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MathGroup Archive 2007

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Re: Flat colour in RegionPlot; millions of little triangles

  • To: mathgroup at smc.vnet.net
  • Subject: [mg81622] Re: Flat colour in RegionPlot; millions of little triangles
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Sat, 29 Sep 2007 06:25:21 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <fdkqst$7bk$1@smc.vnet.net>

Will Robertson wrote:

> I'm creating a bunch RegionPlot figures at the moment and I'm a little
> concerned by the algorithm Mathematica uses to save the figure.
> Consider something like this, adapted from the RegionPlot help:
> 
> RegionPlot[
>  Abs[Nest[(#^2 + x + I y) &, x + I y, 16]] < 2, {x, -2, 1}, {y, -1.5,
> 1.5}]
> Export["region-plot.svg", %];
> 
> (I've chosen SVG just so I can open the image in Inkscape. The effect
> is visible in EPS and PDF images as well.)
> 
> The resulting image is a funny shape that consists of millions (I
> exaggerate) of polygons that fill the region, obviously corresponding
> to the mesh used in Mathematica to create the region. However, it also
> creates a grey outline that is a *single* graphic object that is
> otherwise transparent.
> 
> In Inkscape, I can delete *all* of the polygons and apply a fill
> colour to the single graphic object that defines the outline. This
> reduces the complexity and file size of the image by orders of
> magnitude with the same (or better!) output quality.

<snip>

Could you be more precise about the size of the exported files (before 
and after manual fixing) and about what size you expect and deem as 
reasonable? I am asking because when I tried the following code on my 
system (Windows XP SP2, Mathematica 6.0.1), the exported file (in PDF 
format since I do not have Inkscape) is about 40 KB, size that does not 
look that huge. However, it is possible that the resulting file size is 
dependent of the platform used (Windows, Linux, Mao).

In[1]:= RegionPlot[
  Abs[Nest[(#^2 + x + I y) &, x + I y, 16]] < 2, {x, -2, 1}, {y, -1.5,
   1.5}]
Export["region-plot.pdf", %];

[... graphic deleted ... file is about 40 KB]

In[3]:= $Version

Out[3]= "6.0 for Microsoft Windows (32-bit) (June 19, 2007)"

You can get the file at

http://homepages.nyu.edu/~jmg336/mathematica/region-plot.pdf

Regards,
-- 
Jean-Marc


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