Re: How to plot field lines of conformal mapping

• To: mathgroup at smc.vnet.net
• Subject: [mg26204] Re: [mg26083] How to plot field lines of conformal mapping
• From: Christopher Lee French <clfrench at bellatlantic.net>
• Date: Sat, 2 Dec 2000 02:10:34 -0500 (EST)
• References: <200011280655.BAA02200@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Jos,

ParametricPlot[
Evaluate[
{Re[f], Im[f]} /. List /@ Thread[z -> u + Range[-Pi/2, Pi/2, Pi/15] I],
{u, -3,  3},
PlotPoints -> 700]

This should work for you, right away!
Sorry, I did not provide any explanation or exactly reproduce your
original
lines.

Christopher French

Jos R Bergervoet wrote:

> I would like to plot a family of field lines obtained from a conformal
> mapping, as in the following code snippet. Is there a shorter way?
>
>   f = z + I Sinh[z]
>
>   ParametricPlot[{
>                     {Re[f], Im[f]} /. z->u-Pi/2I,
>                     {Re[f], Im[f]} /. z->u-1.5I,
>                     {Re[f], Im[f]} /. z->u-1.25I,
>                     {Re[f], Im[f]} /. z->u-1.0I,
>                     {Re[f], Im[f]} /. z->u-0.75I,
>                     {Re[f], Im[f]} /. z->u-0.5I,
>                     {Re[f], Im[f]} /. z->u-0.25I,
>                     {Re[f], Im[f]} /. z->u+0I,
>                     {Re[f], Im[f]} /. z->u+0.25I,
>                     {Re[f], Im[f]} /. z->u+0.5I,
>                     {Re[f], Im[f]} /. z->u+0.75I,
>                     {Re[f], Im[f]} /. z->u+1.0I,
>                     {Re[f], Im[f]} /. z->u+1.25I,
>                     {Re[f], Im[f]} /. z->u+1.5I,
>                     {Re[f], Im[f]} /. z->u+Pi/2I
>                  },
>                     {u,-3,3}, PlotPoints->700]
>
> I tried (without success) to do it after creating a table in advance:
>
>   n = 1
>   t = Table[{Re[f], Im[f]} /. z->u+i/n Pi/2I , {i, -n,n}]
>   ParametricPlot[t, {u,-3,3}, PlotPoints->700]
>
> This does not work. Does anyone know an elegant solution?
>
> NB: I do not want the full CartesianMap[F , {-3,3}, {-Pi/2,Pi/2}]
> but only one of the two families of lines.
>
> Thanks in advance,
> Jos
>
> --
>   Dr. Jozef R. Bergervoet                      Electromagnetism and EMC
>   Philips Research Laboratories,             Eindhoven, The Netherlands
>   Building WS01                                     FAX: +31-40-2742224
>   E-mail: Jos.Bergervoet at philips.com              Phone: +31-40-2742403

```

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