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Re: Re: how fill PolarPlot?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg84454] Re: [mg84431] Re: [mg84420] how fill PolarPlot?
*From*: Bob Hanlon <hanlonr at cox.net>
*Date*: Tue, 25 Dec 2007 06:27:34 -0500 (EST)
*Reply-to*: hanlonr at cox.net
PolarPlot[Cos[2 theta], {theta, 0, 2 Pi},
ColorFunction ->
Function[{x, y}, If[-Pi/4 <= ArcTan[x, y] <= Pi/4, Red, Blue]],
ColorFunctionScaling -> False]
Bob Hanlon
---- Murray Eisenberg <murray at math.umass.edu> wrote:
> I was finally able to do this with Epilog->{Inset[RegionPlot[...]]}.
>
> Below is the entire code for the embellished plot I wanted. I am still
> unhappy with at the amount of work I had to do in order to adjust the
> ImageSize of the filled leaf and the thickness of its boundary so as to
> cover up the underlying blue boundary of that leaf from the PolarPlot.
>
> Some of that adjustment could probably be avoided by using a
> ColorFunction for the overall POlarPlot. But how does one set up
> ColorFunction for PolarPlot so as to specify using, say, one color for
> part of the plot and another for another part, depending on the value of
> theta alone?
>
> I found no example of ColorFunction in the documentation. I tried, e.g.,
>
> PolarPlot[Cos[2 theta], {theta, 0, 2 Pi},
> ColorFunction ->
> Function[{theta,r}, If[-Pi/4 <= theta <= Pi/4, Red, Black]]]
>
> but that doesn't work as expected.
>
> The finished figure's code:
>
> txt[t_,{x_,y_}]:=Style[Text[t,{x,y}],FontSize->30,FontWeight->Bold]
> {xmin,xmax}={-1.425,1.425}; {ymin,ymax}={-1.25,1.25};
>
> PolarPlot[Cos[2t],{t,0,2Pi}, PlotRange->{{xmin,xmax},{ymin,ymax}},
> PlotStyle->{ColorData["Legacy","SteelBlue"], Thickness[0.007]},
> Ticks->None,
>
> Epilog->{
> Inset[RegionPlot[(x^2+y^2)^(3/2)<=x^2-y^2,{x,-0.02,1},{y,-1,1},
> PlotStyle->ColorData["HTML","Gold"],
> BoundaryStyle->Directive[Thickness[0.025],
> ColorData["Legacy","CadmiumOrange"]],
> Frame->False,AspectRatio->Automatic,
> ImageSize->2.6*72],
> {0.5,0}],
> Black,Thick,Dashing[{0.045,0.03}],
> Line[{{0,0},{0.85,0.85}}],Line[{{0,0},{0.85,-0.85}}],
> Dashing[{}],Thick,
> Arrow[{{xmin,0},{xmax,0}}],Arrow[{{0,ymin},{0,ymax}}],
> txt[TraditionalForm[HoldForm[r==cos 2t ]],{-0.6,1.0}],
> txt[TraditionalForm[HoldForm[t==Pi/4]],{1.125,0.925}],
> txt[TraditionalForm[HoldForm[t==-Pi/4]],{1.125,-0.99}]
> },
> ImageSize->7*72]
>
> 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
>
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