PCHIP Interpolation of 1D datasets

[NAThompson]

Currently, H5Web support both constant interpolation and linear interpolation. However, in many cases data is nonuniformly sampled at distances that make linear interpolation look quite bad. One example is high-order ODE steppers, which yield ODE solution skeletons which are very sparse.

It would be nice to have a smooth interpolant for such data. Cleve Moler describes a very nice one here which he calls PCHIP. This interpolant is C^1, and never leaves the data bounds. It does this by ascribing to the datapoints derivatives chosen by this formula:

This is implemented in the attached patchfile:

pchip.patch

Here is a short screen recording demonstrating the use:

Screen.Recording.2026-01-15.at.12.47.02.mov