Multi Dimensional Cubic Spline

Hi, I’ve a multi dimensional dataset (3 features and 1 label) and want to interpolate using cubic splines. I have found several documentations on interpolation in 2D but can’t find anything that’ll help with this. Looking forward to any suggestions.


Is the data on a cartesian grid? If so, it should be straightforward to recursively define a 1d spline of 1d splines of 1d splines (by making splines of the coefficients)…

Can you mention any resources that’ll help me implement this effectively. My data is structured such that M*g is the label. I’m showing a few points but I’ve around 18k of them.

#   a/c	a/t	phi	        M*g
0	0.2	0.2	0.162	1.24187
1	0.2	0.2	0.261	1.20996
2	0.2	0.2	0.423	1.18170
3	0.2	0.2	0.581	1.15911
4	0.2	0.2	0.739	1.16206

Radial Basis Functions are a common way to do multidimensional interpolation or more generally function approximation.

They are also relatively easy to understand usually infinitely smooth, and have nice rapid convergence properties for many cases.