,结合计算机编程,为参数化展开封头曲面提供简便、稳定可靠的方法.以曲面理论面积为评判标准,该方法展开精度高于工程上常用的几种近似展开方法和CAD软件的展开精度.According to the two geometric characteristics of geodesics that the path between two points is the shortest and the geodesic curvature at every point equals zero, the boundary of the flattening ellipsoidal head or spherical head is computed by weaving a mesh with geodesics and normal sections on the undevelopable head surface. A simple, stable, reliable and parameterized undevelopable surface flattening method is proposed, and the corresponding mathematical model is established by its computer programming. The theoretical area of surface is used as the criteria for evaluation. It can be seen from the experimental examples that the flattening accuracy of the method is higher than other usual methods and CAD software aided method.

关 键 词：测地线 封头 不可展曲面 数学模型 展开精度 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]