A new method for designing a developable surface utilizing the surface pencil through a given curve

查看全文 作　　者：Hongyan Zhao Guojin [1]Wang

机构地区：[1]Department of Mathematics and State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou 310027, China

出　　处：《Progress in Natural Science:Materials International》索引2008年第18卷第1期,共6页

基　　金：This work was supported by the National Basic Research Program of China(Grant No.2004CB719400);National Natural Science Foundation of China(Grant Nos.60673031,60333010,and 60021201). 摘　　要：This paper proposes a new method for designing a developable surface by constructing a surface pencil passing through a given curve, which is quite in accord with the practice in industry design and manufacture.By utilizing the Frenet trihedron frame,we derive the necessary and suffcient conditions to construct a developable surface through a given curve.Considering the requirements in shoemak- ing and garment-manufacture industries,we also study the special case of specifying the given curve as a geodesic.The given geodesic can be classified into three types corresponding to each type of developable surface.We also present the polynomial representation of the developable surface.The algorithm is convenient and effcient for applications in engineering. 关键词：测地线 CAD/CAM技术测量方法表面记录

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A new method for designing a developable surface utilizing the surface pencil through a given curve

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