       Re: A Bug in Parametric Plot ?

• To: mathgroup at smc.vnet.net
• Subject: [mg5391] Re: A Bug in Parametric Plot ?
• From: "David B. Wagner" <dbwagner at princon.com>
• Date: Thu, 5 Dec 1996 14:50:27 -0500
• Organization: Principia Consulting
• Sender: owner-wri-mathgroup at wolfram.com

Sasho Kalajdzievski wrote:
>
> Take a periodic curve, say x=Cos[t], y=Sin[t], and plot it with t ranging
> between, say -Pi and Pi.  Get a circle (or ellipse - depending on the
> Aspect Ratio). Now repeat the same procedure with a larger range - some
> strange things happen. For example, do the following:
> k=1250; Do[ParametricPlot[{Cos[t], Sin[t]},
> {t, -k*Pi, k*Pi}, PlotLabel -> k ]; k=k+10, {10} ]
> We get some nice designs, but some clearly far removed from the circle -
> or from a very thick circle one expects to get (as in Maple). In
> particular, for k=1280, we get a thin TRIANGLE (?), while for k=1320 the
> plot is EMPTY (?!!).

This sounds like it is being caused by the sampling algorithm used
by the 2-D plotting commands.  The algorithm samples equi-spaced
points on the interval and when k=1250, all of the sampled points
fall on just 3 points on the circle; when k=1320, possibly they all
fall on a single point (which is why the plot looks empty). Try changing
the PlotPoints option and see if you get any different designs.

--

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