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Re: How to rotate a PolarPlot?

• To: mathgroup at smc.vnet.net
• Subject: [mg58008] Re: [mg57982] How to rotate a PolarPlot?
• From: Selwyn Hollis <sh2.7183 at earthlink.net>
• Date: Thu, 16 Jun 2005 05:36:18 -0400 (EDT)
• References: <200506150958.FAA29769@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

On Jun 15, 2005, at 5:58 AM, paul at selfreferral.com wrote:

> Hi All,
>
> Would appreciate some help with this. I would like to know how I can
> rotate the following plot to an arbitrary angle:
>
> PolarPlot[Exp[.2t], {t, 0, 8p}, PlotStyle -> Red,
>   PlotRange -> All, AspectRatio -> Automatic, Ticks -> None]
>
> Thanks
> Paul
>

Paul,

First define the rotation matrix, corresponding to ccw rotations  
through Euler angles psi, phi, theta around the z, x, and z axes,  
respectively:

  rot[psi_, phi_, theta_] =
    {{Cos[theta], -Sin[theta], 0}, {Sin[theta], Cos[theta], 0}, {0,  
0, 1}}.
    {{1, 0, 0}, {0, Cos[phi], -Sin[phi]}, {0, Sin[phi], Cos[phi]}}.
    {{Cos[psi], -Sin[psi], 0}, {Sin[psi], Cos[psi], 0}, {0, 0, 1}}

Now define

   show3DRot[plot2D_, {psi_, phi_, theta_}, opts___] :=
        Show[ Graphics3D[ First[ plot2D /.
                {{x_Real, y_Real} -> rot[theta, phi, psi].{x, y,  
0}} ] ], opts]

Then, for example,

   grf = PolarPlot[Exp[.2t], {t, 0, 8Pi}, PlotStyle -> Red]

   show3DRot[ grf, {Pi/2, Pi/3, Pi/4}, PlotRange -> All]


----------------

Selwyn Hollis
http://www.appliedsymbols.com

• References:
  • How to rotate a PolarPlot?
    • From: paul@selfreferral.com