RE: Polar(List)DensityPlot

• To: mathgroup at smc.vnet.net
• Subject: [mg21298] RE: [mg21273] Polar(List)DensityPlot
• From: "Ersek, Ted R" <ErsekTR at navair.navy.mil>
• Date: Wed, 22 Dec 1999 00:34:50 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Wilfred Meyboom
asked how to make a PolarDensityPlot.
-------------------------

A few weeks ago I thought about writing a package that would do this with
all the options you could want and everything. I decided not to because it
would be a non-trivial effort, and I don't personally have a need for it.

Any way the lines below will make a very nice PolarDensityPlot, except I
don't include the Ticks, for the following case.

PolarDensityPlot[3*theta+1/(0.2+r),{theta, 0, 2 Pi}, {r,0,2}]

--------------------------
You can see that I use DensityPlot with a rectangular to polar
transformation. Also 'mask' paints white space over the part outside the
desired circle. I find DensityPlot needs a very high setting for PlotPoints
to get a nice graphic.

gr=Graphics[DensityPlot[
Sin[3 ArcTan[x,y]]+1/(0.2+Sqrt[x^2+y^2]),
{x,-2,2},{y,-2,2}, PlotPoints->250, Mesh->False,
ColorFunction->Hue, Frame->False, DisplayFunction->Identity
]
];

Polygon[
Join[
Table[{2 Cos[t],2 Sin[t]},{t,0,2*Pi,0.017}],
{{2,0},{50,0},{50,50},{-50,50},{-50,-50},
{50,-50},{50,0}
}
]
]
}];

DisplayFunction->\$DisplayFunction,
PlotRange->{{-2,2},{-2,2}}
];

--------------------
Regards,
Ted Ersek

On 12-18-99 Mathematica tips, tricks at
http://www.dot.net.au/~elisha/ersek/Tricks.html
had a major update

```

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