One interesting group is the compactly supported RBFs, for example those of Wendland https://math.iit.edu/~fass/603_ch4.pdf the advantage being that the resulting linear systems are sparse, useful when you have lots of points to interpolate and "gaps" is not an issue.
RBFs are splendid, but you don't need to have them "decay with distance", indeed, ones which don't (mutliquartics etc) often have better approximation properties and better-conditioned linear systems to solve, give them a go! https://www.sciencedirect.com/science/article/abs/pii/S09557...
A friend and I bought a car with a busted door for £100 some years ago, we got a cheap replacement door, incompetently resprayed it to be roughly the colour of the rest of the car and sold it, for £100 :-|
Interested readers might like to read my original submission at https://drafts.csswg.org/css-mixins/ which details the mixin proposal. No idea why it was changed to this earlier daft which does not :-|