An Approximate Arc-Length Parameterization Method for Bézier Curves

A method for approximating arc-length parameterization for Bézier curves by using the subdivision techniques is presented.By finding the point of approximately half the arc-length of the curve and subdividing the curve at the corresponding parameter value,we got two Bézier curves,which have approximately equal arc-length and parameter interval of unit length.Viewing the two curves as a whole and globaliz ing their parameters,we got a curve such that the point of the approximately half the arc-length corresponds to the midpoint of the new global parameter interval.Repeatedly doing this to the newly generated Bézier curves and we can finally get a piecewise Bézier curve.Then we can get a curve with approximate arclength parameterization by expressing the curve in B-spline form.