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Unstructured Interpolation in V7?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg109658] Unstructured Interpolation in V7?
  • From: Luc Barthelet <luc at tirnua.com>
  • Date: Tue, 11 May 2010 06:25:26 -0400 (EDT)

I have a small data set  (wind in the bay area, automatically extracted
by Mathematica)

testData={{{-121.082`,38.955`},{-0.017250000000004206`,0.02987787643056=
0946`}},{{-122.05`,37.98`},{0.03175000000000239`,0.054992613140314006`}},=
{{-122.12`,37.66`},{0.06795173495784468`,-0.011981724259015891`}},{{-121.=
82`,37.7`},{0.06795173495784468`,0.011981724259015891`}},{{-121.3`,38.58`=
},{0.02599999999999625`,0.04503332099679369`}},{{-122.05`,37.43`},{0.0380=
57551141832846`,0.01385181580469208`}},{{-122.28`,38.21`},{0.070476946558=
94077`,0.02565151074942662`}},{{-122.556`,38.1436`},{0.05121000315664048`=
,0.009029705238681629`}},{{-121.957`,38.378`},{0.03241939541710792`,0.011=
79969494473454`}},{{-122.22`,37.7`},{0.09060231327711676`,0.0159756323453=
5926`}},{{-122.12`,37.48`},{0.05662644579820153`,-0.009984770215851313`}}=
,{{-121.6`,38.7`},{0.018640840680916426`,0.022215288850453874`}},{{-121.5=
`,38.52`},{0.02603289819229815`,0.031024799946315795`}},{{-122.25`,37.53`=
},{0.05121000315664048`,0.009029705238681629`}},{{-122.36`,37.62`},{0.051=
21000315664048`,0.009029705238681629`}},{{-121.93`,37.37`},{0.06495190528=
383432`,0.03750000000000142`}},{{-121.82`,37.34`},{0.06795173495784468`,0=
=2E011981724259015891`}},{{-122.81`,38.51`},{0.03983716857408126`,0.02300=
000000000324`}},{{-121.25`,37.91`},{0.05121000315664048`,0.00902970523868=
1629`}},{{-121.93`,38.28`},{0.09725818625133797`,0.03539908483420362`}},{=
{-122.465`,37.807`},{0.03464101615138304`,0.020000000000003126`}},{{-122.=
21`,37.507`},{0.07386058147591257`,0.013023613325017891`}},{{-122.298`,37=
=2E772`},{0.05967048141990006`,-0.021718279101179405`}},{{-122.33`,37.8`}=
,{0.1039999999999992`,0.`}},{{-122.4`,37.928`},{0.029877876430560946`,0.0=
172499999999971`}},{{-122.975`,37.997`},{0.04530115663855838`,-0.00798781=
617267963`}},{{-122.038`,38.057`},{0.048643822138060955`,0.04081701321509=
712`}},{{-122.881`,37.361`},{0.06598211945181731`,-0.011634427903686628`}=
},{{-122.833`,37.759`},{0.055999999999997385`,0.`}},{{-122.833`,37.759`},=
{0.055999999999997385`,0.`}},{{-122.026`,38.223`},{0.07924132444627219`,0=
=2E04574999999999818`}},{{-122.447`,37.891`},{0.005035797152345367`,0.028=
559424837354186`}}};

That interpolate, extrapolate nicely with

ListVectorPlot[testData]

Now, I would like to build the interpolated data outside of ListVectorPlot,

but Interpolation[testData] returns an error:
Interpolation::indim: The coordinates do not lie on a structured tensor
product grid

Which is an old issue (for MathGroup at least).

The solution are to use the IMS package imsUnstructuredInterpolation or
TWJ's TriangularInterpolation. (or Cases on ListVectorPlot.., which is
my current solution)

But is there a new better way to do that in version 7? the documentation 
avoids the issue and nicely just uses Table to create dataset from a
function! (Which I guess is a hint that this is not resolved)

Thanks,
Luc








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