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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: [mg39458] Re: [mg39447] ParametricPlot - a feature or a bug?
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Mon, 17 Feb 2003 04:33:53 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Essentially the same thing has been mentioned on this list a lot of 
times. You need to either set PlotPoints manually, e.g.

ParametricPlot[{Cos[t], Sin[t]}, {t, 0, 500 Pi}, AspectRatio -> 
Automatic,
        PlotPoints -> 500];
or you can set PlotDivision to a larger value

ParametricPlot[{Cos[t], Sin[t]}, {t, 0, 500 Pi}, AspectRatio -> 
Automatic,
        PlotDivision -> 500];


or you can just use ListPlot, even with quite large step size:

ListPlot[Table[{Cos[t], Sin[t]}, {t, 0, 500 Pi,
       1}], AspectRatio -> Automatic]


The fact that other systems may not need the above adjustment need not 
at all mean that there is a bug in Mathematica or that they do this 
sort of thing better in general. To say that you would have to 
carefully examine how they avoid this problem and  at what price (if 
any). After all, ListPlot which does not do any adaptive sampling does 
not have this problem yet it certainly is not superior, in general, to 
ParametricPlot as a plotting tool.

Andrzej Kozlowski
Yokohama, Japan
http://www.mimuw.edu.pl/~akoz/
http://platon.c.u-tokyo.ac.jp/andrzej/


On Sunday, February 16, 2003, at 08:13 PM, Vladimir Bondarenko wrote:

> Hello,
>
> 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? ;-)
>
>
> Best wishes,
>
> Vladimir Bondarenko
> Mathematical and Production Director
> Symbolic Testing Group
>
> Web  :  No other my site is permitted to me to quote here
>         http://www.CAS-testing.org/  GEMM Project (95% ready)
>
> Email:  vvb at mail.strace.net
> Voice:  (380)-652-447325 Mon-Fri 6 a.m. - 3 p.m. GMT
> ICQ  :  173050619
> Mail :  76 Zalesskaya Str, Simferopol, Crimea, Ukraine
>
>
>
>
>



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