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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
>