Re: Interpolate in polar coordinates or cartesian

• To: mathgroup at smc.vnet.net
• Subject: [mg112775] Re: Interpolate in polar coordinates or cartesian
• From: Ingolf Dahl <Ingolf.Dahl at physics.gu.se>
• Date: Thu, 30 Sep 2010 04:50:47 -0400 (EDT)
• References: <201009281006.GAA26390@smc.vnet.net>

```Hi Szymon,
You might do this without my package with

Show[{ListPlot3D[Data,
PlotRange -> {{-0.3, 0.3}, {-0.3, 0.3}, {-0.1, 0.6}},
MeshFunctions -> {#3 &}, Mesh -> {Range[-0.1, 0.6, 0.1]}],
ListPointPlot3D[Data,
PlotRange -> {{-0.3, 0.3}, {-0.3, 0.3}, {-0.1, 0.6}}]}]

or with my package and with definitions below (shows more detail, takes some time)

test = Interpolation[Data1, Method -> "ObtuseAngle",
InterpolationOrder -> 2];
Show[{Plot3D[test[{x, y}], {x, -0.3, 0.3}, {y, -0.3, 0.3},
PlotRange -> {-0.1, 0.6}, MeshFunctions -> {#3 &},
Mesh -> {Range[-0.1, 0.6, 0.1]}, PlotPoints -> 30],
ListPointPlot3D[Data,
PlotRange -> {{-0.3, 0.3}, {-0.3, 0.3}, {-0.1, 0.6}}]}]

This is sent from Outlook2007 as unformatted text
Best regards

Ingolf Dahl
ingolf.dahl at telia.com

-----Ursprungligt meddelande-----
Fr=E5n: Szymon Roziewski [mailto:szymon.roziewski at gmail.com]
Skickat: den 28 september 2010 12:06
Till: mathgroup at smc.vnet.net
=C4mne: [mg112728] Re: Interpolate in polar coordinates or cartesian

hi there,
the interpolation works fine now,
but I wonder whether it is possible to make a contour lines on Plot3D curve.
What I mean would be like a contour line in geographic map or an isobar but
not in 2D but on 3d object with appropriate values to each of isobars
(e.g.).

Kind regards,
Szymon

2010/9/27 Szymon Roziewski <szymon.roziewski at gmail.com>

> REGISTER OBTUSE (I would like to register Obtuse, my e-mail address is
> szymon.roziewski at gmail.com)
> Thank You very much it works!
>
> kind regards,
> Szymon R.
>
> 2010/9/25 Ingolf Dahl <ingolf.dahl at telia.com>
>
> Oops!
>> A lot of equal signs has been introduced or doubled in the letter below.
>>
>> Data1 = Transpose[{Data[[All, {1, 2}]], Data[[All, 3]]}];
>> test0 = Interpolation[Data1, Method -> "ObtuseAngle"]
>> testDelaunay = Interpolation[Data1, Method -> "Delaunay"]
>>
>> should just have one equal sign each. I wonder how this will appear in
>> MathGroup this time?
>> I have checked that I this time send it as plain text, not HTML.
>>
>> Ingolf Dahl
>> ingolf.dahl at telia.com
>>
>>
>> > -----Original Message-----
>> > From: Ingolf Dahl [mailto:Ingolf.Dahl at physics.gu.se]
>> > Sent: den 25 september 2010 08:20
>> > To: mathgroup at smc.vnet.net
>> > Subject: [mg112660] Re: Interpolate in polar coordinates or cartesian
>> >
>> > Szymon,
>> > You might install my Obtuse package from
>> http://www.familydahl.se/mathemati=
>> > ca/index.html.
>> > If you have defined Data as below, you might do
>> >
>> > Needs["Obtuse`"]
>> >
>> > Data1 == Transpose[{Data[[All, {1, 2}]], Data[[All, 3]]}];
>> >
>> > (* My package needs separated coordinates and function values to be ab=
le
>> to=
>> >  handle various multi-dimensional cases, therefore this reformatting.
