Re: 3D interpolation

• To: mathgroup at smc.vnet.net
• Subject: [mg77503] Re: 3D interpolation
• From: Mathieu G <ellocomateo at free.fr>
• Date: Mon, 11 Jun 2007 04:19:09 -0400 (EDT)
• References: <f4b85l\$3kj\$1@smc.vnet.net> <f4gn9v\$i2l\$1@smc.vnet.net>

```Szabolcs a =E9crit :
> 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:
aptiveVisualization/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.
>

WRI people, or readers, your help on this on would certainly be useful
to many users (including Szabolcs and me!!) and would be much appreciated!
Best regards,
Mathieu

```

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