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. --