两相邻Bézier曲线的近似合并

Approximate Merging of a Pair of Bézier Curves

利用Bézier曲线细分后的矩阵表示,将所定义的原Bézier曲线与合并Bézier曲线间的距离函数取最小值,给出一种把两相邻Bézier曲线合并成一条Bézier曲线的方法.在合并过程中,分别考虑了合并Bézier曲线在左右端点处与原Bézier曲线达到高阶插值的合并以及合并Bézier曲线插值于原Bézier曲线上的某些点的合并.指出提高合并Bézier曲线的次数可减小合并误差,改善合并效果.最后给出数值例子.

This paper deals with the problem of approximate merging of two adjacent Bézier curves into one Bézier curve. We propose a method by using the matrix representation of subdivided Bézier curve and by minimizing the distance function defined between the original B6zier curves and the merged Bézier curve. Continuity at the endpoints of curves has been considered in the merging process, and approximate merging with points constraints are also discussed. It is shown that the degree elevation of the original Bézier curves could reduce the merging error. We provide examples to demonstrate the algorithm.