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I am working on an interpolation problem with a domain in R^2 and values in R. Essentially, I have a rectilinear grid with target values for each point. I have fitted a function against these values, the function being a polynomial of a fixed degree on each subdomain between grid points.

I would like to visualize the results using ParaView in an x-y-plane with z-coordinates according to function values (using the "WarpByScalar" filter). Of course, the resulting surface should be curved for certain polynomials.

Is there a way to pass the polynomial into a VTK file and have "continuous and smooth" data entries? Is there another way to obtain a smooth look consistent with the polynomial values (for example using a very fine mesh instead)?

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IIRC you can input analytical functions into the calculator and plot them along side your numerical values. The input may be quantized nonetheless. See for example: using calculator in paraview

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