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PointSize (and shape) frustration

  • To: mathgroup at smc.vnet.net
  • Subject: [mg85881] PointSize (and shape) frustration
  • From: Szabolcs Horvát <szhorvat at gmail.com>
  • Date: Tue, 26 Feb 2008 07:50:18 -0500 (EST)
  • Organization: University of Bergen

While Mathematica 6 can display beautiful graphics on screen compared to 
previous versions, graphics export became extremely frustrating and buggy.

I complained about several issues before, now here's one more:

I am trying to plot the bifurcation diagram for the logistic map, point 
by point.  The point size needs to be tuned precisely to get a nice plot 
(for print).  Mathematica refuses to export *circular* points to PDF/EPS 
below a certain size, but in this case I can live with that.  However, 
Mathematica refuses to draw points below a certain size, no matter what 
the value of PointSize or AbsolutePointSize is!!  If the points overlap, 
the plot is completely ruined.

Then I tried using Disk[]s instead of points.  On screen it looks fine, 
but when exported to PDF, Mathematica does something very strange, and 
the result doesn't even have the disks any more!  Instead there are some 
little crosses on a *regular* grid, approximating the shape of the plot.

I *know* that 30000 points can inflate the file size, and I know that 
arbitrarily small points are not printable/displayable, but I can solve 
these problems on my own.  I don't want Mathematica to try to be smart 
and make its own decisions about this, because it will just cause trouble.

Here's the code to experiment with (I know that it doesn't produce a 
precise result):

lm[r_] := NestList[r # (1 - #) &, .5, 50000]

bif = Join @@ Table[
     {r, #} & /@
      Union[Take[lm[r], -100], SameTest -> (Abs[#1 - #2] < 1*^-3 &)],
     {r, 2.0, 3.98, .001}
     ];

plot = ListPlot[bif, PlotRange -> All, PlotStyle -> AbsolutePointSize[.05]]

plot = Graphics[{PointSize[.0001], Point[bif]}]

plot = Graphics[Disk[#, 1/1000] & /@ bif]

Now try exporting each of these plots at reasonable sizes (i.e. not half 
a metre).  Remember that exporting PDFs at different sizes only works as 
Export["plot.pdf", Show[plot, ImageSize -> someValue]] because Export is 
buggy and does not respect the ImageSize options for PDFs!


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