平面G2连续的三次PH过渡曲线的构造
Construction of Cubic PH Transition Curve of Plane G2 Continuity
摘要:
本文用三次PH曲线来构造互相包含的两圆之间G2连续的C型过渡曲线。同时证明了互相包含的两圆之间的过渡曲线的唯一性条件。最后，给出过渡曲线的生成步骤，并且通过数值例子证明了该方法的有效性。
Abstract:
In this paper, the cubic PH curves are used to construct the G2 continuous C type transition curves between two circles that contain each other. At the same time, the uniqueness condition of the transition curve between two circles containing each other is proved. Finally, the generating steps of the transition curve are given, and the effectiveness of the method is proved by a numerical example.
参考文献
|
[1]
|
Meek, D.S. and Thomas, R.S.D. (1991) A Guided Clothoid Spline. Computer Aided Geometric Design, 8, 163-174. [Google Scholar] [CrossRef]
|
|
[2]
|
Walton, D.J. and Meek, D.S. (1996) A Planarcubic Bezier Spiral. Journal of Computational and Applied Mathematics, 72, 85-100.
|
|
[3]
|
Farouki, R.T. (1994) The Conformal Map z→z2 of the Hodograph Plane. Computer Aided Geometric Design, 11, 363-390. [Google Scholar] [CrossRef]
|
|
[4]
|
Walton, D.J. and Meek, D.S. (1998) G2 Curves Composed of Planar Cubic and Pythagorean Hodograph Quintic Spirals. Computer Aided Geometric Design, 15, 547-566. [Google Scholar] [CrossRef]
|
|
[5]
|
Walton, D.J. and Meek, D.S. (1996) A Pythagorean Hodogtaph Quintic Spiral. Computer Aided Design, 28, 943-950. [Google Scholar] [CrossRef]
|
|
[6]
|
Walton, D.J. and Meek, D.S. (2007) G2 Curves Design with a Pair of Pythagorean Hodograph Quintic Spiral Segments. Computer Aided Geometric Design, 24, 267-285. [Google Scholar] [CrossRef]
|
|
[7]
|
Zheng, Z.-H. and Wang, G.-Z. (2018) A Note on Pythagorean Hodograph Quartic Spiral. Applied Mathematics: A Journal of Chinese Universities, 33, 234-252. [Google Scholar] [CrossRef]
|
|
[8]
|
郑志浩, 汪国昭. 三次PH曲线的曲率单调性及过渡曲线构造[J]. 计算机辅助几何设计与图形学报, 2014, 26(8): 1003-9775.
|
|
[9]
|
刘莹莹, 王旭辉. 平面三次PH过渡曲线的构造[J]. 合肥工业大学学报, 2016, 39(9): 1003-5060.
|