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RE: Polar Grids in Mathematica


Phil,

This is one method using PolarMap from the ComplexMap package:

Needs["Graphics`Graphics`"]
Needs["Graphics`ComplexMap`"]
Needs["Graphics`Colors`"]

plot1 = PolarMap[Identity, {0, 2.5}, {0, 2*Pi}, PlotStyle -> GrayLevel[0.5],
    DisplayFunction -> Identity];
plot2 = PolarPlot[1 - Cos[t], {t, 0, 2*Pi},
    PlotStyle -> {AbsoluteThickness[2], Blue}, DisplayFunction -> Identity];

Show[plot1, plot2, DisplayFunction -> $DisplayFunction, Background -> Linen,
   PlotLabel -> "Cardioid on a Polar Grid", ImageSize -> 500];

Using my DrawingPaper package, available at my web site below it is possible
to obtain a more controlled polar grid with tailored labels.

Needs["Graphics`DrawingPaper`"]

Module[{circles, radii},
 circles = MapThread[DrawPolarR[#1, {t, 0, 2*Pi}] & ,
      {{0.25, 0.5, 1., 1.5, 2., 2.5}}];
 radii = Table[DrawPolar\[Theta][\[Theta], {r, 0.25, 3}], {\[Theta], 0,
2*Pi - Pi/8,
       Pi/8}];
 Show[Graphics[{Blue, AbsoluteThickness[2],
       DrawPolarR[1 - Cos[t], {t, 0, 2*Pi}], GrayLevel[0.5],
       AbsoluteThickness[1], circles, radii,
       Black,
       DrawLineLabels[Sqrt[#1^2 + #2^2] & , 0.5 & , DrawLLTextOptions ->
          {Background -> Gold, TextStyle -> {FontSize -> 10}}][circles],
       DrawLineLabels[ArcTan[#1, #2] & , 0.25 & , DrawLLFormat ->
          (Rationalize[#1/Pi]*Pi & ), DrawLLTextOptions ->
          {Background -> LightBlue, TextStyle -> {FontSize ->
10}}][radii]}],
     AspectRatio -> Automatic, PlotRange -> {{-2.1, 1}, {-1.5, 1.5}},
     Background -> Linen, {Frame -> True, FrameTicks -> None,
      ImageSize -> 500, TextStyle -> {FontSize -> 12, FontWeight -> "Bold"},
      PlotLabel -> "Cardioid on a Polar Grid"}]];

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/


> From: Phil Larson [mailto:PLarson at bju.edu]
To: mathgroup at smc.vnet.net
>
> Does anyone know how to get polar grids for PolarPlot functions? Or
> even semi-log grids? (I can get rectangular grids, of course.)
>



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