平面三次PH过渡曲线的构造

Construction of planar cubic PH transition curve

文章采用三次PH曲线构造两圆之间的过渡曲线(两圆不相互包含的情况),该过渡曲线满足G^2连续条件。因为在两圆不相互包含的情况下,曲线两端点处曲率同号,所以能构造出C型过渡曲线。在一定条件下,可以证明两圆之间存在唯一的三次PH过渡曲线。此外,文章还给出了该过渡曲线的构造算法,并通过实例验证了该方法的有效性。

Cubic PH curves were used to construct the transition curves between two circles where one circle is not included in the other one .The transition curves are G2 continuous at the two endpoints . Under the assumption that one circle is not included in the other one ,the curvature of the curve at the endpoints is positive or negative simultaneously .Thus ,C‐shaped transition curves can be construc‐ted .Moreover ,under some special conditions ,the cubic PH transition curve is unique .An algorithm is also provided to generate the cubic PH transition curves .Finally ,the effectiveness of the presented method is demonstrated by some numerical examples .