Bézier样条曲线的近似弧长参数化方法

提出了Bézier样条曲线近似弧长参数化的方法及相应的算法。通过求出曲线近似二分之一弧长的点及其相应的参数值,可将曲线分割为两条Bézier样条曲线。这两条曲线的弧长近似相等,因此让它们带有相同的权1。对新生成的Bézier样条曲线不断重复上述工作,最终得到一条由多条Bézier样条曲线所构成的新的曲线。将这多条Bézier样条曲线合并为一条Bézier样条曲线,进而通过节点插入技术将其转化为B样条形式的曲线以便得到全局参数,其中各段Bézier曲线在全局参数域中所占子区间的长度与它们所具有的权成比例,这样便得到一条近似弧长参数化曲线。

AN APPROXIMATE ARC-LENGTH PARAMETERIZATION METHOD FOR BeZIER SPLINE CURVES

A method of approximate arc-length parameterization for Bezier spline curves and the corresponding algorithm are proposed. The point of approximately half arc-length of the curve is found, and the curve is subdivided at the corresponding parameter value. Thus; two Bezier spline curves are obtained. The two curves have approximately equal arc-length, and weight 1 is assigned to each of them. Repeated work is done on the newly generated Bezier spline curves, and finally a new curve consisting of several Bezier spline curves is obtained. These Bezier spline curves are merged into one, and by means of knot inserting technique,it is converted into a curve of B-spline form. The new curve has a global parameter, in which each Bezier curve has a parameter sub-interval of length proportional to its weight. Thus, a curve with approximate arc-length parameterization is obtained.