A C¹ Continuous Algorithm to Optimize the Parameterization of NURBS Curves

The results of path planning and motion control applications are highly dependent on the curves representations.In this paper, an algorithm is presented to optimize the parameterization of NURBS curves based on C¹ continuous piecewise-cubic reparameterization, which generates closer approximations to the arc-length parameterization.The formulated energy is discretized by the Simpson method, and its initial value is obtained by the extreme value method, which is further optimized by the Levenberg-Marquardt method.Compared with C¹ continuous piecewise-rational reparameterization method, better results are obtained with less segmentation.Examples are given to show the performance of our algorithm.