When plotting a closed curve with parametricplot several times,

ParametricPlot[{Cos[u], Sin[u]}, {u, 0, 100000}]

the curve becomes a filled region, instead of overwriting the previous curve. Of course in this example I know it is sufficient for u to run in a 2 Pi interval, but I am working on a case where I do not know if the curve is closed or not, so I need to know if the area is filled because the curve is actually not closed rather than being just numerical garbage.

I can fix this behavior by increasing the number of plotpoints, but I'd rather not use too much memory unnecessarily. Does anyone know how to address this problem in some other way?

  • 4
    $\begingroup$ FunctionPeriod[{Cos[u], Sin[u]}, u] $\endgroup$ – Bob Hanlon Jun 23 at 0:53

Instead of showing the lines generated by ParametricPlot, which are indeed prone to artifacts even in your simple case, you could show the points where the function has been evaluated instead. Particularly if you have quite a few of them, they will be as closely spaced that they might well fuse into the semblance of a line:

  {Cos[u], Sin[u]}, {u, 0, 100000},
  PlotStyle -> None,
  Mesh -> All, MeshStyle -> Black

Plot with mesh points only

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ParametricPlot[{Cos[u], Sin[u]}, {u, 0,100000},MaxRecursion -> 15]  
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