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: >> http://video.google.com/videoplay?docid=-3761503348838584940&hl=en >> > > 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[10]]; > > 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 >> >> >