Mesh and ParametricPlot

Question

Is this a bug, or something going over my head? When using the following code, nothing "special" happens:

ParametricPlot[a {Cos[t], Sin[t]}, {a, 1, 2}, {t, 0, 2 Pi}, 
 Mesh -> None, PlotStyle -> Opacity[0.2]]

it works as expected, one gets this graphic, without any mesh lines:

enter image description here

When adding Graphics[] in front of that—as I'd like to Show such a ParametricPlot with some other graphics, I get this:

Show[
 Graphics[],
 ParametricPlot[a {Cos[t], Sin[t]}, {a, 1, 2}, {t, 0, 2 Pi}, 
  Mesh -> None, PlotStyle -> Opacity[0.2]]
 ]

yields:

enter image description here

Why do those mesh-lines come up? Are those actually Mesh-lines, as I used Mesh -> None? How can I delete those lines, while still using Show and others Graphics[]?

Thanks for all help!

I've thought that it's because Show is taking Options from the first element but then I couldn't reproduce your second image. What version are you working on? — Kuba, Dec 01 '13 at 09:12
@Kuba, thanks for your fast answer. I'm using Mathematica version 9, I think that's the latest? — Gabriel, Dec 01 '13 at 09:13
I'm on a mac. Anyone else on a mac having the same problem? Thanks! — Gabriel, Dec 01 '13 at 09:24
Try Show[Graphics[{}, Method -> {"TransparentPolygonMesh" -> True} ], ParametricPlot[a {Cos[t], Sin[t]}, {a, 1, 2}, {t, 0, 2 Pi}, Mesh -> None, PlotStyle -> Opacity[0.2]]] - see this Q&A for more... — cormullion, Dec 01 '13 at 12:01
@cormullion: this works on my end! Thanks a lot! I don't see this is documented, have I badly looked? Thanks once again! — Gabriel, Dec 01 '13 at 16:28
I don't think this is documented - I can't find it myself. There are a lot of undocumented things in Mathematica - it wouldn't be so much fun if everything was documented... :) — cormullion, Dec 01 '13 at 16:55
I don't this is a duplicate of this question. I think it's our old friend Show taking it options from its first argument. — m_goldberg, Apr 28 '14 at 03:30
Why not eschew Show and just put the graphics in a prolog to ParametricPlot? — m_goldberg, Apr 28 '14 at 04:22

score 2 · Answer 1 · answered Apr 28 '14 at 03:24

2

I can reproduce the problem on V9.0.1 running on OS X. I don't think it's a bug. I think it's the old problem of Show taking its options from its first argument. I say this because reversing the order of the arguments fixes the problem.

Show[
  Graphics[],
  ParametricPlot[a {Cos[t], Sin[t]}, {a, 1, 2}, {t, 0, 2 Pi}, 
    Mesh -> None, PlotStyle -> Opacity[0.2]],
  ImageSize -> Small]

plot

Show[
  ParametricPlot[a {Cos[t], Sin[t]}, {a, 1, 2}, {t, 0, 2 Pi}, 
    Mesh -> None, PlotStyle -> Opacity[0.2]],
  Graphics[],
  ImageSize -> Small]

plot

answered Apr 28 '14 at 03:24

m_goldberg

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So you are agreeing with what @cormullion essentially observed, too. The problem with changing the order of presentation in Show is that the purpose of setting Opacity in the first place was so that it can be placed on top of a Graphics that comes before the RegionPlot. So changing the order doesn't really seem to be a solution. – Jens Apr 28 '14 at 04:07
@Jens. Maybe doesn't solve the OP's real problem, but it explains his results. I would advise him to put his graphics in a prolog and eschew Show. – m_goldberg Apr 28 '14 at 04:18
yes, that sounds like the best route. eschew Show... Gesundheit. – Jens Apr 28 '14 at 04:26
eschew...Gesundheit... +1 for the lol (and nice answer, of course). – ciao Apr 28 '14 at 06:28

Mesh and ParametricPlot

1 Answers1