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You have to re-parametrize your data; i.e. x=rcos(theta),y=rsin(theta); but that's for circle :) In general, you do need to re-parametrize; x=f(s),y=g(s).
Or read:http://evoq-eval.siam.org/Portals/0/Publications/SIURO/Vol1_Issue1/A_Simple_Expression_for_Multivariate.pdf?ver=2018-03-30-130233-050
That might give you continuity. Incidentally, "interpolation" and "approximation" is a field in itself.
If this is a class assignment (which it shouldn't be); then the book/teacher gave you "hints"/facts that will indicate what approach you should take. Lean back and replay the class and readings; it's almost certainly there.