Re: Re: Re: how fill PolarPlot?

*To*: mathgroup at smc.vnet.net*Subject*: [mg84465] Re: [mg84455] Re: [mg84431] Re: [mg84420] how fill PolarPlot?*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Wed, 26 Dec 2007 05:09:07 -0500 (EST)*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst*References*: <20071224091350.HNWYO.62626.root@eastrmwml30> <200712251128.GAA18408@smc.vnet.net> <BF07250C-54A5-4FB6-BB56-9606455077BD@wolfram.com>*Reply-to*: murray at math.umass.edu

My fault: I didn't find what I was looking for about ColorFunction with PolarPlot on the ColorFunction reference page, and I failed to seek it on the PolarPlot page. But this would probably not have happened had PolarPlot also been mentioned on that ColorFunction page. (Or did I overlook it there?) Brett Champion wrote: > On Dec 25, 2007, at 5:28 AM , Murray Eisenberg wrote: > >> Your response suggests that perhaps it's not possible directly to use >> polar coordinates themselves as arguments to the ColorFunction function. >> >> If so, that's a shame. >> > > From the PolarPlot documentation: > > "The arguments supplied to functions in MeshFunctions and > RegionFunction are x, y, \[Theta], r. Functions in ColorFunction are > by default supplied with scaled versions of these arguments. " > > > You can find examples under PolarPlot > Examples > Options > ColorFunction. > > Brett Champion > Wolfram Research > > > >> Bob Hanlon wrote: >>> 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 >>>> >>> >> >> -- >> 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

**Follow-Ups**:**Re: Re: Re: Re: how fill PolarPlot?***From:*Brett Champion <brettc@wolfram.com>

**References**:**Re: Re: how fill PolarPlot?***From:*Murray Eisenberg <murray@math.umass.edu>