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I have a smooth [itex]f(x,y)[/itex] in some region of ℝ2 that I know to be [itex]0\le f(x,y)\le 1[/itex]. The region has holes. I also know that inside the holes, f(x,y)=0, and outside of the region, f(x,y)=0. I'm looking for a good choice of polynomials or other functions I can expand f on in order to fit my data to. Is there a standard choice for something like this? (see attachment)

Thanks

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# Kernel/basis function for multiply connected region

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