>> The
>> n=
>> > ext commands takes some time to evaluate. *)
>> >
>> > test0 == Interpolation[Data1, Method -> "ObtuseAngle"]
>> >
>> > Show[{ContourPlot[test0[{x, y}], {x, -0.3, 0.3}, {y, -0.3, 0.3},
>> >    PlotPoints -> 30, PlotRange -> {-0.1, 0.6}],
>> >   ListPlot[Data1[[All, 1]]]}]
>> >
>> > (* Or if you prefer Delaunay interpolation: *)
>> >
>> > testDelaunay == Interpolation[Data1, Method -> "Delaunay"]
>> >
>> > Show[{ContourPlot[
>> >    testDelaunay[{x, y}], {x, -0.3, 0.3}, {y, -0.3, 0.3},
>> >    PlotPoints -> 30, PlotRange -> {-0.1, 0.6}],
>> >   ListPlot[Data1[[All, 1]]]}]
>> >
>> > Best regards
>> >
>> > Ingolf Dahl
>> > ingolf.dahl at telia.com
>> >
>> > -----Ursprungligt meddelande-----
>> > Fr=E5n: Szymon Roziewski [mailto:szymon.roziewski at gmail.com]
>> > Skickat: den 24 september 2010 10:12
>> > Till: mathgroup at smc.vnet.net
>> > =C4mne: [mg112650] Re: Interpolate in polar coordinates or cartesian=
but
>> on=
>> >  non-uniform grid
>> >
>> > Despite attachments are not allowed here I post the notebook code.
>> >
>> >
>> > << /home/szymon/Mathematica/Imtek/Interpolation.m
>> >
>> > imsUnstructuredInterpolation[a]
>> >
>> > imsUnstructuredInterpolation[a]
>> >
>> > Data == {{-0.04037569953888305`, -0.010818636085285369`,
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>> >     0.165`}, {-0.1492702415084802`, -0.14927024150848017`,
>> >     0.02`}, {-0.05463670042114213`, -0.20390694192962233`,
>> >     0.`}, {0.05463670042114215`, -0.20390694192962233`,
>> >     0.`}, {0.14927024150848017`, -0.1492702415084802`,
>> >     0.`}, {0.20390694192962233`, -0.0546367004211421`,
>> >     0.`}, {0.2039069419296223`, 0.05463670042114222`,
>> >     0.001`}, {0.14927024150848023`, 0.14927024150848017`,
>> >     0.05`}, {0.05463670042114211`, 0.20390694192962233`,
>> >     0.264`}, {-0.054636700421142215`, 0.2039069419296223`,
>> >     0.347`}, {-0.14927024150848014`, 0.14927024150848023`,
>> >     0.409`}, {-0.20390694192962233`, 0.05463670042114212`,
>> >     0.364`}, {-0.22438456944695057`, -0.06012366417731558`,
>> >     0.073`}, {-0.164260905269635`, -0.164260905269635`,
>> >     0.01`}, {-0.06012366417731557`, -0.22438456944695057`,
>> >     0.`}, {0.06012366417731559`, -0.22438456944695057`,
>> >     0.`}, {0.164260905269635`, -0.164260905269635`,
>> >     0.`}, {0.22438456944695057`, -0.06012366417731553`,
>> >     0.`}, {0.22438456944695054`, 0.06012366417731567`,
>> >     0.`}, {0.16426090526963502`, 0.164260905269635`,
>> >     0.021`}, {0.060123664177315544`, 0.22438456944695057`,
>> >     0.106`}, {-0.06012366417731566`, 0.22438456944695054`,
