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: > http://www.wolfram.com/products/mathematica/newin6/content/HighImpactAd= 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

**Follow-Ups**:**RE: Re: 3D interpolation***From:*José Luis Gómez-Muñoz <jose.luis.gomez@itesm.mx>