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
- References:
- Re: rotating rings illusion
- From: "Ricardo Samad" <resamad@gmail.com>
- Re: rotating rings illusion