Shape preserving C-3 data interpolation and C-2 histopolation with splines on threefold refined grids

This paper is concerned with the convex C-3 interpolation of univariate data sets. An algorithm based on Me use of quartic splines on threefold refined grids is presented which is always successful for data sets in strictly convex position. These splines are suitable also for monotone as well as positive C-3 interpolation. Further, the derived algorithms apply to the monotone and positive C-2 histopolation with cubic splines on grids refined as before.