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RE: Bug or feature ?

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  • Subject: [mg72440] RE: [mg72368] Bug or feature ?
  • From: "David Annetts" <davidannetts at>
  • Date: Thu, 28 Dec 2006 04:47:48 -0500 (EST)

Hi Giovanni,

> Please, try this with Mathematica (5.2):
> << Graphics`Graphics`
> PolarPlot[Sin[t]^2 Cos[t]^2, {t, 0, 2Pi}]
> PolarPlot[Sin[t]^2 Cos[t]^2, {t, 0, 21}]
> compare the two graphics.
> In the second (t is between zero and twentyone) I got a 
> spurios segment between 3rd and 4th quadrants.
> Can you tell me why ?
> (Btw, I got this just playing for one minute or two with 
> PolarPlot. The "21" was a typo...)

It's a feature!

The effect you see is caused by not sampling your function finely enough.
You can get another spurious segment using 

	PolarPlot[Sin[t]^2 Cos[t]^2, {t, 0, 21}, PlotPoints -> 13]

And this suggests the cure ....

Increasing the number of plot points results in a correct plot.
Interestingly, reducing it (from the default of 25) also works (eg
PlotPoints->20) provided you don't hit a pathological value like (eg) 13.

For effects like this, the cure usually lies in fine tuning any of the
values of PlotPoints, MaxBend or PlotDivision.  For another feature, look at

	PolarPlot[Sin[t]^2 Cos[t]^2, {t, 0, 21}, PlotDivision -> 4].



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