Parameterization for curve interpolation

A common task in geometric modelling is to interpolate a sequence of points or derivatives, sampled from a curve, with a parametric polynomial or spline curve. To do this we must first choose parameter values corresponding to the interpolation points. The important issue of how this choice affects the accuracy of the approximation is the focus of this paper. The underlying principle is that full approximation order can be achieved if the parameterization is an accurate enough approximation to arc length. The theory is illustrated with numerical examples.