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parametric plot extremely slow

  • To: mathgroup at smc.vnet.net
  • Subject: [mg90634] parametric plot extremely slow
  • From: "Cristina Ballantine" <cballant at holycross.edu>
  • Date: Thu, 17 Jul 2008 05:34:04 -0400 (EDT)

 Hi,

 I am working on a project involving many parametric plots and Mathematica 
6 is extremely slow. The plot below takes about 5 minutes. I also need 
plots coloring regions with specific colors depending on the plotted 
point. They take about two hours.

 Any hints on increasing plot speed are very much appreciated. I am new to 
Mathematica and I cannot use Version 5 for Graphics. The plot below takes 
less than 10 seconds in other systems (but but they cannot be used for the 
more complicated region plots).

 Here is the code I used for the plot.


 a1 := 2/3*Exp[I*Pi/4]
a2 := 2/5 Exp[I*4*Pi/5]

 zr0[t_] :=
  Re[(Exp[I*0*Pi/4]*t - Abs[a1])/(Exp[I*0*Pi/4]*t*Abs[a1] - 1)*a1/(Abs[a1])]

 zr1[t_] :=
  Re[(Exp[I*2*Pi/4]*t - Abs[a1])/(Exp[I*2*Pi/4]*t*Abs[a1] - 1)*a1/(Abs[a1])]

zr2[t_] :=
 Re[(Exp[I*4*Pi/4]*t - Abs[a1])/(Exp[I*4*Pi/4]*t*Abs[a1] - 1)*a1/(Abs[a1])]

 zr3[t_] :=
  Re[(Exp[I*6*Pi/4]*t - Abs[a1])/(Exp[I*6*Pi/4]*t*Abs[a1] - 1)*a1/(Abs[a1])]

 zr0[t_] :=
  Re[(Exp[I*0*Pi/4]*t - Abs[a1])/(Exp[I*0*Pi/4]*t*Abs[a1] - 1)*a1/(Abs[a1])]

 zi1[t_] :=
  Im[(Exp[I*2*Pi/4]*t - Abs[a1])/(Exp[I*2*Pi/4]*t*Abs[a1] - 1)*a1/(Abs[a1])]

zi2[t_] :
  Im[(Exp[I*4*Pi/4]*t - Abs[a1])/(Exp[I*4*Pi/4]*t*Abs[a1] - 1)*a1/(Abs[a1])]

 zi3[t_] :=
  Im[(Exp[I*6*Pi/4]*t - Abs[a1])/(Exp[I*6*Pi/4]*t*Abs[a1] - 1)*a1/(Abs[a1])]

 zi0[t_] :=
  Im[(Exp[I*0*Pi/4]*t - Abs[a1])/(Exp[I*0*Pi/4]*t*Abs[a1] - 1)*a1/(Abs[a1])]


cx[t_] := Sin[t*2*Pi]
cy[t_] := Cos[t*2*Pi]

 plotbasic :=
  ParametricPlot[{{cx[t], cy[t]}, {zr0[t], zi0[t]}, {zr1[t],
     zi1[t]}, {zr2[t], zi2[t]}, {zr3[t], zi3[t]}}, {t, 0, 1000},
   PlotRange -> 6, PlotPoints -> 150, MaxRecursion -> 10,
   PlotStyle -> {{Black, Thick}, Red, Blue, Magenta, Purple},
   PerformanceGoal -> "Speed" ]

 Show[plotbasic]


Thank you in advance for your help.

Best wishes,

Cristina


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