Show[] on 3D graphics, rotation by mouse, how to improve performance

*To*: mathgroup at smc.vnet.net*Subject*: [mg108873] Show[] on 3D graphics, rotation by mouse, how to improve performance*From*: "Nasser M. Abbasi" <nma at 12000.org>*Date*: Mon, 5 Apr 2010 08:01:08 -0400 (EDT)*Reply-to*: "Nasser M. Abbasi" <nma at 12000.org>

Hello; This is on XP SP2, M7.0 I noticed that when I have 3D graphics, and then I use the mouse to rotate the image, sometimes Mathematica will pause for longer time, and the rotation is not always smooth. May be I am not doing this the right way. I am visualizing the Z transform in 3D with the unit circle add in. So, I create a Cylinder (to see the unit circle), then do a Plot3D of the magnitude of Z transform, then I use Show[] to display them together. The 3D plots looks fine, but when it comes to rotating the plot generated, one has to be really slow with the mouse, else if I move the mouse fast, _sometimes_ I get strange results. I captured 2 such effects in the following folder: http://12000.org/tmp/zt_040410/ Is there a more "efficient" way for me to do this? Other than Show[], I could not find a way to combine these. Using Epiloge gave me some hard time to make it work, I need to look at it again.... I remember there used to be a function called DisplayTogother[], was going to try it, but it is not there anymore? Any way, here is the code which generated the above 2 results: ClearAll["Global`*"]; sequence = n^2*a^(2*n); zt = ZTransform[sequence, n, z] zt = zt /. z -> {x + I*y}; ztMag = ComplexExpand[Abs[zt]] unitCircle = Graphics3D[Cylinder[{{0, 0, 0}, {0, 0, 0.5}}, 1]]; Show[{Plot3D[ztMag /. a -> 3, {x, -12, 12}, {y, -6, 6}, PlotRange -> {Automatic, Automatic, {-20, 20}}], unitCircle}] ClearAll["Global`*"]; zt = (z^(-1) - z^(-2))/(1 - 2/3/z + 1/3/z^2) zt = zt /. z -> {x + I*y}; ztMag = ComplexExpand[Abs[zt]] unitCircle = Graphics3D[Cylinder[{{0, 0, 0}, {0, 0, 2}}, 1]]; Show[{Plot3D[ztMag, {x, -2, 2}, {y, -2, 2}, PlotRange -> {Automatic, Automatic, {-20, 20}}], unitCircle}] thanks --Nasser