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