Re: how fill PolarPlot?

*To*: mathgroup at smc.vnet.net*Subject*: [mg84450] Re: how fill PolarPlot?*From*: m.r at inbox.ru*Date*: Tue, 25 Dec 2007 06:25:23 -0500 (EST)*References*: <200712230934.EAA03990@smc.vnet.net> <fknv4f$62o$1@smc.vnet.net>

RegionPlot by default has PlotRange -> Full, so the x range is 1.02 and the inset with width 1.02 will be aligned exactly: PolarPlot[Cos[2 t], {t, 0, 2 Pi}, PlotStyle -> Green, Epilog -> Inset[RegionPlot[(x^2 + y^2)^(3/2) <= x^2 - y^2, {x, -0.02, 1}, {y, -1, 1}, AspectRatio -> Automatic, Frame -> False, PlotRangePadding -> 0], {0, 0}, {0, 0}, 1.02]] Also you can simply extract the graphics primitives from RegionPlot: PolarPlot[Cos[2 t], {t, 0, 2 Pi}, PlotStyle -> Green, Epilog -> First@ RegionPlot[(x^2 + y^2)^(3/2) <= x^2 - y^2, {x, -0.02, 1}, {y, -1, 1}]] Maxim Rytin m.r at inbox.ru On Dec 24, 3:45=A0am, Murray Eisenberg <mur... 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. =A0I 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. =A0But 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. =A0I tried, e.g.= , > > =A0 PolarPlot[Cos[2 theta], {theta, 0, 2 Pi}, > =A0 =A0 ColorFunction -> > =A0 =A0 =A0 Function[{theta,r}, If[-Pi/4 <= theta <= Pi/4, Red, Black]= ]] > > but that doesn't work as expected. > > The finished figure's code: > > =A0 =A0txt[t_,{x_,y_}]:=Style[Text[t,{x,y}],FontSize->30,FontWeight->Bol= d] > =A0 =A0{xmin,xmax}={-1.425,1.425}; {ymin,ymax}={-1.25,1.25}; > > =A0 =A0PolarPlot[Cos[2t],{t,0,2Pi}, PlotRange->{{xmin,xmax},{ymin,ymax}}, > =A0 =A0 =A0PlotStyle->{ColorData["Legacy","SteelBlue"], Thickness[0.007]},= > =A0 =A0 =A0Ticks->None, > > =A0 =A0 =A0Epilog->{ > =A0 =A0 =A0 =A0Inset[RegionPlot[(x^2+y^2)^(3/2)<=x^2-y^2,{x,-0.02,1},{y,= -1,1}, > =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0PlotStyle->ColorData["HTML","Gold"], > =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0BoundaryStyle->Directive[Thickness[0.025], > =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0ColorData["Legacy","CadmiumOrange"]], > =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0Frame->False,AspectRatio->Automatic, > =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0ImageSize->2.6*72], > =A0 =A0 =A0 =A0 =A0 {0.5,0}], > =A0 =A0 =A0 =A0 Black,Thick,Dashing[{0.045,0.03}], > =A0 =A0 =A0 =A0 Line[{{0,0},{0.85,0.85}}],Line[{{0,0},{0.85,-0.85}}], > =A0 =A0 =A0 =A0 Dashing[{}],Thick, > =A0 =A0 =A0 =A0 Arrow[{{xmin,0},{xmax,0}}],Arrow[{{0,ymin},{0,ymax}}], > =A0 =A0 =A0 =A0 txt[TraditionalForm[HoldForm[r==cos 2t ]],{-0.6,1.0}],= > =A0 =A0 =A0 =A0 txt[TraditionalForm[HoldForm[t==Pi/4]],{1.125,0.925}],= > =A0 =A0 =A0 =A0 txt[TraditionalForm[HoldForm[t==-Pi/4]],{1.125,-0.99}]= > =A0 =A0 =A0}, > =A0 =A0ImageSize->7*72] > > > > Murray Eisenberg wrote: > > I Mathematica 6 I have a PolarPlot, e.g., a 4-leaved rose: > > > =A0 =A0PolarPlot[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 : > > > =A0 =A0Prolog->RegionPlot[(x^2 + y^2)^(3/2) <= x^2-y^2, {x,-0.02,1},{y= ,-1,1}, > > =A0 =A0 =A0 =A0Frame->False, AspectRatio->Automatic] > > > However, that led to a mysterious error message: > > > =A0 =A0$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 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 mur... at math.umass= .edu > Mathematics & Statistics Dept. > Lederle Graduate Research Tower =A0 =A0 =A0phone 413 549-1020 (H) > University of Massachusetts =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0413 545-2859 (W= ) > 710 North Pleasant Street =A0 =A0 =A0 =A0 =A0 =A0fax =A0 413 545-1801 > Amherst, MA 01003-9305

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