Re: several plots in manipulate
- To: mathgroup at smc.vnet.net
- Subject: [mg90870] Re: several plots in manipulate
- From: "Cristina Ballantine" <cballant at holycross.edu>
- Date: Sun, 27 Jul 2008 02:31:18 -0400 (EDT)
The enclosed message solved the problem I posted on the discussion group.
Thank you!
On Jul 23, 12:20= pm, "Cristina Ballantine" <cball... at holycross.edu>
wrote:
> I would like to manipulate a plot created from three different parametric
> plots. I display the plot with Show[plot1,plot2,plot3] (see code below).
> If I try this in Manipulate, the plots are displayed next to each other. I
> need them in a single plot. I cannot combine them in a single ParameterPlot
> because the options are different.
On my system, the following works as expected: the three plots are
drawn on the same graph, though it takes few seconds for the complete
rendering to be completed. (Note that I have written the expressions
for the plots as function of three parameters and added the option
MaxRecursion->0 to speed up computations.)
With[{r1 == 1/4, u == Pi/3},
Manipulate[
Show[plot1[r1, r2, u], plot2[r1, r2, u],
plot3[r1, r2, u]], {{r2, 2/3}, r1, 1}]]
HTH,
- Jean-Marc
$Version
"6.0 for Mac OS X x86 (64-bit) (May 21, 2008)"
plot1[r1_, r2_, u_] :==
ParametricPlot[{{Re[
1*Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[1*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[
1*Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[1*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[
I*Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[I*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[
I*Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[I*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[(-1)*
Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[(-1)*
Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[(-1)*
Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[(-1)*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[(-I)*
Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[(-I)*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[(-I)*
Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[(-I)*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}}, {t, 10^(-10), 2*Pi - 10^(-10)}, {r, 0,
r1^4*r2^4 - 10^(-6)}, PlotRange -> All,
ColorFunction -> Function[{x, y, t, r}, Hue[.5, t, r]],
PlotPoints -> 25, MaxRecursion -> 0, Mesh -> False]
plot2[r1_, r2_, u_] :==
ParametricPlot[{{Re[
1*Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[1*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[
1*Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[1*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[
I*Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[I*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[
I*Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[I*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[(-1)*
Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[(-1)*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[(-1)*
Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[(-1)*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[(-I)*
Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[(-I)*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[(-I)*
Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[(-I)*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}}, {t, 10^(-10), 2*Pi - 10^(-10)}, {r,
r1^4*r2^4 - 10^(-6), r1^4*r2^4 + 10^(-2)}, PlotRange -> All,
ColorFunction -> Function[{x, y, t, r}, Hue[1, t, r]],
PlotPoints -> 45, MaxRecursion -> 0, Mesh -> False]
plot3[r1_, r2_, u_] :==
ParametricPlot[{{Re[
1*Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[1*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[
1*Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[1*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[
I*Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[I*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[
I*Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[I*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[(-1)*
Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[(-1)*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[(-1)*
Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[(-1)*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[(-I)*
Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[(-I)*
Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) +
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}, {Re[(-I)*
Exp[I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/4)],
Im[(-I)*Exp[
I*u]*(((r1^4 + r2^4)*(1 - r*Exp[I*t]) -
Sqrt[(r1^4 + r2^4)^2*(1 - r*Exp[I*t])^2 -
4*(1 - r1^4*r2^4*r*Exp[I*t])*(r1^4*r2^4 -
r*Exp[I*t])])/(2*(1 - r1^4*r2^4*r*Exp[I*t])))^(1/
4)]}}, {t, 10^(-10), 2*Pi - 10^(-10)}, {r,
r1^4*r2^4 + 10^(-2), 1}, PlotRange -> All,
ColorFunction -> Function[{x, y, t, r}, Hue[.1, t, r]],
PlotPoints -> 25, MaxRecursion -> 0, Mesh -> False]
With[{r1 == 1/4, u == Pi/3},
Manipulate[
Show[plot1[r1, r2, u], plot2[r1, r2, u],
plot3[r1, r2, u]], {{r2, 2/3}, r1, 1}
]
]