Bézier 曲线的多项式重新参数化检测

研究了一种用于精确检测一条Bézier 曲线的次数是否可以通过多项式重新参数化降低的算法。该算法对任意一条Bézier 曲线，将重新参数化前后的基函数的关系用方程组的形式表达，但不需要解方程，而是通过系数表示的金字塔算法直接计算，可以精确求出用于重新参数化的多项式和降低次数后的Bézier 曲线的控制顶点，并且该重新参数化的多项式在相差一个线性变换的前提下是唯一的。通过实例应用，该算法运算速度较之前的算法快。

Polynomial reparameterization detection of Bézier curves

An algorithm is presented to determine whether the degree of Bézier curve can be reducedby polynomial reparameterization. In the algorithm, for any Bézier curve, the relation between thebasis functions before and after reparameterization is expressed as a system of equations. Instead ofsolving the equations, the polynomial for reparameterization and the control points of the lowerdegree Bézier curve can be calculated directly by a pyramid algorithm of coefficientreparameterization. In addition, the polynomial for reparameterization is unique to within a scalefactor and a constant. Compared with the previous algorithm by examples, this algorithm possessesshorter computational time.