Google Groups no longer supports new Usenet posts or subscriptions. Historical content remains viewable.

Dismiss

several plots in manipulate

5 views

Skip to first unread message

Cristina Ballantine

unread,

Jul 23, 2008, 6:20:00 AM7/23/08

Hi,

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.

Any help is very much appreciated.

Cristina

---------------------------------------------------------------------------=
--------------

In the plot r2=2/3. In Manipulate r2 should be between r1 and 1.

r1 := 1/4
r2 := 2/3
u := Pi/3

plot1 := 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, Mesh -> False]

plot2 := 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, Mesh -> False]

plot3 := 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, Mesh -> False]

Jean-Marc Gulliet

unread,

Jul 25, 2008, 6:19:36 AM7/25/08

On Jul 23, 12:20 pm, "Cristina Ballantine" <cball...@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 ParameterPl=

ot
> 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 -