       Re: rotating rings illusion

• To: mathgroup at smc.vnet.net
• Subject: [mg81136] Re: rotating rings illusion
• From: "Margaux" <margaux.izarn at orange.fr>
• Date: Thu, 13 Sep 2007 06:33:23 -0400 (EDT)
• References: <fbar32\$qgu\$1@smc.twtelecom.net> <fbdngs\$pre\$1@smc.twtelecom.net>

```Merci

"Szabolcs" <szhorvat at gmail.com> a écrit dans le message de news:
fbdngs\$pre\$1 at smc.twtelecom.net...
> Imran Akbar wrote:
>> Hi,
>>    i'm just starting to use mathematica...
>>
>> i'm trying to mathematically model the two rotating rings illusion as
>> shown
>> in this video:
>>
>
> I am sure that there are better ways than the following, but this one
> works too ;-)  You did not mention what Mathematica version you are
> using, so I will assume 6.0.
>
>> 1)  how do you create a ring in mathematica?  i found the circle command,
>> but that's only 2d.
>
> torus[radius_: 1, thickness_: 1] :=
>   ParametricPlot3D[
>     {Cos[u] (radius + thickness/2 Cos[v]),
>      Sin[u] (radius + thickness/2 Cos[v]),
>      thickness/2 Sin[v]},
>     {u, 0, 2 Pi}, {v, 0, 2 Pi}]
>
>> 2)  how can I orient each ring so that they're perpendicular to each
>> other?
>
> Get the graphics data from inside the Graphics3D[],
>
> tt = First[torus];
>
> and use Rotate[],
>
> gr = Graphics3D[{Rotate[tt, Pi/2, {1,0,0}], tt}]
>
> BTW the rings on the video you posted are not perpendicular to each other.
>
>> 3)  how do I vary the # of rotations per minute in an animation?
>>
>
> Manipulate[
>  Graphics3D[Rotate[First[gr], j, {1, 1, 1}],
>   PlotRange -> {{-11, 11}, {-11, 11}, {-11, 11}}], {j, 0, 2 Pi}]
>
> Use the interactive animation controls.
>
>> much obliged,
>> imran
>>
>>
>

```

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