A one-pass algorithm for shape-preserving quadratic spline interpolation

Schumaker (1983) and McAllister and Roulier (1981) have proposed algorithms for shape-preserving interpolation using quadratic splines. The former requires the user to provide and perhaps to adjust estimates of the slope at the data points. Here we show that, for a particular slope estimation technique, the two methods are identical, and that in this case the Schumaker algorithm automatically generates shape-preserving interpolants. Furthermore, in case of convex data the slopes are improved iteratively to produce more visually pleasing curves.     

An algorithm for convexity-preserving surface interpolation

A simple and efficient method of convexity-preserving interpolation for grid data is introduced. An earlier algorithm due to Roulier (1987), based on a shape-preserving curve interpolation scheme due to McAllister and Roulier (1981), is modified to use a simpler but equivalent curve interpolation scheme described in Iqbal (1992). Numerical examples are provided to test the performance of the method with the slopes that are further improved using iterative technique to produce more visually pleasing surfaces.