surface: he didn't sat that. he just said points,
it could be a cloud, it could be a folded surface.
yeah, that's more clear.
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I've written such programs, it's just a matter of finding a suitable interpolation scheme (cubic splines is one good scheme, another is Tchebyshev polynomials which has extrapolation advantages). The problem is, you want to include many points near your target, when you do that interpolation, and that means you have to define 'near'. Then, you have to select the close-by ones. The identification of the active patch in your data set, different in general for each target point, is the hairy part.
It's simplest to use bi-linear interpolation, but that won't ever notice curvature that puts a peak (or dip) at the target region.
Fancier curvilinear interpolation starts with a least-squares fit to a cubic or quartic surface.
I've even heard of folk doing a Fourier transform on irregular-grid input data, then inverting FFT-style to get data on a regular grid.
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