Using transparency in ContourPlot makes mesh visible

Question

I am trying to use a ColorFunction with Opacity in ContourPlot. Here's my code:

data = RandomVariate[BinormalDistribution[.75], 10];
d = SmoothKernelDistribution[data];
cf[z_] := {Opacity[z], Red};
sc1 = ContourPlot[
   Evaluate@PDF[d, {x, y}], {x, -3, 3}, {y, -3, 3}, 
   PlotRange -> All, PlotPoints -> 50, ColorFunction -> cf, 
   ColorFunctionScaling -> True]

And here's what it produces:

enter image description here

How can the ugly mesh be avoided? I am using Mathematica 8.0.1 in OS X.

does Mesh -> None give what you need? Btw, I don't get the "ugly mesh" with Version 9 on Windows Vista 64 bit. — kglr, Feb 28 '13 at 20:34
Mesh -> None is not a legal option for ContourPlot for me. I am using Mathematica 8.0.1 for OS X. — Guillochon, Feb 28 '13 at 20:37
@belisarius It is a duplicate, but not of that question. Check here: http://mathematica.stackexchange.com/q/1400/12 Mike also gave the solution. I think this is Mac specific. @Guillochon -- if you're on OS X, can you tag this question with osx? — Szabolcs, Feb 28 '13 at 20:53
Perfectly fine with closing it, but opacity never explicitly appeared in that question, which is when this issue arises. — Guillochon, Feb 28 '13 at 20:54
@Szabolcs I knew that was out there somewhere. I had the method written down in my "scrapbook" of tips and tricks but not the source. — Mike Honeychurch, Feb 28 '13 at 20:56
As above, what platform are you on? Can you please include that information. — Mike Honeychurch, Feb 28 '13 at 21:05
One observation: none of the solutions so far work when you export the plot to pdf format (although they do work in the notebook - depending on platform as was stated). — Jens, Mar 01 '13 at 01:26
That's OK, running rasterizeBackground (from here) on the result works well — Guillochon, Mar 01 '13 at 02:47

Mike Honeychurch · Accepted Answer · 2013-02-28T21:11:02.913

10

If you are using OS X the use undocumented Method -> {"TransparentPolygonMesh" -> True}

enter image description here

edited Feb 28 '13 at 21:11

answered Feb 28 '13 at 20:52

Mike Honeychurch

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Well, it doesn't solve the problem here – Dr. belisarius Feb 28 '13 at 20:57
How do you mean? Am I misreading the question? I thought he wanted the mesh to go (??) – Mike Honeychurch Feb 28 '13 at 20:59
In my machine the mesh disappears with Style[sc1, Antialiasing -> False] but not with this solution. Probably version/platform dependent – Dr. belisarius Feb 28 '13 at 21:01
@belisarius Yes, the problem is Mac-specific. – Szabolcs Feb 28 '13 at 21:02
@Szabolcs I'm on Windows, and I have the same problem. The solution is Mac-specific :) – Dr. belisarius Feb 28 '13 at 21:03
@belisarius Did you change your default options to include antialiasing? I don't see any problem on Windows: Mathematica graphics – Szabolcs Feb 28 '13 at 21:04
@Szabolcs The antialiasing option hasn't a "reset to default" here, so it's difficult to know – Dr. belisarius Feb 28 '13 at 21:06
@belisarius To be more specific, here on Windows sc1 looks fine and has anitaliasing. Style[sc1, Antialiasing -> True] has the artefact, and has antialiasing. Style[sc1, Antialiasing -> False] doesn't have the artefact and doesn't have antialiasing. – Szabolcs Feb 28 '13 at 21:07
@MikeHoneychurch Done – Dr. belisarius Feb 28 '13 at 21:12
If you'd like to export antialiased bitmap graphics, but run into this problem, here's a way: http://mathematica.stackexchange.com/questions/198/antialiasing-in-3d And here's what I got: http://i.stack.imgur.com/lkl25.png Unfortunately the ticks are made very subtle. – Szabolcs Mar 01 '13 at 00:46

score 3 · Answer 2 · answered Feb 28 '13 at 21:00

3

Since you are looking at a PDF, I would use SmoothDensityHistogram to plot it, instead.

data = RandomVariate[BinormalDistribution[.75], 10];
d = SmoothKernelDistribution[data];
cf[z_] := {Opacity[z], Red};

sc1 = SmoothDensityHistogram[data , Automatic, "PDF", 
  PlotRange -> All, ColorFunction -> cf, Mesh -> 10, 
  MeshStyle -> Directive[Opacity[0.5], Black]]

enter image description here

By default, in this case, it was not displaying the contours, so I added them via Mesh and MeshStyle. Modify to taste.

answered Feb 28 '13 at 21:00

rcollyer

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I looked at this as an option, but the problem was not being able to get flat shading between the contours. – Guillochon Feb 28 '13 at 21:01
@Guillochon, why do you want the flat shading they don't truly represent the function? – s0rce Feb 28 '13 at 21:02
2

It's a stylistic choice, the smooth coloring is hard to see, and is harder to notice when printed to paper. – Guillochon Feb 28 '13 at 21:15

score 3 · Answer 3 · answered Feb 28 '13 at 21:12

3

Just for behavior documentation. Mathematica 8.0 on WinXP.

GraphicsRow[Style[sc1, Antialiasing -> #] & /@ {True, False}]

Mathematica graphics

answered Feb 28 '13 at 21:12

Dr. belisarius

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When I tested this on Windows 7, sc1 without any antialiasing option produced an antialiased graphic without a visible mesh. (I.e. when not specifying Antialiasing at all, the problem didn't appear.) – Szabolcs Feb 28 '13 at 21:51
I get the same with mma 9.0.0 win7 64 bit http://i.stack.imgur.com/f9um4.png – Ajasja Feb 28 '13 at 21:57
@Szabolcs So it's definitely due to a change in defaults. I think specifying the Antialiasing makes the results portable – Dr. belisarius Feb 28 '13 at 21:58
@Ajasja Try including Automatic too in the list of options, not just True and False. This is what I got with Automatic: http://i.stack.imgur.com/Vtpi1.png – Szabolcs Mar 01 '13 at 00:24
I have to comment on this again, because it's misleading: on all Windows systems I tried, there's no problem with the mesh if you don't use any anti-aliasing setting at all. A fair example would show Antialiasing -> Automatic as well. This example prevented the original question from being closed as a duplicate even though it really should be. It's a Mac OS X specific issue which is solved by the suggestion in the accepted answer. – Szabolcs Apr 04 '13 at 14:09
@Szabolcs This is a cooperatively edited site. Please feel free to update my answer if you feel it's misleading. – Dr. belisarius Apr 04 '13 at 14:15
@belisarius I'd have to wait until I get to my office where we have a Windows machine, so it's a bit troublesome ... do you get the mesh with Antialiasing -> Automatic? – Szabolcs Apr 04 '13 at 14:16
@Szabolcs Nope. – Dr. belisarius Apr 04 '13 at 14:19
It seems that there's no issue on Windows then, in the sense that the default settings (Antialiasing -> Automatic) do not produce a visible mesh. On OS X there's still a mesh with Antialiasing -> False. The only solution seems to be Show[..., Method -> {"TransparentPolygonMesh" -> True}]. Do you think we could close this as a duplicate of this one? (My close vote is already expired.) – Szabolcs Apr 04 '13 at 14:24
@Szabolcs Ok. I can't vote bc JM already marked it as dup – Dr. belisarius Apr 04 '13 at 14:28

Using transparency in ContourPlot makes mesh visible

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