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Re: rotating rings illusion
*To*: mathgroup at smc.vnet.net
*Subject*: [mg80801] Re: [mg80787] rotating rings illusion
*From*: "Ricardo Samad" <resamad at gmail.com>
*Date*: Sun, 2 Sep 2007 02:53:56 -0400 (EDT)
*References*: <200709010436.AAA26729@smc.twtelecom.net>
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
>
>
>
--
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Ricardo Elgul Samad
tel: (+55 11) 3816-9314
fax: (+55 11) 3816-9315
Centro de Lasers e Aplica=E7=F5es
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S=E3o Paulo - SP
Brazil
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