How does Mathematica interpolate in higher dimensions ?

*To*: mathgroup at smc.vnet.net*Subject*: [mg97712] How does Mathematica interpolate in higher dimensions ?*From*: ben.whitehouse at gmail.com*Date*: Thu, 19 Mar 2009 02:12:31 -0500 (EST)

Hi, I have tri-variate histograms, which count the number of points from a large group of (x,y,z)'s that fall within a 3D grid. I then use func = Interpolation[histogram, InterpolationOrder->1] to create a linear Interpolation over the histogram's grid for the various "heights" of the grid. My question, though, is what is mathematica doing to make this interpolation? My best guess is that it is solving f = a1 +a2 x + a3 y + a4 z + a5 x y + a6 x z + a7 y z + a8 x y z using the 8 corner points of each cube. It is not clear to me how this generalizes to higher orders, but I am only interested in the linear case anyway. Is the method documented anywhere ? or does anyone know ? Thanks Ben