Re: Interpolate in polar coordinates or cartesian

• To: mathgroup at smc.vnet.net
• Subject: [mg112668] Re: Interpolate in polar coordinates or cartesian
• From: "Ingolf Dahl" <ingolf.dahl at telia.com>
• Date: Sun, 26 Sep 2010 02:42:20 -0400 (EDT)

```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 able
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`,
>     0.`}, {-0.029557063453597685`, -0.02955706345359768`,
>     0.`}, {-0.010818636085285367`, -0.04037569953888305`,
>     0.`}, {0.01081863608528537`, -0.04037569953888305`,
>     0.`}, {0.02955706345359768`, -0.029557063453597685`,
>     0.`}, {0.04037569953888305`, -0.01081863608528536`,
>     0.`}, {0.04037569953888305`, 0.010818636085285384`,
>     0.`}, {0.029557063453597692`, 0.02955706345359768`,
>     0.`}, {0.010818636085285362`, 0.04037569953888305`,
>     0.`}, {-0.010818636085285382`, 0.04037569953888305`,
>     0.`}, {-0.029557063453597678`, 0.029557063453597692`,
>     0.`}, {-0.04037569953888305`, 0.010818636085285363`,
>     0.`}, {-0.04433599542666824`, -0.011879794170205705`,
>     0.`}, {-0.032456201256462536`, -0.03245620125646253`,
>     0.`}, {-0.011879794170205703`, -0.04433599542666824`,
>     0.`}, {0.011879794170205708`, -0.04433599542666824`,
>     0.`}, {0.03245620125646253`, -0.032456201256462536`,
>     0.`}, {0.04433599542666824`, -0.011879794170205696`,
>     0.`}, {0.04433599542666823`, 0.011879794170205724`,
>     0.`}, {0.03245620125646254`, 0.03245620125646253`,
>     0.`}, {0.011879794170205698`, 0.04433599542666824`,
>     0.`}, {-0.01187979417020572`, 0.04433599542666823`,
>     0.`}, {-0.03245620125646253`, 0.03245620125646254`,
>     0.`}, {-0.04433599542666824`, 0.011879794170205701`,
>     0.`}, {-0.048779254227597955`, -0.0130703617776773`,
>     0.`}, {-0.035708892449920655`, -0.03570889244992065`,
>     0.`}, {-0.013070361777677298`, -0.048779254227597955`,
>     0.`}, {0.013070361777677304`, -0.048779254227597955`,
>     0.`}, {0.03570889244992065`, -0.035708892449920655`,
>     0.`}, {0.048779254227597955`, -0.01307036177767729`,
>     0.`}, {0.04877925422759795`, 0.013070361777677321`,
>     0.`}, {0.03570889244992066`, 0.03570889244992065`,
>     0.`}, {0.013070361777677293`, 0.048779254227597955`,
>     0.`}, {-0.013070361777677317`, 0.04877925422759795`,
>     0.`}, {-0.03570889244992064`, 0.03570889244992066`,
>     0.`}, {-0.048779254227597955`, 0.013070361777677295`,
>     0.`}, {-0.053705475941672194`, -0.014390338907700155`,
>     0.`}, {-0.03931513703397204`, -0.039315137033972034`,
>     0.`}, {-0.014390338907700152`, -0.053705475941672194`,
>     0.`}, {0.014390338907700159`, -0.053705475941672194`,
>     0.`}, {0.039315137033972034`, -0.03931513703397204`,
>     0.`}, {0.053705475941672194`, -0.014390338907700143`,
>     0.`}, {0.05370547594167219`, 0.014390338907700176`,
>     0.`}, {0.03931513703397205`, 0.039315137033972034`,
>     0.`}, {0.014390338907700147`, 0.053705475941672194`,
>     0.`}, {-0.014390338907700174`, 0.05370547594167219`,
>     0.`}, {-0.039315137033972034`, 0.03931513703397205`,
>     0.`}, {-0.053705475941672194`, 0.014390338907700148`,
>     0.`}, {-0.059114660568890975`, -0.01583972556027427`,
>     0.`}, {-0.04327493500861671`, -0.043274935008616705`,
