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MathGroup Archive 2003

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Re: ParametricPlot - a feature or a bug?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg39461] Re: [mg39447] ParametricPlot - a feature or a bug?
  • From: BobHanlon at aol.com
  • Date: Mon, 17 Feb 2003 04:34:03 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 2/16/03 7:14:36 AM, vvb at mail.strace.net writes:


> While trying to plot complex parametric plots with large values
> of the parameter I run into a problem which boils down to the
> following simple observation.
>
> a) ParametricPlot[{Cos[t], Sin[t]}, {t, 0, 1 Pi}, AspectRatio ->
> Automatic];
>
>      A perfect circumference.
>
> b) ParametricPlot[{Cos[t], Sin[t]}, {t, 0, 200 Pi}, AspectRatio ->
> Automatic];
>
>      Instead of a circumference, not a very wide annulus.
>
> c) ParametricPlot[{Cos[t], Sin[t]}, {t, 0, 500 Pi}, AspectRatio ->
> Automatic];
>
>      An annulus which width is equal to the radius of the inner
>      circumference.
>
> d) ParametricPlot[{Cos[t], Sin[t]}, {t, 0, 1000 Pi}, AspectRatio ->
> Automatic];
>
>      A black ring with tiny white spots.
>
> e) ParametricPlot[{Cos[t], Sin[t]}, {t, 0, 10^19 Pi}, AspectRatio ->
> Automatic];
>
>      A funny net.
>
> f) ParametricPlot[{Cos[t], Sin[t]}, {t, 0, 10^20 Pi}, AspectRatio ->
> Automatic];
>
>      A segment.
>
> g) ParametricPlot[{Cos[t], Sin[t]}, {t, 0, 10^26 Pi}, AspectRatio ->
> Automatic];
>
>      Only the axes are shown. There is no graph itself.
>
>
> Is (at least a part of the shown output) a feature or a bug?
>
> (By the way, before answering why do not try to solve the same
> problems with a couple of other systems? ;-)
>
>

It is the natural consequence of undersampling.   Increase the PlotPoints.

n = 2000;

ParametricPlot[{Cos[t], Sin[t]}, {t, 0, n* Pi},

     AspectRatio -> Automatic, PlotPoints -> 10*n];


Bob Hanlon



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