Fast and Accurate Parametric Curve Length Computation

Abstract

This paper describes a simple technique for evaluating the length of a parametric curve. The technique approximates sections of the curve to the arc of a circle using only sample points on the curve; no computation of derivatives or other properties is required. This method is almost as quick to implement and compute as chord-length summation, but it is much more accurate. It also provides recursion criteria for adaptive sampling. An extension of the algorithm to estimate the area of a parametric surface is discussed briefly.