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ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2009, Vol. 10 Issue (4): 562-569    DOI: 10.1631/jzus.A0820267
Computer-aided Geometric Design     
A new method in highway route design: joining circular arcs by a single C-Bézier curve with shape parameter
Hua-hui CAI, Guo-jin WANG
Institute of Computer Graphics and Image Processing; State Key Lab of CAD & CG, Zhejiang University, Hangzhou 310027, China
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Abstract  We constructed a single C-Bézier curve with a shape parameter for G2 joining two circular arcs. It was shown that an S-shaped transition curve, which is able to manage a broader scope about two circle radii than the Bézier curves, has no curvature extrema, while a C-shaped transition curve has a single curvature extremum. Regarding the two kinds of curves, specific algorithms were presented in detail, strict mathematical proofs were given, and the effectiveness of the method was shown by examples. This method has the following three advantages: (1) the pattern is unified; (2) the parameter able to adjust the shape of the transition curve is available; (3) the transition curve is only a single segment, and the algorithm can be formulated as a low order equation to be solved for its positive root. These advantages make the method simple and easy to implement.

Key words： Transition curve      C-Bézier curve      Monotone curvature      Shape parameter     
Received: 08 April 2008     
CLC:  TP391.7  
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Hua-hui CAI
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Hua-hui CAI, Guo-jin WANG. A new method in highway route design: joining circular arcs by a single C-Bézier curve with shape parameter. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2009, 10(4): 562-569.

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http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.A0820267     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2009/V10/I4/562

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