We propose a novel method for fitting planar B-spline curves to unorganized data points. In traditional methods, optimization of control points and foot points are performed in two very time-consuming steps in each iteration: 1) control points are updated by setting up and solving a linear system of equations; and 2) foot points are computed by projecting each data point onto a B-spline curve. Our method uses the L-BFGS optimization method to optimize control points and foot points simultaneously and therefore it does not need to perform either matrix computation or foot point projection in every iteration. As a result, our method is much faster than existing methods.
Abstract For approximation of a set of points P j ϵ R d by a parametric curve X ( t ) the choice of parameters t j is essential. None of the parametrization strategies is optimal. To obtain good approximation results, reparametrization (parameter correction) of the points is necessary. In general, these reparametrization methods work only locally. We present a global reparametrization method which leads to dramatically better results.