Exporting a dashed plot with a color gradient to a vector graphics format ruins the dashing

Question

When exporting a dashed plot with a color gradient to a vector graphics format such as EPS or PDF, the dashing is partly ruined. For example, this command:

Plot[x^2, {x, -2, 2}, PlotStyle -> Directive[Dashed, Thick], ColorFunction -> Hue]

Creates the following plot:

However, when exporting the plot to EPS or PDF, I get this plot (notice the ruined dashing, especially near the vertex of the parabola):

• Am I doing something wrong, or is this a bug?
• If it is a bug, is there a workaround?

I am using Mathematica version 8.0.4.0 (edit: on Win7 64bit)

Edit: I got an email from wolfram support, which I understand confirms this is a bug. Until they fix it, any workarounds which properly export the plot as vector graphics are welcome.

Answer 1

The VertexColors that get introduced when a ColorFunction is specified are not rendered smoothly in the exported PDF - no matter what other options (such as Dashed) you specify. So we really have two problems here. Bad color gradients along the line, and incorrect computation of the dash spacing.

If you don't care too much about the bad color gradients and just want a plot with an acceptable dashing, you could do something like this:

Show[#,
   Graphics[{Thickness[.01], White, Dashing[{.02, .04}], 
     Cases[Normal@#[[1]], Line[_], Infinity]}]] &@
 Plot[x^2, {x, -2, 2}, PlotStyle -> Thickness[.008], 
  ColorFunction -> Hue]

Here I have taken your original Plot and initially removed the dashing. Before showing this plot, I extract from it the Line that was produced, re-draw it a second time with dashing and slightly larger thickness at the background color (White).

Finally, I place the dashed white line on top of the continuous colored line to get the appearance of a dashed colored line. For this to look correct in the exported PDF, you have to play with the Dashing and Thickness manually.

The dashing in the export will look different from the notebook. In particular, the second number in Dashing[{0.02,0.04}] must always be bigger than the first, or else you don't see anything!

Here is what the exported PDF looks like with the above command:

If you do care about the bad color gradients in addition to the dashing, then I would suggest going with bitmap export right now because it would take a bitmap-based hack to get smooth color gradients in the PDF anyway.

Answer 2

The wrong dashing goes away if you use the following rule, which I found in this MathGroup post by Jens, as a hint to downsize the pdf-size and to eliminate the spurious edges coming up with saved DensityPlots, ParametricPlot3D etc. The setting is:

rasterProlog={{EdgeForm[], Texture[{{0, 0, 0, 0}}], 
  Polygon[{{0, 0}, {1, 0}, {1, 1}}, 
   VertexTextureCoordinates -> {{0, 0}, {1, 0}, {1, 1}}]}}

All one has to do to write: pl = Plot[..., Prolog -> rasterProlog] and then Export.

Export[filename, Show[pl, Prolog->rasterProlog] works as well, if you don't want to include the Prolog in Plot, DensityPlot, etc.