>     0.`}, {-0.015839725560274267`, -0.059114660568890975`,
>     0.`}, {0.015839725560274274`, -0.059114660568890975`,
>     0.`}, {0.043274935008616705`, -0.04327493500861671`,
>     0.`}, {0.059114660568890975`, -0.01583972556027426`,
>     0.`}, {0.05911466056889097`, 0.015839725560274295`,
>     0.`}, {0.04327493500861672`, 0.043274935008616705`,
>     0.`}, {0.015839725560274263`, 0.059114660568890975`,
>     0.`}, {-0.01583972556027429`, 0.05911466056889097`,
>     0.`}, {-0.0432749350086167`, 0.04327493500861672`,
>     0.`}, {-0.059114660568890975`, 0.015839725560274267`,
>     0.`}, {-0.0650068081092543`, -0.01741852173539965`,
>     0.`}, {-0.04758828637385465`, -0.04758828637385464`,
>     0.`}, {-0.017418521735399647`, -0.0650068081092543`,
>     0.`}, {0.017418521735399654`, -0.0650068081092543`,
>     0.`}, {0.04758828637385464`, -0.04758828637385465`,
>     0.`}, {0.0650068081092543`, -0.017418521735399633`,
>     0.`}, {0.06500680810925429`, 0.017418521735399674`,
>     0.`}, {0.047588286373854656`, 0.04758828637385464`,
>     0.`}, {0.017418521735399636`, 0.0650068081092543`,
>     0.`}, {-0.01741852173539967`, 0.06500680810925429`,
>     0.`}, {-0.047588286373854635`, 0.047588286373854656`,
>     0.`}, {-0.0650068081092543`, 0.017418521735399643`,
>     0.`}, {-0.07147851114539105`, -0.01915260933758654`,
>     0.`}, {-0.05232590180780452`, -0.05232590180780451`,
>     0.`}, {-0.019152609337586533`, -0.07147851114539105`,
>     0.`}, {0.019152609337586543`, -0.07147851114539105`,
>     0.`}, {0.05232590180780451`, -0.05232590180780452`,
>     0.`}, {0.07147851114539105`, -0.019152609337586522`,
>     0.`}, {0.07147851114539104`, 0.019152609337586567`,
>     0.`}, {0.052325901807804526`, 0.05232590180780451`,
>     0.`}, {0.019152609337586526`, 0.07147851114539105`,
>     0.`}, {-0.019152609337586564`, 0.07147851114539104`,
>     0.`}, {-0.0523259018078045`, 0.052325901807804526`,
>     0.`}, {-0.07147851114539105`, 0.01915260933758653`,
>     0.`}, {-0.07862636225993017`, -0.021067870271345192`,
>     0.`}, {-0.057558491988584974`, -0.05755849198858496`,
>     0.`}, {-0.02106787027134519`, -0.07862636225993017`,
>     0.`}, {0.0210678702713452`, -0.07862636225993017`,
>     0.`}, {0.05755849198858496`, -0.057558491988584974`,
>     0.`}, {0.07862636225993017`, -0.021067870271345174`,
>     0.`}, {0.07862636225993015`, 0.021067870271345223`,
>     0.`}, {0.05755849198858498`, 0.05755849198858496`,
>     0.`}, {0.021067870271345178`, 0.07862636225993017`,
>     0.`}, {-0.02106787027134522`, 0.07862636225993015`,
>     0.`}, {-0.05755849198858495`, 0.05755849198858498`,
>     0.`}, {-0.07862636225993017`, 0.021067870271345185`,
>     0.`}, {-0.0864503614528716`, -0.02316430453667561`,
>     0.`}, {-0.063286056916196`, -0.063286056916196`,
>     0.`}, {-0.023164304536675607`, -0.0864503614528716`,
>     0.`}, {0.023164304536675614`, -0.0864503614528716`,
>     0.`}, {0.063286056916196`, -0.063286056916196`,
>     0.`}, {0.0864503614528716`, -0.02316430453667559`,
>     0.`}, {0.0864503614528716`, 0.023164304536675645`,
>     0.`}, {0.06328605691619602`, 0.063286056916196`,
>     0.`}, {0.023164304536675596`, 0.0864503614528716`,
>     0.`}, {-0.02316430453667564`, 0.0864503614528716`,
