Re: Incorrect plotting of Lissajous-figures

• To: mathgroup at smc.vnet.net
• Subject: [mg25915] Re: [mg25890] Incorrect plotting of Lissajous-figures
• From: Matt.Johnson at autolivasp.com
• Date: Tue, 7 Nov 2000 23:05:01 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Rene-

the plot filling up has nothing to do with the coefficients in your
equation, it is how the plot points are generated and connected.   With
increasing coefficients, the distance along the path of the ellipse that is
travelled is increased.  As mathematica generates the plot by joining
points with straight lines, these lines start crossing the interior of the
elliipse, creating the "filled" ellipse.  This can be avoided by increasing
the PlotPoints option.  Although, for large coefficients, the time to
create the plot will greatly increase.  Here is a quicker option, although
the plot is just of points that are not joined:

In[7]:=
n = 1000;
pp1 = ParametricPlot[{Cos[n t], Cos[n t + Pi/4]}, {t, 0, 2Pi}];
In[9]:=
pp1Input = InputForm[pp1];
In[10]:=
points = Cases[pp1Input, {x_, y_}, Infinity];
In[16]:=
ListPlot[points];

-matt

Rene Meyer <rene.meyer at s2000.tu-chemnitz.de> on 11/07/2000 12:56:00 AM

cc:
Subject: [mg25915]  [mg25890] Incorrect plotting of Lissajous-figures

Hello,

while using Mathematica 4.0.2.0 to plot a Lissajous-figure with

ParametricPlot[{Cos[500t], Cos[500t + Pi/4]}, {t, 0, 2Pi}]

I found that with growing coefficients of t the figure (which should
be a ellipse with an angle of 45 degrees between its longer main axis and
the x axis) have the effect of filling up the whole ellipse with
points. Is this an effect of rounding errors or is this a bug in
mathematica?

--
Rene Meyer
Student of Physics - Chemnitz University of Technology

```

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