>> >     0.138`}, {-0.16426090526963497`, 0.16426090526963502`,
>> >     0.153`}, {-0.22438456944695057`, 0.06012366417731556`,
>> >     0.143`}, {-0.24679404861685697`, -0.06612826602369407`,
>> >     0.044`}, {-0.1806657825931629`, -0.18066578259316288`,
>> >     0.01`}, {-0.06612826602369405`, -0.24679404861685697`,
>> >     0.`}, {0.06612826602369408`, -0.24679404861685697`,
>> >     0.`}, {0.18066578259316288`, -0.1806657825931629`,
>> >     0.`}, {0.24679404861685697`, -0.06612826602369401`,
>> >     0.`}, {0.24679404861685694`, 0.06612826602369416`,
>> >     0.`}, {0.18066578259316293`, 0.18066578259316288`,
>> >     0.015`}, {0.06612826602369402`, 0.24679404861685697`,
>> >     0.053`}, {-0.06612826602369415`, 0.24679404861685694`,
>> >     0.068`}, {-0.18066578259316285`, 0.18066578259316293`,
>> >     0.076`}, {-0.24679404861685697`, 0.06612826602369404`,
>> >     0.069`}, {-0.24679404861685697`, -0.06612826602369407`,
>> >     0.028`}, {-0.1806657825931629`, -0.18066578259316288`,
>> >     0.007`}, {-0.06612826602369405`, -0.24679404861685697`,
>> >     0.`}, {0.06612826602369408`, -0.24679404861685697`,
>> >     0.`}, {0.18066578259316288`, -0.1806657825931629`,
>> >     0.`}, {0.24679404861685697`, -0.06612826602369401`,
>> >     0.`}, {0.24679404861685694`, 0.06612826602369416`,
>> >     0.`}, {0.18066578259316293`, 0.18066578259316288`,
>> >     0.011`}, {0.06612826602369402`, 0.24679404861685697`,
>> >     0.033`}, {-0.06612826602369415`, 0.24679404861685694`,
>> >     0.044`}, {-0.18066578259316285`, 0.18066578259316293`,
>> >     0.05`}, {-0.24679404861685697`, 0.06612826602369404`,
>> >     0.042`}, {-0.298567672905951`, -0.08000096684118918`,
>> >     0.022`}, {-0.21856670606476183`, -0.2185667060647618`,
>> >     0.007`}, {-0.08000096684118915`, -0.298567672905951`,
>> >     0.`}, {0.0800009668411892`, -0.298567672905951`,
>> >     0.`}, {0.2185667060647618`, -0.21856670606476183`,
>> >     0.`}, {0.298567672905951`, -0.08000096684118911`,
>> >     0.`}, {0.298567672905951`, 0.08000096684118929`,
>> >     0.`}, {0.2185667060647619`, 0.2185667060647618`,
>> >     0.009`}, {0.08000096684118913`, 0.298567672905951`,
>> >     0.025`}, {-0.08000096684118928`, 0.298567672905951`,
>> >     0.033`}, {-0.21856670606476178`, 0.2185667060647619`,
>> >     0.036`}, {-0.298567672905951`, 0.08000096684118914`,
>> >     0.031`}, {-0.32841478093828325`, -0.08799847533485708`,
>> >     0.017`}, {-0.2404163056034262`, -0.24041630560342617`,
>> >     0.006`}, {-0.08799847533485705`, -0.32841478093828325`,
>> >     0.`}, {0.08799847533485709`, -0.32841478093828325`,
