Re: How does Mathematica interpolate in higher dimensions ?
- To: mathgroup at smc.vnet.net
- Subject: [mg97731] Re: How does Mathematica interpolate in higher dimensions ?
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Thu, 19 Mar 2009 05:24:56 -0500 (EST)
- Organization: Uni Leipzig
- References: <gpsr8e$mkj$1@smc.vnet.net>
- Reply-to: kuska at informatik.uni-leipzig.de
Hi, http://www.nrbook.com/a/bookcpdf/c3-6.pdf ? Regards Jens ben.whitehouse at gmail.com wrote: > 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 >