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《Journal of Zhejiang University(Engineering Science)》 2010-01
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Construction of cubic C-Bézier spiral and its application in highway design

CAI Hua-hui 1,2 ,WANG Guo-jin 1 (1.Institute of Computer Images and Graphics,State Key Laboratory of CAD&CG,Zhejiang University,Hangzhou 310027,China;2.School of Information Engineering,Jingdezhen Ceramic Institute,Jingdezhen 333403,China)  
A planar cubic C-Bézier spiral with monotone curvature of constant sign was constructed to meet the requirement of highway design,and then the transition curves between straight lines and/or circular arcs were derived in detail.As it is done with clothoids in engineering,a single spiral is used for straight line to circular arc,two spirals suiting C-shaped or S-shaped transition for circular arc to circular arc,two spirals for straight line to straight line,and a single spiral for circular to circular arc when the latter is contained within the former.The concrete expressions for the first four cases were given.In the fifth case,the solution cannot always be obtained.Because straight line segments and circular arcs can be represented precisely by C-Bézier curves,the issues such as highway design can be handled in the system by C-Bézier model,avoiding the difficult situation for computer-aided design system to use the clothoids defined in terms of the Fresnel integral.
【Fund】: 国家自然科学基金资助项目(60933007 60873111)
【CateGory Index】: TP391.41
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