       RE: ParametricPlot - a feature or a bug?

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

```Vladimir,

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]];
Length[pts]
901

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

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

Show[Graphics[
{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

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
retraced.

David Park

From: Vladimir Bondarenko [mailto:vvb at mail.strace.net]
To: mathgroup at smc.vnet.net

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,

Mathematical and Production Director
Symbolic Testing Group

Web  :  No other my site is permitted to me to quote here

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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