Bézier曲线的一种重新参数化新方法

A New Re-Parameterization Method of Bézier Curve

曲线重新参数化的关键是重新参数化方法。对Bézier曲线的重新参数化方法进行了讨论,找到了一种新方法,比常用的有理线性参数变换计算简单,通用性强。论证了利用新方法的自由度,可以求出Bézier曲线的最优参数化方程。给出了求解Bézier曲线最优参数化方程的新算法。新算法具有单一自由度,最优值通过求解一个二次方程的根得到,算法简单可靠,文中给出了计算实例。

The key problem of re-parameterization of curves is the re-parameterization method. The re-parameterization methods are discussed and a new method is developed. It is proved that the optimal parameterization of an integral Bézier curve can be acquired with new method which is simpler than bilinear transformation. A new algorithm is presented. With the new algorithm the problem to acquire the optimal parameterization of an integral Bézier curve admits a single degree of freedom, whose optimal value can be easily determined as the root of a quadratic equation. Experiments for the efficiency of this algorithm are also included.