Re: several plots in manipulate
- To: mathgroup at smc.vnet.net
- Subject: [mg90827] Re: several plots in manipulate
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Fri, 25 Jul 2008 06:17:32 -0400 (EDT)
- References: <g670kg$s2i$1@smc.vnet.net>
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 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 - 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} ] ] -------------- End of Code