Fast [formula omitted] polynomial spline interpolation algorithm with shape-preserving properties

Abstract

In this article, we address the problem of interpolating data points by regular L 1 -spline polynomial curves of smoothness C k , k ⩾ 1 , that are invariant under rotation of the data. To obtain a C 1 cubic interpolating curve, we use a local minimization method in parallel on five data points belonging to a sliding window. This procedure is extended to create C k -continuous L 1 splines, k ⩾ 2 , on larger windows. We show that, in the C k -continuous ( k ⩾ 1 ) interpolation case, this local minimization method preserves the linear parts of the data well, while a global L 1 minimization method does not in general do so. The computational complexity of the procedure is linear in the global number of data points, no matter what the order C k of smoothness of the curve is.