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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
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
retraced.
David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/
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,
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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