Displaying cylinders

*To*: mathgroup at smc.vnet.net*Subject*: [mg110831] Displaying cylinders*From*: "S. B. Gray" <stevebg at ROADRUNNER.COM>*Date*: Thu, 8 Jul 2010 03:13:56 -0400 (EDT)*Reply-to*: stevebg at ROADRUNNER.COM

I have displays like this: th = .01; cp1 = { 1, -1, 2}; cp2 = { 2, 0, 1}; cp3 = {-1, 3, 2}; Graphics3D[{Opacity[.4], Yellow, Cylinder[{cp1, cp1 + {th, -th, th}}, 12], Green, Cylinder[{cp2, cp2 - {th, th, -th}}, 15], Red, Cylinder[{cp3, cp3 + {-th, -th, -th}}, 12]}, Boxed -> False] but the cylinders are stand-ins for what I really want, which is circles in 3D. (I would like a 3D circle primitive with circles defined by three points, rather than the way cylinders are specified.) The smallest number of circles in the actual application is 20, so it is almost impossible to see how they interact, no matter what Opacity is set to. It would be much better if I could make the edges thicker and opaque (with EdgeForm), and have the cylinder ends or sides transparent. That way the edges (rings or circles) would occlude each other so it would be clear what is in front of what. So far as I know, the edges cannot be contolled separately. If you set "th" to a higher value, you get a double ring which is really the cylinder side, which also cannot be given its own Opacity. I've tried parametric plot to display thick torii, but it's glacially slow. Any tips will be appreciated. Steve Gray