       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]