A new method in highway route design：joining circular arcs by a single C-Bezier curve with shape paramete

作     者：Hua-hui CAI Guo-jin WANG 

作者机构：Institute of Computer Graphics and Image Processing State Key Lab of CAD & CG Zhejiang University 

出 版 物：《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 

年 卷 期：2009年第10卷第4期

主　　题：Transition curve Shape parameter C-Bezier curve Monotone curvature 

摘      要：We constructed a single C-B zier 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 B zier curves, has no curvature extrema, while a C-shaped transition curve has a single curvature extremum. Regarding the two kinds of curves, specific algo- rithms 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 tran- sition 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.