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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: [mg81631] Re: Flat colour in RegionPlot; millions of little triangles
  • From: "Steve Luttrell" <steve at _removemefirst_luttrell.org.uk>
  • Date: Sat, 29 Sep 2007 06:36:59 -0400 (EDT)
  • References: <fdkqst$7bk$1@smc.vnet.net>

You can use Mathematica to automatically delete all of the polygons used to 
simulate the fill.

This creates the raw graphic.

g = RegionPlot[
  Abs[Nest[(#^2 + x + I y) &, x + I y, 16]] < 2, {x, -2, 1}, {y, -1.5,
    1.5}]

This filters the graphic to remove all of the polygons.

g2 = g /. {Polygon[__] -> {}}

If you want to look at the expression that Mathematica uses to represent a 
graphic (or anything else) then wrap it in FullForm. Thus FullForm[g] will 
show the expression with all of the polygons present, and FullForm[g2] will 
show the filtered version of the expression without polygons.

-- 
Steve Luttrell
West Malvern, UK


"Will Robertson" <wspr81 at gmail.com> wrote in message 
news:fdkqst$7bk$1 at smc.vnet.net...
> Hello,
>
> 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.
>
> Is there a way to replicate this process within Mathematica itself
> before I output to PDF? I am loath to perform this task manually in
> Inkscape every time I generate an image.
>
> Many thanks,
> Will Robertson
>
> 



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