Re: vertical lines in plot
- To: mathgroup at smc.vnet.net
- Subject: [mg94236] Re: vertical lines in plot
- From: Szabolcs Horvát <szhorvat at gmail.com>
- Date: Mon, 8 Dec 2008 06:27:21 -0500 (EST)
- Organization: University of Bergen
- References: <ghavog$o8c$1@smc.vnet.net>
Cristina Ballantine wrote:
> In plotting the inverse image of the unit circle under the function B
> below, I get all kinds of vertical lines. They are obviously jump
> discontinuities, very likely caused by choices of branch cuts. I there any
> way of getting rid of the vertical lines without redefining the brunch
> cuts? I looked at the value of different solutions in sol4 close to a
> point of discontinuity and it looks like the order of the solutions is
> switched when t gets to that point. I am not sure if this is just a
> coincidence. I also tried ExclusionsStyle->Red but there don't seem to be
> any exclusions.
>
>
> alpha := Pi/3
> r := 2/3
> a := r*Exp[I*alpha]
> n := 3
>
> B[z] := 1/(z^n)*((Conjugate[a]/a)*(a^2 - z^2)/(1 - (Conjugate[a])^2*z^2))^n
>
> sol4 := Solve[B[z] == Exp[I*t], z]
>
> ParametricPlot[Evaluate[{Re[z], Im[z]} /. sol4], {t, 0, 2 Pi}, PlotRange -> All]
>
Hello Cristina,
How about this alternative approach?
ContourPlot[Abs[B[x + I y]] == 1, {x, -3, 3}, {y, -3, 3},
MaxRecursion -> 3]
Note that there is a little mistake in your code above---it is necessary
to correct B[z] := ... to B[z_] := ... for this to work correctly.
Szabolcs