Research On The Optimal Parametric Algorithms Of Freedom Curves

The results of path planning and motion control applications are highly dependent on the curves representations. A NURBS curve using different parameterizations with different parametric equations and different speeds of parametric equations, how to find the closeness to arc-length parametric equation from these re-parameterizations is called optimal re-parameterization. In summary, the less segments C1continuous curves satisfy the requirements of CAD applications makes piecewise-cubic parameterization be better applied to the actual CAD applications or path planning applications. The much greater computational complexity of schemes for optimal C1re-parameterization, and the absence of elementary closed-form solutions, makes such schemes highly non-linear.In this paper, an algorithm is presented to optimize the parameterization of NURBS curves based on C1continuous piecewise-cubic re-parameterization, 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 C1continuous piecewise-rational re-parameterization method, better results are obtained with less segmentation. Examples are given to show the performance of our algorithm.