Hi Mark,
The docs you linked reference
https://epubs.siam.org/doi/10.1137/0720057 which is gated, so only an impression: this seems to construct a shape-preserving piecewise quadratic interpolant. We have two shape-preserving cubic interpolants, PCHIP and Akima. Do you have an overview of how this one compares to them?
Off the cuff, I guess we can add a shape-preserving quadratic, too. This should be based on either BSpline or PPoly, depending on the basis the construction is in.
(My impression is that it's the latter in the R package).
The API should mirror that of Akima1DInterpolator.