Fast L1kCk polynomial spline interpolation algorithm with shape-preserving properties

In this article, we address the problem of interpolating data points by regular L1L1-spline polynomial curves of smoothness CkCk, k⩾1k⩾1, that are invariant under rotation of the data. To obtain a C1C1 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 CkCk-continuous L1L1 splines, k⩾2k⩾2, on larger windows. We show that, in the CkCk-continuous (k⩾1k⩾1) interpolation case, this local minimization method preserves the linear parts of the data well, while a global L1L1 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 CkCk of smoothness of the curve is.

Research highlights
► Shape preserving interpolation of data points by L1 polynomial spline curves.
► Five-point window interpolation.
► Exact calculation of the nonlinear minimization problem.