       Re: How to plot field lines of conformal mapping

• To: mathgroup at smc.vnet.net
• Subject: [mg26186] Re: [mg26083] How to plot field lines of conformal mapping
• From: "Mark Harder" <harderm at ucs.orst.edu>
• Date: Thu, 30 Nov 2000 01:04:24 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Jos,
The problem I had when I tried to run your code was that t was not
recognized by ParametricPlot as a function, even though the evaluated form
of t, when evaluated outside of PP, was clearly an expression in functions
of u.  So I forced evaluation of t inside the argument list of PP, and this
now produced a graph of two curves: a step-like function, and a curve with
vertical asymptotes near x=+/-2:

ParametricPlot[Evaluate[t ], {u, -3, 3}, PlotPoints -> 700]

But, I don't know if this is what you wanted, since your NB was a little
unclear to me.

good luck,
mark e. harder

-----Original Message-----
From: Jos R Bergervoet <Jos.Bergervoet at philips.com>
To: mathgroup at smc.vnet.net
Subject: [mg26186] [mg26083] How to plot field lines of conformal mapping

>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.
>
>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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