The user of an Approximate or Interpolate object doesn't care which of these they have, once the object has been constructed, and we should make these inherit from a common base class that only contains an interface for accessing the interpolated/approximated function while making no assumptions about its functional form.

The new class will represent a scalar field defined over an integer bounding box, and will have methods for evaluating the field at a point and creating an image of the field. We could also consider giving it arithmetic interoperability with Image. I don't have a strong candidate for the name; I've called it "BoundedField" on the HSC side but would like that to be revisited.

Adding derived classes to replace the functionality currently in the Approximate and Interpolate classes will be on a separate issue. The main work on this issue is tweaking the design on the HSC side and getting signoff on the final design from LSST developers; the actual coding should be minimal, as it's just an interface and we already have a good starting point for it.

The HSC-side issue (which also includes work that is part of DM-1124) is here:
https://hsc-jira.astro.princeton.edu/jira/browse/HSC-796
and the associated git commits are here:
https://github.com/HyperSuprime-Cam/afw/compare/releases/S14A_0...tickets/DM-796