       RE: Polar Grids in Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg28221] RE: [mg28201] Polar Grids in Mathematica
• From: "David Park" <djmp at earthlink.net>
• Date: Thu, 5 Apr 2001 03:00:34 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```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, 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`"]

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,
DrawPolarR[1 - Cos[t], {t, 0, 2*Pi}], GrayLevel[0.5],
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 ->
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

> 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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