Bézier样条曲线改进的近似弧长参数化方法

提出了Bézier样条曲线利用分割技术近似弧长参数化的一种方法,并给出了相应的算法。通过求出曲线上所谓的‘最坏点’并在相应点处进行分割,可得到两条Bézier样条曲线。让这两条Bézier样条曲线具有与它们的近似弧长成比例的权,并对所得到的新的Bézier样条曲线进行同样的工作最终可得到一条由多条Bézier样条曲线所构成的新曲线。将这多条Bézier样条曲线合并成为一条Bézier样条曲线并通过节点插入技术将所得Bézier样条曲线转化为B-样条曲线的形式可得到全局参数域,其中各条Bézier曲线在全局参数域中所占子区间的长度与它们的权成比例,这样便得到了一条近似弧长参数化曲线。

Improved approximate arc-length parameterization method for Bézier spline curves

We provide a method for approximate arc-length parameterization for Bézier spline curves by using the subdivision techniques and give the corresponding algorithm.By finding the so-called ‘worst point’ of the curve and subdividing the curve at the corresponding parameter value，we got two Bézier spline curves.Let the two curves have weights that are proportional to their approximate arc-lengths and repeatedly do the same to the newly generated Bézier spline curves and we can finally get a curve consisting of several Bézier spline curves.Merge these Bézier spline curves into one and by means of knots inserting technique convert it into such a curve that has the B-spline form.Now this new curve has a global parameter and in the interval of which each Bézier curve will have a parameter sub-interval of length proportional to its weight.Thus we get a curve with approximate arc-length parameterization.