>> >     0.`}, {0.24041630560342617`, -0.2404163056034262`,
>> >     0.`}, {0.32841478093828325`, -0.087998475334857`,
>> >     0.`}, {0.3284147809382832`, 0.0879984753348572`,
>> >     0.`}, {0.24041630560342622`, 0.24041630560342617`,
>> >     0.007`}, {0.08799847533485702`, 0.32841478093828325`,
>> >     0.019`}, {-0.08799847533485719`, 0.3284147809382832`,
>> >     0.024`}, {-0.2404163056034261`, 0.24041630560342622`,
>> >     0.026`}, {-0.32841478093828325`, 0.08799847533485704`,
>> >     0.022`}, {-0.36125625903211156`, -0.09679832286834278`,
>> >     0.01`}, {-0.2644579361637688`, -0.2644579361637687`,
>> >     0.004`}, {-0.09679832286834275`, -0.36125625903211156`,
>> >     0.`}, {0.09679832286834279`, -0.36125625903211156`,
>> >     0.`}, {0.2644579361637687`, -0.2644579361637688`,
>> >     0.`}, {0.36125625903211156`, -0.0967983228683427`,
>> >     0.`}, {0.3612562590321115`, 0.09679832286834292`,
>> >     0.`}, {0.26445793616376884`, 0.2644579361637687`,
>> >     0.005`}, {0.09679832286834271`, 0.36125625903211156`,
>> >     0.011`}, {-0.0967983228683429`, 0.3612562590321115`,
>> >     0.014`}, {-0.2644579361637687`, 0.26445793616376884`,
>> >     0.016`}, {-0.36125625903211156`, 0.09679832286834274`,
>> >     0.013`}, {-0.39738188493532267`, -0.10647815515517706`,
>> >     0.006`}, {-0.29090372978014567`, -0.2909037297801456`,
>> >     0.002`}, {-0.10647815515517703`, -0.39738188493532267`,
>> >     0.`}, {0.10647815515517707`, -0.39738188493532267`,
>> >     0.`}, {0.2909037297801456`, -0.29090372978014567`,
>> >     0.`}, {0.39738188493532267`, -0.10647815515517696`,
>> >     0.`}, {0.39738188493532267`, 0.10647815515517721`,
>> >     0.`}, {0.2909037297801457`, 0.2909037297801456`,
>> >     0.003`}, {0.10647815515517699`, 0.39738188493532267`,
>> >     0.006`}, {-0.1064781551551772`, 0.39738188493532267`,
>> >     0.008`}, {-0.29090372978014556`, 0.2909037297801457`,
>> >     0.009`}, {-0.39738188493532267`, 0.106478155155177`, 0.007`}};
>> >
>> > imsUnstructuredInterpolation[Data]
>> >
>> > imsUnstructuredInterpolation[{{-0.0403757, -0.0108186,
>> >    0.}, {-0.0295571, -0.0295571, 0.}, {-0.0108186, -0.0403757,
>> >    0.}, {0.0108186, -0.0403757, 0.}, {0.0295571, -0.0295571,
>> >    0.}, {0.0403757, -0.0108186, 0.}, {0.0403757, 0.0108186,
>> >    0.}, {0.0295571, 0.0295571, 0.}, {0.0108186, 0.0403757,
>> >    0.}, {-0.0108186, 0.0403757, 0.}, {-0.0295571, 0.0295571,
>> >    0.}, {-0.0403757, 0.0108186, 0.}, {-0.044336, -0.0118798,
>> >    0.}, {-0.0324562, -0.0324562, 0.}, {-0.0118798, -0.044336,
>> >    0.}, {0.0118798, -0.044336, 0.}, {0.0324562, -0.0324562,
