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I was wondering how I could fit a polynomial surface through a set of points in two variables. When I look up this problem in the literature, I usually see two options:

  • Use a tensor product, but this only seems to work in the case the points are evaluated in a grid
  • Use some special point layouts, like Padua or Chebyshev points.

Neither options seems feasible for pseudo-random point sets. Does anyone have an idea? (I guess I could use the standard Lagrange formula in two variables, but that doesn't seem like a numerically stable solution.)

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    A curve, or a surface?2011-11-06
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    A surface; sorry.2011-11-06

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