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Re: how fill PolarPlot?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg84444] Re: [mg84420] how fill PolarPlot?
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Mon, 24 Dec 2007 04:50:37 -0500 (EST)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <200712230934.EAA03990@smc.vnet.net> <67371FD7-F63D-4CB0-9D5C-7017815C5BD7@mimuw.edu.pl>
  • Reply-to: murray at math.umass.edu

That does not show the entire four-leaved rose together with a shaded 
leaf in the right half-plane.

What I'm seeing is a shaded leaf in the right half-plane along with 
shaded pieces of the top and bottom leaves that stick into the right 
half-plane and are within the top and bottom boundaries of the 
right-hand leaf.

Andrzej Kozlowski wrote:
> 
> On 23 Dec 2007, at 18:34, Murray Eisenberg wrote:
> 
>> I Mathematica 6 I have a PolarPlot, e.g., a 4-leaved rose:
>>
>>   PolarPlot[Cos[2 theta], {theta, 0, 2 Pi}]
>>
>> How can I fill the inside -- or, what I really want, just the leaf in
>> the right half-plane -- with some color?
>>
>> I note that Filling does not seem to be an option for PolarPlot (or for
>> what would be almost as good, ParametricPlot).
>>
>> I tried including the following (obtained by converting from :
>>
>>   Prolog->RegionPlot[(x^2 + y^2)^(3/2) <= x^2-y^2, {x,-0.02,1},{y,-1,1},
>>       Frame->False, AspectRatio->Automatic]
>>
>> However, that led to a mysterious error message:
>>
>>   $Aborted is not a Graphics primitive or directive.
>>
>> (Perhaps because of an incompatibility of a Prolog with cartesian
>> coordinates inside a polar coordinate plot??)
>>
>> -- 
>> Murray Eisenberg                     murray at math.umass.edu
>> Mathematics & Statistics Dept.
>> Lederle Graduate Research Tower      phone 413 549-1020 (H)
>> University of Massachusetts                413 545-2859 (W)
>> 710 North Pleasant Street            fax   413 545-1801
>> Amherst, MA 01003-9305
>>
> 
> 
> How about simply:
> 
> 
> s1 = PolarPlot[Cos[2 theta], {theta, -Pi/4, Pi/4}] /. Line -> Polygon;
> s2 = PolarPlot[Cos[2 theta], {theta, Pi/2, Pi/2 + Pi/4}] /. Line -> 
> Polygon;
> s3 = PolarPlot[Cos[2 theta], {theta, 3 Pi/2 - Pi/4, 3 Pi/2}] /.Line -> 
> Polygon;
> 
> Show[ss, s1, s2, s3]
> 
> 
> Andrzej Kozlowski
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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