>> >    0.}, {0.044336, -0.0118798, 0.}, {0.044336, 0.0118798,
>> >    0.}, {0.0324562, 0.0324562, 0.}, {0.0118798, 0.044336,
>> >    0.}, {-0.0118798, 0.044336, 0.}, {-0.0324562, 0.0324562,
>> >    0.}, {-0.044336, 0.0118798, 0.}, {-0.0487793, -0.0130704,
>> >    0.}, {-0.0357089, -0.0357089, 0.}, {-0.0130704, -0.0487793,
>> >    0.}, {0.0130704, -0.0487793, 0.}, {0.0357089, -0.0357089,
>> >    0.}, {0.0487793, -0.0130704, 0.}, {0.0487793, 0.0130704,
>> >    0.}, {0.0357089, 0.0357089, 0.}, {0.0130704, 0.0487793,
>> >    0.}, {-0.0130704, 0.0487793, 0.}, {-0.0357089, 0.0357089,
>> >    0.}, {-0.0487793, 0.0130704, 0.}, {-0.0537055, -0.0143903,
>> >    0.}, {-0.0393151, -0.0393151, 0.}, {-0.0143903, -0.0537055,
>> >    0.}, {0.0143903, -0.0537055, 0.}, {0.0393151, -0.0393151,
>> >    0.}, {0.0537055, -0.0143903, 0.}, {0.0537055, 0.0143903,
>> >    0.}, {0.0393151, 0.0393151, 0.}, {0.0143903, 0.0537055,
>> >    0.}, {-0.0143903, 0.0537055, 0.}, {-0.0393151, 0.0393151,
>> >    0.}, {-0.0537055, 0.0143903, 0.}, {-0.0591147, -0.0158397,
>> >    0.}, {-0.0432749, -0.0432749, 0.}, {-0.0158397, -0.0591147,
>> >    0.}, {0.0158397, -0.0591147, 0.}, {0.0432749, -0.0432749,
>> >    0.}, {0.0591147, -0.0158397, 0.}, {0.0591147, 0.0158397,
>> >    0.}, {0.0432749, 0.0432749, 0.}, {0.0158397, 0.0591147,
>> >    0.}, {-0.0158397, 0.0591147, 0.}, {-0.0432749, 0.0432749,
>> >    0.}, {-0.0591147, 0.0158397, 0.}, {-0.0650068, -0.0174185,
>> >    0.}, {-0.0475883, -0.0475883, 0.}, {-0.0174185, -0.0650068,
>> >    0.}, {0.0174185, -0.0650068, 0.}, {0.0475883, -0.0475883,
>> >    0.}, {0.0650068, -0.0174185, 0.}, {0.0650068, 0.0174185,
>> >    0.}, {0.0475883, 0.0475883, 0.}, {0.0174185, 0.0650068,
>> >    0.}, {-0.0174185, 0.0650068, 0.}, {-0.0475883, 0.0475883,
>> >    0.}, {-0.0650068, 0.0174185, 0.}, {-0.0714785, -0.0191526,
>> >    0.}, {-0.0523259, -0.0523259, 0.}, {-0.0191526, -0.0714785,
>> >    0.}, {0.0191526, -0.0714785, 0.}, {0.0523259, -0.0523259,
>> >    0.}, {0.0714785, -0.0191526, 0.}, {0.0714785, 0.0191526,
>> >    0.}, {0.0523259, 0.0523259, 0.}, {0.0191526, 0.0714785,
>> >    0.}, {-0.0191526, 0.0714785, 0.}, {-0.0523259, 0.0523259,
>> >    0.}, {-0.0714785, 0.0191526, 0.}, {-0.0786264, -0.0210679,
>> >    0.}, {-0.0575585, -0.0575585, 0.}, {-0.0210679, -0.0786264,
>> >    0.}, {0.0210679, -0.0786264, 0.}, {0.0575585, -0.0575585,
>> >    0.}, {0.0786264, -0.0210679, 0.}, {0.0786264, 0.0210679,
>> >    0.}, {0.0575585, 0.0575585, 0.}, {0.0210679, 0.0786264,
>> >    0.}, {-0.0210679, 0.0786264, 0.}, {-0.0575585, 0.0575585,
