参数曲线的最优参数化

利用有理重新参数化的自由度求解参数曲线的最优参数化问题,提出一种度量曲线的参数速度与弧长参数化接近程度的方法.利用该方法求得的最优参数化在曲线的重新参数化曲线族中,参数速度偏离单位速度的最大值达到最小.最后,通过计算实例对该方法与其他算法得到的最优参数化的参数速度进行了比较.

Optimal Parameterization of Parametric Curves

The problem of exercising the freedoms of reparameterization of polynomial curve segments to achieve a "parametric flow" closest to the unit-speed or arc-length representation is addressed. A new quantitative measure of "closeness" to arc-length parameterization is presented and according to this measure, the problem of identifying the optimum rational reparameterization of a degree n polynomial curve is shown. The advantage of this measure is that the optimum rational reparameterization's parametric speed satisfies that the maximum deviation from unity is the minimum in this family. Experiments for comparing the efficiency of this algorithm with other methods are also included.