平面三次Bézier曲线间的一种延拓方法

An extension method for plane cubic Bézier curves

文章在保持G1连续的条件下,将一条已知的平面三次Bézier曲线延拓到另一条与其不相邻接的三次Bézier曲线,其中的过渡曲线也为三次Bézier曲线,而且中间的过渡曲线形状可以由用户加以调整,进而对近似于曲线弧长、曲线能量、曲率变化率的几类目标函数分别极小化,以生成各种光顺的曲线;利用所给方法做了一些2条不相连接的平面三次Bézier曲线延拓的实例,并与已有结果进行比较,结果表明所提出的方法优于已有的方法。

This paper presents a method to extend a given plane cubic Bézier curve to another nonadjacent cubic Bézier curve under G1 continuous conditions.The transition curves are also cubic Bézier curves.The shape of the transition curves can be adjusted by the user and various fairing curves are constructed by minimizing the objective functions of approximate arc length,energy and curvature variation of the curves respectively.Some examples of the extension of two nonadjacent plane cubic Bézier curves are given and the obtained results are compared with the known ones.It is proved that the presented method is better than the known ones.