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Re: 3D interpolation

• To: mathgroup at smc.vnet.net
• Subject: [mg77491] Re: 3D interpolation
• From: Szabolcs <szhorvat at gmail.com>
• Date: Sun, 10 Jun 2007 07:22:13 -0400 (EDT)
• Organization: University of Bergen
• References: <f4b85l$3kj$1@smc.vnet.net>

Mathieu G wrote:
> I would like to do
> =A4 a 3D interpolation of Meas(x,y,z) using the real position

I too would very much like to know how this is done in Mathematica.

I am sure that there is a simple way to do this, because ListPlot3D[] 
already supports interpolation with arbitrarily positioned points:
http://www.wolfram.com/products/mathematica/newin6/content/HighImpactAdaptiveVisualization/VoronoiRegionInterpolation.html

But Interpolation[] gives an error:

In[1]:= RandomReal[{0, 1}, {10, 3}] /. {x_, y_, f_} -> {{x, y}, f}

Out[1]= {{{0.29816, 0.887332}, 0.240481}, {{0.90088, 0.965822},
   0.387489}, {{0.34728, 0.682987}, 0.827958}, {{0.818205, 0.17033},
   0.343763}, {{0.582784, 0.746518}, 0.562276}, {{0.101323, 0.562885},
   0.592576}, {{0.307368, 0.113622}, 0.911536}, {{0.146258, 0.303898},
   0.152228}, {{0.0440035, 0.377023}, 0.164235}, {{0.41297, 0.128645},
   0.851261}}

In[2]:= Interpolation[%]

During evaluation of In[2]:= Interpolation::indim: The coordinates do \
not lie on a structured tensor product grid.

Out[2]= Interpolation[{{{0.29816, 0.887332},
    0.240481}, {{0.90088, 0.965822}, 0.387489}, {{0.34728, 0.682987},
    0.827958}, {{0.818205, 0.17033}, 0.343763}, {{0.582784, 0.746518},
    0.562276}, {{0.101323, 0.562885}, 0.592576}, {{0.307368, 0.113622},
     0.911536}, {{0.146258, 0.303898},
    0.152228}, {{0.0440035, 0.377023}, 0.164235}, {{0.41297, 0.128645},
     0.851261}}]

Unfortunately I could not find any information in the docs about 
interpolation with points that do not lie on a grid.