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Re: ParametricPlot - a feature or a bug?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg39469] Re: [mg39447] ParametricPlot - a feature or a bug?
*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>
*Date*: Mon, 17 Feb 2003 04:34:58 -0500 (EST)
*Sender*: owner-wri-mathgroup at wolfram.com
Here is another easy fix for the problem. I doubt however that it woudl
be useful to try to make it a built-in feature of ParametricPlot:
Show[ParametricPlot[{Cos[t], Sin[t]}, {t, 0, 5000*Pi}, AspectRatio ->
Automatic,
DisplayFunction -> Identity] /. Line[l_List] :> Line[Sort[l,
Arg[Complex @@ #1] <= Arg[Complex @@ #2] & ]],
DisplayFunction -> $DisplayFunction]
On Sunday, February 16, 2003, at 10:34 PM, Andrzej Kozlowski wrote:
> 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
>>
>>
>>
>>
>>
>
>
Andrzej Kozlowski
Yokohama, Japan
http://www.mimuw.edu.pl/~akoz/
http://platon.c.u-tokyo.ac.jp/andrzej/
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