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MathGroup Archive 2003

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RE: ParametricPlot - a feature or a bug?

  • To: mathgroup at
  • Subject: [mg39459] RE: [mg39447] ParametricPlot - a feature or a bug?
  • From: "David Park" <djmp at>
  • Date: Mon, 17 Feb 2003 04:33:56 -0500 (EST)
  • Sender: owner-wri-mathgroup at


Not a bug. ParametricPlot has a default for how many plot points and
subdivisions it will use.

Options[ParametricPlot, {PlotPoints, PlotDivision}]
{PlotDivision -> 30., PlotPoints -> 25}

Let's look at the most illustrative case. With...

plot1 =
    ParametricPlot[{Cos[t], Sin[t]}, {t, 0, 500 Pi},
      AspectRatio -> Automatic];

you obtain an inaccurate plot because you are only obtaining 3 or 4 points
each time you traverse the circle. If more PlotPoints are used a better plot
is obtained.

ParametricPlot[{Cos[t], Sin[t]}, {t, 0, 500 Pi},
    PlotPoints -> 1000,
    AspectRatio -> Automatic];

To understand better what is happening to your plot, let's extract the
points that Mathematica used and plot them.

pts = (First[plot1] /. Line[a_] :> a)[[1,1]];

We have only 901 points for 250 circuits of the circle.

If just the points are plotted a fairly good circle is obtained.

      {Point /@ pts}],
    AspectRatio -> Automatic];

If only the first 15 points are used to draw a line, then you can see how an
annular region will slowly be filled in.

I believe the same phenomenon explains all of your cases. If Mathematica
attempted to continue subdividing the plot until a smooth curve was
obtained, it could easily fall into an infinite recursion, for example when
the curve had a cusp.

It is up to the user to specify an appropriate domain and number of plot
points. Generally, better looking curves are obtained if regions are not

David Park
djmp at

From: Vladimir Bondarenko [mailto:vvb at]
To: mathgroup at


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 ->

     Instead of a circumference, not a very wide annulus.

c) ParametricPlot[{Cos[t], Sin[t]}, {t, 0, 500 Pi}, AspectRatio ->

     An annulus which width is equal to the radius of the inner

d) ParametricPlot[{Cos[t], Sin[t]}, {t, 0, 1000 Pi}, AspectRatio ->

     A black ring with tiny white spots.

e) ParametricPlot[{Cos[t], Sin[t]}, {t, 0, 10^19 Pi}, AspectRatio ->

     A funny net.

f) ParametricPlot[{Cos[t], Sin[t]}, {t, 0, 10^20 Pi}, AspectRatio ->

     A segment.

g) ParametricPlot[{Cos[t], Sin[t]}, {t, 0, 10^26 Pi}, AspectRatio ->

     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  GEMM Project (95% ready)

Email:  vvb at
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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