Re: ParametricPlot help please
- To: mathgroup at smc.vnet.net
- Subject: [mg17143] Re: ParametricPlot help please
- From: "Allan Hayes" <hay at haystack.demon.co.uk>
- Date: Sat, 17 Apr 1999 03:35:26 -0400
- References: <7es30f$cbh@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Rob, What is suitable depends on hw you want to use the code, but here is a simple way of getting your plot. ParametricPlot[#, {u, -Pi, Pi}, AspectRatio -> Automatic ]&[ {(u+1+Exp[u]Cos[#])/Pi,(#+ Exp[u])/Pi}&/@{ Pi/1.2, Pi/1.5, Pi/2, Pi/4, Pi/8, Pi/16 } ] The behaviour of slot functions like (#1+ #2 #3 )& is as follows With a=va,b=vb; c=vc the evaluation steps are (#1+ #2 #3 )&[a,b.c] (#1+ #2 #3 )& [va,vb,vc] (va+vb vc) Allan --------------------- Allan Hayes Mathematica Training and Consulting Leicester UK www.haystack.demon.co.uk hay at haystack.demon.co.uk Voice: +44 (0)116 271 4198 Fax: +44 (0)870 164 0565 Rob Peterson <robpeterson at iname.com> wrote in message news:7es30f$cbh at smc.vnet.net... > Some time ago several kind souls on this ng helped me do some conformal > transformation plots (this one is part of the curves describing the fields > in a parallel plate capacitor). We used a series of ParametricPlots. Now > I would like to understand how this worked - maybe I can learn something > about Mathematica. I think I get the use of Map[] but I am stuck on the use of > ParametricPlot[#1,.....]. I have looked high and low and I do not find any > mention of the #1 parameter. If I ever get thru this, I'll start trying to > understand the Partition[Thread[].... ] part. > > Here's the code. Any help/suggestions appreciated. > > By the way, I got about 5 good suggestions on how to do these plots. Some > were faster, some more understandable, but all had more characters than the > code below: > > (* part of conformal transformation for parallel plate capacitor *) > x[u_,v_]:=(u+1+Exp[u] Cos[v])/\[Pi]; > y[u_,v_]:=(v+ Exp[u] Sin[v])/\[Pi]; > > {a,b,c,d,e,f} = > Map[ParametricPlot[#1, {u,-Pi,Pi},AspectRatio->Automatic, > DisplayFunction->Identity]&, > {x[u,v],y[u,v]}/. > Partition[Thread[v->{Pi/1.2,Pi/1.5,Pi/2,Pi/4,Pi/8,Pi/16}], 1]] > > Show[{a,b,c,d,e,f}, DisplayFunction->$DisplayFunction] > > Thanks, Rob > > > > > robpeterson at iname.com > <http://www.flash.net/~eterson> >