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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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