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