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Re: .eps file in MATHEMATICA

  • To: mathgroup at smc.vnet.net
  • Subject: [mg105920] Re: [mg105862] .eps file in MATHEMATICA
  • From: Patrick Scheibe <pscheibe at trm.uni-leipzig.de>
  • Date: Sat, 26 Dec 2009 19:06:20 -0500 (EST)
  • References: <200912220905.EAA16678@smc.vnet.net>

Hi,

this happens since RegionPlot does not draw one region but divides the
region to scan into smaller ones and draws polygons for every small area
which fullfils your region-inequality.

I assume your weird patterns look like these

RegionPlot[Abs[Nest[#1^2 + x + I*y & , x + I*y, 8]] < 2, 
     {x, -2, 1}, {y, -1.5, 1.5}, Mesh -> All, PlotPoints -> 5, 
     MaxRecursion -> 5, Frame -> False]

?

The problem is to force Mathematica to really plot only one region. It
is (always?) a composition of many polygons even if you (in the case of
a region plot) are only interested in one region.

Here is a quick hack.
Try to export the graphics p1 and p2 to eps and compare the drawing
speed (takes a few seconds to calculate):

p1 = RegionPlot[Abs[Nest[#1^2 + x + I*y & , x + I*y, 8]] < 2, 
     {x, -2, 1}, {y, -1.5, 1.5},  PlotPoints -> 30, 
     MaxRecursion -> 7, Frame -> False, 
  BoundaryStyle -> {Darker[Blue]}, PlotStyle -> Darker[Blue]]

p2 = RegionPlot[Abs[Nest[#1^2 + x + I*y & , x + I*y, 8]] < 2, 
      {x, -2, 1}, {y, -1.5, 1.5},  PlotPoints -> 30, 
      MaxRecursion -> 7, Frame -> False, 
   BoundaryStyle -> {Darker[Blue]}, PlotStyle -> None] /. 
  Line[pts__] :> Polygon[pts]

Cheers
Patrick


On Tue, 2009-12-22 at 04:05 -0500, Andong He wrote:
> I created an .eps plot using MATHEMATICA, and wanna add it into my .pdf file. The plot has a rigion filled using command "RegionPlot" in MATHEMATICA. The picture looks fine in MATHEMATICA and PHOTOSHOP, but when I insert into a .tex file and generate a .pdf file, the filled region shows weird pattern of grids and diagonal lines. 
> 
> How does that happen? Thanks
> 



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