What methods & algorithms are used by matlab multivariate (especially 3d) interpolation functions?

Hello,

I am wondering what methods & algorithms are used by matlab multivariate (especially 3d) interpolation functions, such as:

-interp2, interp3, interpn -griddedInterpolant

There is a good descriptions about 1 dimensional 'linear', 'cubic' and 'spline' interpolation techniques ( on Wikipedia and also in Cleve Moler's "Numerical Computing with MATLAB" textbook ), but no where I can find explanation of how those methods are extended to multivariate case.

Does anyone nows how this is done or where is it described?

Thanks in advance, Ivan