Re: how fill PolarPlot?

• To: mathgroup at smc.vnet.net
• Subject: [mg84446] Re: [mg84420] how fill PolarPlot?
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Mon, 24 Dec 2007 04:51:40 -0500 (EST)

```Because Prolog needs a list of graphics primitives. Use

PolarPlot[Cos[2 theta], {theta, 0, 2 Pi}, PlotStyle -> Red,
Prolog ->
RegionPlot[(x^2 + y^2)^(3/2) <= x^2 - y^2, {x, 0, 1}, {y, -1/2,
1/2}][[1]]]

Bob Hanlon

---- Murray Eisenberg <murray at math.umass.edu> wrote:
> Yes, that does it, thank you.  But I'm still puzzled as to why I cannot
> use the Prolog as I gave it to do the filled right-hand leaf.
>
> Bob Hanlon wrote:
> > Show[{
> >   RegionPlot[(x^2 + y^2)^(1/2) <= Cos[2 ArcTan[y/x]],
> >    {x, 0, 1}, {y, -1/2, 1/2}],
> >   PolarPlot[Cos[2 theta], {theta, 0, 2 Pi},
> >    PlotStyle -> Red]},
> >  PlotRange -> All]
> >
> > Show[{
> >   RegionPlot[(x^2 + y^2)^(3/2) <= x^2 - y^2,
> >    {x, 0, 1}, {y, -1/2, 1/2}],
> >   PolarPlot[Cos[2 theta], {theta, 0, 2 Pi},
> >    PlotStyle -> Red]},
> >  PlotRange -> All]
> >
> >
> > Bob Hanlon
> >
> > ---- Murray Eisenberg <murray at math.umass.edu> 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
> >>
> >
>
> --
> 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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