Length Estimation of Rational Bézier Curves and Application to CAD Parametrization

We want to estimate the chord length Λ of a given rational Bézier curve efficiently. Since rational Bézier are nonlinear function, it is generally impossible to evaluate its length exactly. We approximate the length by using subdivision and we investigate the accuracy of the approximation Λn. In order to improve the efficiency, we use adaptivity with some length estimator. Additionally, we will give a rigorous theoretical analysis of the rate of convergence of Λn to Λ. We analyze also the required number of subdivisions in order to attain a prescribed accuracy. At the end, we briefly describe an application in CAD surface parametrization. Keywords—Rational Bézier, Length, Parametrization, Adaptivity.