>> >    0.}, {-0.0786264, 0.0210679, 0.}, {-0.0864504, -0.0231643,
>> >    0.}, {-0.0632861, -0.0632861, 0.}, {-0.0231643, -0.0864504,
>> >    0.}, {0.0231643, -0.0864504, 0.}, {0.0632861, -0.0632861,
>> >    0.}, {0.0864504, -0.0231643, 0.}, {0.0864504, 0.0231643,
>> >    0.}, {0.0632861, 0.0632861, 0.}, {0.0231643, 0.0864504,
>> >    0.}, {-0.0231643, 0.0864504, 0.}, {-0.0632861, 0.0632861,
>> >    0.}, {-0.0864504, 0.0231643, 0.}, {-0.0951437, -0.0254937,
>> >    0.}, {-0.06965, -0.06965, 0.}, {-0.0254937, -0.0951437,
>> >    0.}, {0.0254937, -0.0951437, 0.}, {0.06965, -0.06965,
>> >    0.}, {0.0951437, -0.0254937, 0.}, {0.0951437, 0.0254937,
>> >    0.}, {0.06965, 0.06965, 0.}, {0.0254937, 0.0951437,
>> >    0.}, {-0.0254937, 0.0951437, 0.}, {-0.06965, 0.06965,
>> >    0.}, {-0.0951437, 0.0254937, 0.}, {-0.10461, -0.0280301,
>> >    0.}, {-0.0765797, -0.0765797, 0.}, {-0.0280301, -0.10461,
>> >    0.}, {0.0280301, -0.10461, 0.}, {0.0765797, -0.0765797,
>> >    0.}, {0.10461, -0.0280301, 0.}, {0.10461, 0.0280301,
>> >    0.}, {0.0765797, 0.0765797, 0.}, {0.0280301, 0.10461,
>> >    0.}, {-0.0280301, 0.10461, 0.}, {-0.0765797, 0.0765797,
>> >    0.}, {-0.10461, 0.0280301, 0.}, {-0.115138, -0.0308512,
>> >    0.}, {-0.0842871, -0.0842871, 0.}, {-0.0308512, -0.115138,
>> >    0.}, {0.0308512, -0.115138, 0.}, {0.0842871, -0.0842871,
>> >    0.}, {0.115138, -0.0308512, 0.}, {0.115138, 0.0308512,
>> >    0.}, {0.0842871, 0.0842871, 0.}, {0.0308512, 0.115138,
>> >    0.}, {-0.0308512, 0.115138, 0.}, {-0.0842871, 0.0842871,
>> >    0.001}, {-0.115138, 0.0308512, 0.001}, {-0.126633, -0.0339312,
>> >    0.003}, {-0.0927017, -0.0927017, 0.}, {-0.0339312, -0.126633,
>> >    0.}, {0.0339312, -0.126633, 0.}, {0.0927017, -0.0927017,
>> >    0.}, {0.126633, -0.0339312, 0.}, {0.126633, 0.0339312,
>> >    0.}, {0.0927017, 0.0927017, 0.001}, {0.0339312, 0.126633,
>> >    0.004}, {-0.0339312, 0.126633, 0.005}, {-0.0927017, 0.0927017,
>> >    0.008}, {-0.126633, 0.0339312, 0.008}, {-0.139287, -0.0373217,
>> >    0.019}, {-0.101965, -0.101965, 0.003}, {-0.0373217, -0.139287,
>> >    0.}, {0.0373217, -0.139287, 0.}, {0.101965, -0.101965,
>> >    0.}, {0.139287, -0.0373217, 0.}, {0.139287, 0.0373217,
>> >    0.}, {0.101965, 0.101965, 0.007}, {0.0373217, 0.139287,
>> >    0.031}, {-0.0373217, 0.139287, 0.043}, {-0.101965, 0.101965,
>> >    0.06}, {-0.139287, 0.0373217, 0.056}, {-0.153196, -0.0410487,
>> >    0.058}, {-0.112147, -0.112147, 0.007}, {-0.0410487, -0.153196,
>> >    0.}, {0.0410487, -0.153196, 0.}, {0.112147, -0.112147,
>> >    0.}, {0.153196, -0.0410487, 0.}, {0.153196, 0.0410487,
