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

作　　者：宋九锡 王研 沈洋 秦凌云 彭兴璇[1] 

机构地区：[1]辽宁师范大学数学学院,辽宁 大连

出　　处：《应用数学进展》2021年第9期3148-3158,共11页Advances in Applied Mathematics

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。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.

关 键 词：三次PH曲线 过渡曲线 G²连续 C型 

分 类 号：G63[文化科学—教育学]