Multidimensional interpolation


I would like to fit a dipole moment surface for tri- and tetra-atomic molecules. That means that the dipole moment depends on 3 variables for the first case and on 6 variables for the tetra-atomic case.

For that purpose, I need to know how the dipole changes with respect to the distances of the system, so if we stick to the 3-atomic case, the data I need to fit will look as:

1.3 0.8 0.9 4.5
1.3 0.7 1.0 5.4
1.4 0.7 0.9 5.1

and so on. Being the first column the first distance, the second column the second distance, the third column the third distance, and the fourth column the value of the dipole.

I would like to interpolate in such a way that I can insert three values of the distances and get an interpolated value for the dipole moment.

I do not know how to make the package Interpolations work for the multidimensional case (I do not even know if it is possible). I have taken a look at GridInterpolations ( but, unfortunately, the cut points must be sorted.

Any suggestions about any package or possible solutions for this issue would be highly appreciated.

All the best,