>> >    0.001}, {0.112147, 0.112147, 0.021}, {0.0410487, 0.153196,
>> >    0.102}, {-0.0410487, 0.153196, 0.164}, {-0.112147, 0.112147,
>> >    0.221}, {-0.153196, 0.0410487, 0.191}, {-0.168554, -0.0451639,
>> >    0.078}, {-0.12339, -0.12339, 0.009}, {-0.0451639, -0.168554,
>> >    0.}, {0.0451639, -0.168554, 0.}, {0.12339, -0.12339,
>> >    0.}, {0.168554, -0.0451639, 0.}, {0.168554, 0.0451639,
>> >    0.}, {0.12339, 0.12339, 0.028}, {0.0451639, 0.168554,
>> >    0.147}, {-0.0451639, 0.168554, 0.216}, {-0.12339, 0.12339,
>> >    0.28}, {-0.168554, 0.0451639, 0.241}, {-0.185361, -0.0496674,
>> >    0.183}, {-0.135694, -0.135694, 0.021}, {-0.0496674, -0.185361,
>> >    0.}, {0.0496674, -0.185361, 0.}, {0.135694, -0.135694,
>> >    0.}, {0.185361, -0.0496674, 0.}, {0.185361, 0.0496674,
>> >    0.001}, {0.135694, 0.135694, 0.06}, {0.0496674, 0.185361,
>> >    0.333}, {-0.0496674, 0.185361, 0.482}, {-0.135694, 0.135694,
>> >    0.582}, {-0.185361, 0.0496674, 0.52}, {-0.203907, -0.0546367,
>> >    0.165}, {-0.14927, -0.14927, 0.02}, {-0.0546367, -0.203907,
>> >    0.}, {0.0546367, -0.203907, 0.}, {0.14927, -0.14927,
>> >    0.}, {0.203907, -0.0546367, 0.}, {0.203907, 0.0546367,
>> >    0.001}, {0.14927, 0.14927, 0.05}, {0.0546367, 0.203907,
>> >    0.264}, {-0.0546367, 0.203907, 0.347}, {-0.14927, 0.14927,
>> >    0.409}, {-0.203907, 0.0546367, 0.364}, {-0.224385, -0.0601237,
>> >    0.073}, {-0.164261, -0.164261, 0.01}, {-0.0601237, -0.224385,
>> >    0.}, {0.0601237, -0.224385, 0.}, {0.164261, -0.164261,
>> >    0.}, {0.224385, -0.0601237, 0.}, {0.224385, 0.0601237,
>> >    0.}, {0.164261, 0.164261, 0.021}, {0.0601237, 0.224385,
>> >    0.106}, {-0.0601237, 0.224385, 0.138}, {-0.164261, 0.164261,
>> >    0.153}, {-0.224385, 0.0601237, 0.143}, {-0.246794, -0.0661283,
>> >    0.044}, {-0.180666, -0.180666, 0.01}, {-0.0661283, -0.246794,
>> >    0.}, {0.0661283, -0.246794, 0.}, {0.180666, -0.180666,
>> >    0.}, {0.246794, -0.0661283, 0.}, {0.246794, 0.0661283,
>> >    0.}, {0.180666, 0.180666, 0.015}, {0.0661283, 0.246794,
>> >    0.053}, {-0.0661283, 0.246794, 0.068}, {-0.180666, 0.180666,
>> >    0.076}, {-0.246794, 0.0661283, 0.069}, {-0.246794, -0.0661283,
>> >    0.028}, {-0.180666, -0.180666, 0.007}, {-0.0661283, -0.246794,
>> >    0.}, {0.0661283, -0.246794, 0.}, {0.180666, -0.180666,
>> >    0.}, {0.246794, -0.0661283, 0.}, {0.246794, 0.0661283,
>> >    0.}, {0.180666, 0.180666, 0.011}, {0.0661283, 0.246794,
>> >    0.033}, {-0.0661283, 0.246794, 0.044}, {-0.180666, 0.180666,
>> >    0.05}, {-0.246794, 0.0661283, 0.042}, {-0.298568, -0.080001,