>     0.`}, {-0.06328605691619599`, 0.06328605691619602`,
>     0.`}, {-0.0864503614528716`, 0.0231643045366756`,
>     0.`}, {-0.09514369388947323`, -0.0254936759425983`,
>     0.`}, {-0.06965001794687493`, -0.06965001794687493`,
>     0.`}, {-0.025493675942598295`, -0.09514369388947323`,
>     0.`}, {0.025493675942598305`, -0.09514369388947323`,
>     0.`}, {0.06965001794687493`, -0.06965001794687493`,
>     0.`}, {0.09514369388947323`, -0.025493675942598278`,
>     0.`}, {0.09514369388947322`, 0.025493675942598337`,
>     0.`}, {0.06965001794687495`, 0.06965001794687493`,
>     0.`}, {0.025493675942598285`, 0.09514369388947323`,
>     0.`}, {-0.025493675942598333`, 0.09514369388947322`,
>     0.`}, {-0.06965001794687492`, 0.06965001794687495`,
>     0.`}, {-0.09514369388947323`, 0.025493675942598288`,
>     0.`}, {-0.1046097669871061`, -0.028030102584603`,
>     0.`}, {-0.07657966440250309`, -0.07657966440250309`,
>     0.`}, {-0.028030102584602996`, -0.1046097669871061`,
>     0.`}, {0.028030102584603006`, -0.1046097669871061`,
>     0.`}, {0.07657966440250309`, -0.07657966440250309`,
>     0.`}, {0.1046097669871061`, -0.028030102584602975`,
>     0.`}, {0.10460976698710608`, 0.02803010258460304`,
>     0.`}, {0.0765796644025031`, 0.07657966440250309`,
>     0.`}, {0.028030102584602982`, 0.1046097669871061`,
>     0.`}, {-0.028030102584603037`, 0.10460976698710608`,
>     0.`}, {-0.07657966440250308`, 0.0765796644025031`,
>     0.`}, {-0.1046097669871061`, 0.02803010258460299`,
>     0.`}, {-0.11513835849365694`, -0.03085123017622048`,
>     0.`}, {-0.08428712831743647`, -0.08428712831743645`,
>     0.`}, {-0.030851230176220473`, -0.11513835849365694`,
>     0.`}, {0.030851230176220486`, -0.11513835849365694`,
>     0.`}, {0.08428712831743645`, -0.08428712831743647`,
>     0.`}, {0.11513835849365694`, -0.030851230176220452`,
>     0.`}, {0.11513835849365693`, 0.030851230176220525`,
>     0.`}, {0.08428712831743648`, 0.08428712831743645`,
>     0.`}, {0.03085123017622046`, 0.11513835849365694`,
>     0.`}, {-0.030851230176220518`, 0.11513835849365693`,
>     0.`}, {-0.08428712831743644`, 0.08428712831743648`,
>     0.001`}, {-0.11513835849365694`, 0.030851230176220466`,
>     0.001`}, {-0.12663287582649685`, -0.03393117681294047`,
>     0.003`}, {-0.09270169901355638`, -0.09270169901355636`,
>     0.`}, {-0.033931176812940465`, -0.12663287582649685`,
>     0.`}, {0.03393117681294048`, -0.12663287582649685`,
>     0.`}, {0.09270169901355636`, -0.09270169901355638`,
>     0.`}, {0.12663287582649685`, -0.033931176812940445`,
>     0.`}, {0.12663287582649685`, 0.03393117681294053`,
>     0.`}, {0.09270169901355639`, 0.09270169901355636`,
>     0.001`}, {0.03393117681294045`, 0.12663287582649685`,
>     0.004`}, {-0.03393117681294052`, 0.12663287582649685`,
>     0.005`}, {-0.09270169901355635`, 0.09270169901355639`,
>     0.008`}, {-0.12663287582649685`, 0.03393117681294046`,
>     0.008`}, {-0.13928650415088364`, -0.037321706303783495`,
>     0.019`}, {-0.10196479784710015`, -0.10196479784710014`,
>     0.003`}, {-0.03732170630378349`, -0.13928650415088364`,
>     0.`}, {0.03732170630378351`, -0.13928650415088364`,
>     0.`}, {0.10196479784710014`, -0.10196479784710015`,
