       Re: how fill PolarPlot?

• To: mathgroup at smc.vnet.net
• Subject: [mg84439] Re: [mg84420] how fill PolarPlot?
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Mon, 24 Dec 2007 04:47:56 -0500 (EST)

```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
>

```

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