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

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 Hangzhou 310027 China 

出 版 物：《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 (浙江大学学报（英文版）A辑（应用物理与工程）)

年 卷 期：2009年第10卷第4期

页      面：562-569页

核心收录：

学科分类：1305[艺术学-设计学（可授艺术学、工学学位）] 13[艺术学] 08[工学] 080203[工学-机械设计及理论] 081304[工学-建筑技术科学] 0802[工学-机械工程] 0813[工学-建筑学] 0814[工学-土木工程] 082301[工学-道路与铁道工程] 080201[工学-机械制造及其自动化] 0823[工学-交通运输工程] 

基　　金：supported by the National Natural Science Foundation ofChina (No. 60673031) the National Basic Research Program(973) of China (No. 2004CB719400) 

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

摘      要：We constructed a single C-Bezier curve with a shape parameter for G^2 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 Bezier 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.