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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: [mg39464] Re: ParametricPlot - a feature or a bug?
  • From: Bill Rowe <listuser at earthlink.net>
  • Date: Mon, 17 Feb 2003 04:34:17 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

On 2/16/03 at 6:13 AM, vvb at mail.strace.net (Vladimir Bondarenko) wrote:

>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.

<examples snipped>

The problem you are seeing is due to the way the automatic plot routines in Mathematica work. In essence, you have an oscillatory function you are sampling at relatively few points compared to the range you have specified for t. Consequently, subsequent samples are likely to be spaced many cycles apart.

Mathematica connects each computed point with straight lines. Since the samples are essentially random points on a unit circle, these lines will be chords rather than straight line approximations to the perimeter.

If you are going to use large values of t and require the resulting plot resemble the true curve you will have to increase the number of plot points.

For example, contrast

ParametricPlot[{Cos[t],Sin[t]},{t,0,200},AspectRatio->Automatic];

with

ParametricPlot[{Cos[t],Sin[t]},{t,0,200},AspectRatio->Automatic, PlotPoints->100];


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