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MathGroup Archive 2007

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Re: Re: rotating rings illusion

  • To: mathgroup at smc.vnet.net
  • Subject: [mg80820] Re: [mg80801] Re: [mg80787] rotating rings illusion
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Mon, 3 Sep 2007 06:11:33 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <200709010436.AAA26729@smc.twtelecom.net> <200709020653.CAA25909@smc.twtelecom.net>
  • Reply-to: murray at math.umass.edu

\[Rho] below should be r.  Evidently a change of notation along the way!

Ricardo Samad wrote:
> Dear Imran,
> 
> I have a solution that works in Mathematica 6; first of all, create a torus
> with Radii R and r:
> 
> R = 1;
> r = 0.1;
> 
> torus = ParametricPlot3D[{(R + r Cos[2 \[Pi] u])
>     Cos[2 \[Pi] t], (R + r Cos[2 \[Pi] u]) Sin[2 \[Pi] t],
>    r Sin[2 \[Pi] u]}, {u, 0, 1}, {t, 0, 1}, Mesh -> None]
> 
> then rotate the torus by an angle Theta in the horizontal plane to create
> ring1; rotate ring 1 180 degrees around the vertical axis and translate it
> by the adequate amount in the vertical direction; create a graphic adding
> them (rings):
> 
> \[Theta] = 10 Degree;
> 
> ring1 = Graphics3D[Rotate[torus[[1]], \[Theta], {1, 0, 0}]];
> ring2 = Graphics3D[
>    Translate[
>     Rotate[ring1[[1]], 180 Degree, {0, 0, 1}], {0, 0,
>      2 (R Sin[\[Theta]] + \[Rho])}]];
> rings = Show[{ring1, ring2}, Boxed -> False, SphericalRegion -> True]
> 
> Finally, using manipulate, rotate the graphic "rings"along the vertical
> axis:
> 
> Manipulate[
>  Graphics3D[Rotate[rings[[1]], 2 \[Pi] \[Theta], {0, 0, 1}],
>   Boxed -> False], {\[Theta], 0, 1, 0.02}]
> 
> 
> With the above parametrization, if you change  the variables R, r and Theta,
> the rings will always touch.
> 
> Ricardo Samad
> 
> 
> 
> On 9/1/07, Imran Akbar <imran at sulug.stanford.edu> 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:
>> http://video.google.com/videoplay?docid=-3761503348838584940&hl=en
>>
>> 1)  how do you create a ring in mathematica?  i found the circle command,
>> but that's only 2d.
>> 2)  how can I orient each ring so that they're perpendicular to each
>> other?
>> 3)  how do I vary the # of rotations per minute in an animation?
>>
>> much obliged,
>> imran
>>
>>
>>
> 
> 
> --
> ____________________________________
> Ricardo Elgul Samad
> 
> tel: (+55 11) 3816-9314
> fax: (+55 11) 3816-9315
> 
> Centro de Lasers e Aplica=E7=F5es
> IPEN/CNEN-SP
> AV. Prof. Lineu Prestes 2242
> Cidade Universit=E1ria
> 05508-000
> S=E3o Paulo - SP
> Brazil
> ____________________________________
> 
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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