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 > > > -- ____________________________________ 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 ____________________________________

**Follow-Ups**:**Re: Re: rotating rings illusion***From:*Murray Eisenberg <murray@math.umass.edu>