>     0.`}, {0.13928650415088364`, -0.03732170630378347`,
>     0.`}, {0.13928650415088362`, 0.03732170630378355`,
>     0.`}, {0.10196479784710018`, 0.10196479784710014`,
>     0.007`}, {0.037321706303783474`, 0.13928650415088364`,
>     0.031`}, {-0.03732170630378354`, 0.13928650415088362`,
>     0.043`}, {-0.10196479784710012`, 0.10196479784710018`,
>     0.06`}, {-0.13928650415088364`, 0.03732170630378348`,
>     0.056`}, {-0.15319583604944623`, -0.04104870055325979`,
>     0.058`}, {-0.11214713549618643`, -0.11214713549618642`,
>     0.007`}, {-0.041048700553259786`, -0.15319583604944623`,
>     0.`}, {0.041048700553259806`, -0.15319583604944623`,
>     0.`}, {0.11214713549618642`, -0.11214713549618643`,
>     0.`}, {0.15319583604944623`, -0.04104870055325976`,
>     0.`}, {0.1531958360494462`, 0.041048700553259855`,
>     0.001`}, {0.11214713549618646`, 0.11214713549618642`,
>     0.021`}, {0.04104870055325977`, 0.15319583604944623`,
>     0.102`}, {-0.04104870055325985`, 0.1531958360494462`,
>     0.164`}, {-0.1121471354961864`, 0.11214713549618646`,
>     0.221`}, {-0.15319583604944623`, 0.04104870055325978`,
>     0.191`}, {-0.16855405668744242`, -0.04516392337038987`,
>     0.078`}, {-0.12339013331705255`, -0.12339013331705252`,
>     0.009`}, {-0.045163923370389866`, -0.16855405668744242`,
>     0.`}, {0.04516392337038989`, -0.16855405668744242`,
>     0.`}, {0.12339013331705252`, -0.12339013331705255`,
>     0.`}, {0.16855405668744242`, -0.04516392337038984`,
>     0.`}, {0.1685540566874424`, 0.04516392337038994`,
>     0.`}, {0.12339013331705256`, 0.12339013331705252`,
>     0.028`}, {0.045163923370389845`, 0.16855405668744242`,
>     0.147`}, {-0.045163923370389936`, 0.1685540566874424`,
>     0.216`}, {-0.12339013331705251`, 0.12339013331705256`,
>     0.28`}, {-0.16855405668744242`, 0.04516392337038986`,
>     0.241`}, {-0.18536116606487218`, -0.049667374755173736`,
>     0.183`}, {-0.13569379130969847`, -0.13569379130969844`,
>     0.021`}, {-0.04966737475517373`, -0.18536116606487218`,
>     0.`}, {0.04966737475517375`, -0.18536116606487218`,
>     0.`}, {0.13569379130969844`, -0.13569379130969847`,
>     0.`}, {0.18536116606487218`, -0.049667374755173695`,
>     0.`}, {0.18536116606487218`, 0.04966737475517381`,
>     0.001`}, {0.1356937913096985`, 0.13569379130969844`,
>     0.06`}, {0.04966737475517371`, 0.18536116606487218`,
>     0.333`}, {-0.0496673747551738`, 0.18536116606487218`,
>     0.482`}, {-0.1356937913096984`, 0.1356937913096985`,
>     0.582`}, {-0.18536116606487218`, 0.049667374755173715`,
>     0.52`}, {-0.20390694192962233`, -0.054636700421142145`,
>     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,-1.06004,<=
> ==
>
<17>>,-1.0702,-1.07372,-1.07726,-1.07584,-1.07196,-1.06667,-1.0614,-1.05755=
> ==
>
,-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.
> > How can I work around this problem?
> > I attach appropriate files to this letter.
> >
> > best regards,
> > Szymon Roziewski
> >
>
>
>
> --
> Z wyrazami szacunku,
> Szymon Roziewski

```

• Prev by Date: Re: calculate vertex of a parabola
• Next by Date: Histogram
• Previous by thread: Re: Interpolate in polar coordinates or cartesian
• Next by thread: Re: Interpolate in polar coordinates or cartesian