An improved approximate arc-length parameterization method for Bezier curves

We provide a method for approximate arc-length parameterization for Bezier 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 Bezier curves. Let the two curves have weights that are proportional to their approximate arc-lengths. Then we repeatedly do the same to the newly generated Bezier curves and finally we can get a piecewise Bezier curve. By means of knot inserting technique we 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 Bezier curve will have a parameter sub-interval of length proportional to its weight. Thus we get a curve with approximate arc-length parameterization