Re: Re: Re: how fill PolarPlot?

*To*: mathgroup at smc.vnet.net*Subject*: [mg84463] Re: [mg84455] Re: [mg84431] Re: [mg84420] how fill PolarPlot?*From*: Brett Champion <brettc at wolfram.com>*Date*: Wed, 26 Dec 2007 05:08:04 -0500 (EST)*References*: <20071224091350.HNWYO.62626.root@eastrmwml30> <200712251128.GAA18408@smc.vnet.net>

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

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