One interesting group is the compactly supported RBFs, for example those of Wendland https://math.iit.edu/~fass/603_ch4.pdf https://math.iit.edu/~fass/603_ch4.p

One interesting group is the compactly supported RBFs, for example those of Wendland https://math.iit.edu/~fass/603_ch4.pdf 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.