Re: rotating rings illusion

*To*: mathgroup at smc.vnet.net*Subject*: [mg80811] Re: rotating rings illusion*From*: Szabolcs <szhorvat at gmail.com>*Date*: Sun, 2 Sep 2007 02:59:07 -0400 (EDT)*Organization*: University of Bergen*References*: <fbar32$qgu$1@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 > >