Re: Interpolate in polar coordinates or cartesian

• To: mathgroup at smc.vnet.net
• Subject: [mg112660] Re: Interpolate in polar coordinates or cartesian
• From: Ingolf Dahl <Ingolf.Dahl at physics.gu.se>
• Date: Sat, 25 Sep 2010 02:20:03 -0400 (EDT)

```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]

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imsUnstructuredInterpolation[Data]

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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

```

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