>> >    0.022}, {-0.218567, -0.218567, 0.007}, {-0.080001, -0.298568,
>> >    0.}, {0.080001, -0.298568, 0.}, {0.218567, -0.218567,
>> >    0.}, {0.298568, -0.080001, 0.}, {0.298568, 0.080001,
>> >    0.}, {0.218567, 0.218567, 0.009}, {0.080001, 0.298568,
>> >    0.025}, {-0.080001, 0.298568, 0.033}, {-0.218567, 0.218567,
>> >    0.036}, {-0.298568, 0.080001, 0.031}, {-0.328415, -0.0879985,
>> >    0.017}, {-0.240416, -0.240416, 0.006}, {-0.0879985, -0.328415,
>> >    0.}, {0.0879985, -0.328415, 0.}, {0.240416, -0.240416,
>> >    0.}, {0.328415, -0.0879985, 0.}, {0.328415, 0.0879985,
>> >    0.}, {0.240416, 0.240416, 0.007}, {0.0879985, 0.328415,
>> >    0.019}, {-0.0879985, 0.328415, 0.024}, {-0.240416, 0.240416,
>> >    0.026}, {-0.328415, 0.0879985, 0.022}, {-0.361256, -0.0967983,
>> >    0.01}, {-0.264458, -0.264458, 0.004}, {-0.0967983, -0.361256,
>> >    0.}, {0.0967983, -0.361256, 0.}, {0.264458, -0.264458,
>> >    0.}, {0.361256, -0.0967983, 0.}, {0.361256, 0.0967983,
>> >    0.}, {0.264458, 0.264458, 0.005}, {0.0967983, 0.361256,
>> >    0.011}, {-0.0967983, 0.361256, 0.014}, {-0.264458, 0.264458,
>> >    0.016}, {-0.361256, 0.0967983, 0.013}, {-0.397382, -0.106478,
>> >    0.006}, {-0.290904, -0.290904, 0.002}, {-0.106478, -0.397382,
>> >    0.}, {0.106478, -0.397382, 0.}, {0.290904, -0.290904,
>> >    0.}, {0.397382, -0.106478, 0.}, {0.397382, 0.106478,
>> >    0.}, {0.290904, 0.290904, 0.003}, {0.106478, 0.397382,
>> >    0.006}, {-0.106478, 0.397382, 0.008}, {-0.290904, 0.290904,
>> >    0.009}, {-0.397382, 0.106478, 0.007}}]
>> >
>> > 397382
>> >
>> > f == imsUnstructuredInterpolation[Data, imsSpline[x, xi, 3]];
>> >
>> > LinearSolve::luc: Result for LinearSolve of badly conditioned matrix
>> >
>>
>> {{-1.07146,-1.0704,-1.0675,-1.06354,-1.0596,-1.05672,-1.05567,-1.05672,-=
1.0=
>> > ==
>> >
>>
>> 596,-1.06354,-1.0675,-1.0704,-1.07308,-1.07191,-1.06873,-1.06438,-1.0600=
4,<=
>> > ==
>> >
>>
>> <17>>,-1.0702,-1.07372,-1.07726,-1.07584,-1.07196,-1.06667,-1.0614,-1.05=
755=
>> > ==
>> >
>>
>> ,-1.05614,-1.05755,-1.0614,-1.06667,-1.07196,-1.07584,-1.07988,-1.07831,=
<<2=
>> > ==
>> > 51>>},<<49>>,<<251>>}
>> > may contain significant numerical errors. >>
>> >
>> > 2010/9/23 Szymon Roziewski <szymon.roziewski at gmail.com>
>> >
>> > > How can I interpolate a function which is set on a non-uniform
>> > > non-rectangle grid.
>> > > I tried to do that by using a package Interpolation.m from Imtek and
>> what=
>> > ==
>> >  I
>> > > got is:
>> > > LinearSolve::luc: Result for LinearSolve of badly conditioned matrix=

```

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