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/