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 algo- rithms were presented in detail, strict mathematical proofs were given, and the effectiveness of the method was shown by examples. This me...
【英文摘要】
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 algo- rithms were presented in detail, strict mathematical proofs were given, and the effectiveness of the method was shown by examples. This me...
【基金】
supported by the National Natural Science Foundation ofChina (No. 60673031);
the National Basic Research Program(973) of China (No. 2004CB719400)
【更新日期】
2009-04-28
【分类号】
U412.3
【正文快照】
INTRODUCTION In many applications such as highway and rail- way route design (Hartman, 1957; Baass, 1984) and car-like robot path planning (Fleury et al., 1995), it is complicated and important to construct a transition curve of G2 contact between two cir
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