fitting - 2D smoothing spline interpolation

Does Mathematica have 2D smoothing spline interpolation built in? I requires an interpolation method with smooth first derivatives and cubic bivariate splines fulfill this nicely. In python I would use RectBivariateSpline or SmoothBivariateSpline.

A quick search only revealed this answer, which I guess could be adapted to 2D with some effort.

Here is some test data:

RANGEX = 8;
RANGEY = 8;
F[x_, y_] := 
 Sin[.5 y] Cos[.9 x]/Sec[0.1 x y] - 
  0.01 (x^2 + y^2) RiemannSiegelZ[1.5 Sqrt[x^2 + y^2]]
data = N[Flatten[

    Table[{x, y, F[x, y]}, {x, -RANGEX, RANGEX, 1}, {y, -RANGEY, 
      RANGEY, 1}], 1]];
(*add some noise*)
data[[All, 3]] = 
  data[[All, 3]] + 
   RandomVariate[NormalDistribution[0, 0.1], Length[data]];

PlotPointsAndSurface[points_, surface_, label_] := Module[{},
   Show[
    ListPointPlot3D[points, 

     PlotStyle -> {Directive[PointSize[0.01], Red], 
       Directive[PointSize[0.01], Green]}, PlotLabel -> label, 
     ImageSize -> Medium],
    Plot3D[surface, {x, -RANGEX, RANGEX}, {y, -RANGEY, RANGEY}, 
     PlotStyle -> Directive[Purple, Opacity[0.2]]]
    ]];
PlotPointsAndSurface[data, F[x, y], "orig and noise"]

enter image description here

Comments

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