带参数PH曲线几何特征及过渡曲线构造
Geometric Characteristics of PH Curve with Parameters and Construction of Transition Curve
DOI: 10.12677/AAM.2021.109329, PDF,   
作者: 宋九锡, 王 研, 沈 洋, 秦凌云, 彭兴璇：辽宁师范大学数学学院，辽宁 大连
关键词: 三次PH曲线；过渡曲线；G2连续；C型；Cubic PH Curve； Transition Curve； G2 Continuous； Type C
摘要: 本文通过选取恰当的带参数Bézier曲线模型，得到其成为PH曲线的几何特征条件，构造了一类带参数的三次PH曲线。基于该曲线，构造了不互相包含两圆之间的过渡曲线，该曲线是G2连续的C型过渡曲线，并且在一定条件下，曲线内部的曲率有且仅有一个曲率极值点。数值例子验证了该方法的有效性。
Abstract: In this paper, by selecting the appropriate Bézier curve model with parameters, the geometric characteristic conditions of PH curve are obtained. A kind of cubic PH curve with parameters is constructed. Based on this curve, a transition curve is constructed. The curve is a second order continuous c-type transition curve, and the curvature inside the curve has only one curvature extreme point under certain conditions. Numerical examples show the effectiveness of the proposed method.
文章引用：宋九锡, 王研, 沈洋, 秦凌云, 彭兴璇. 带参数PH曲线几何特征及过渡曲线构造[J]. 应用数学进展, 2021, 10(9): 3148-3158. https://doi.org/10.12677/AAM.2021.109329

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