Re: Re: Fast interactive graphics

*To*: mathgroup at smc.vnet.net*Subject*: [mg78023] Re: [mg77946] Re: Fast interactive graphics*From*: DrMajorBob <drmajorbob at bigfoot.com>*Date*: Thu, 21 Jun 2007 05:52:47 -0400 (EDT)*References*: <f58d3p$8cl$1@smc.vnet.net> <29422309.1182337642231.JavaMail.root@m35>*Reply-to*: drmajorbob at bigfoot.com

> n=10; > dy=4/n; > Show[Table[RegionPlot3D[g[-2+(k+1/2)dy]^2 <= x^2+y^2 <= > f[-2+(k+1/2)dy]^2,{x,-3,3},{y,-3,3},{z,-2+k*dy,-2+(k+1)dy}, > PlotPoints->25,Mesh->False],PlotRange->Automatic] Sluggish? At my machine, it very rapidly returns an error, because the brackets aren't balanced. Table doesn't appear to have an iterator. Bobby On Wed, 20 Jun 2007 04:34:27 -0500, Helen Read <read at math.uvm.edu> wrote: > John Fultz wrote: >> On Mon, 18 Jun 2007 06:50:42 -0400 (EDT), Helen Read wrote: >>> >>> On a somewhat related note, >>> I find that rotating 3D graphics with the mouse in some situations >>> completely freezes up my 5-year-old PC (2.26 GHz, 1 GB RAM). It's quick >>> for a Plot3D or ParametricPlot3D of a simple surface, but if I combine >>> multiple graphics, the response is incredibly slow to the point of >>> freezing up. I ran into this when making up illustrations of >>> approximating the volume of a surface of revolution with 8 or so disks >>> / >>> washers / cylindrical shells, which I put together with Table and Show. >>> The graphic renders pretty quickly (a lot faster than 5.2, on the same >>> PC), but it's pretty much impossible to rotate with the mouse. >>> Hopefully >>> it will be more responsive in the classrooms where I teach, which have >>> newer computers. >> >> Feel free to send me some of the examples you're seeing problems with , >> and >> perhaps I can help you out. Since you weren't very specific in this >> email, I >> can't say too much. You did, though, mention that you were plotting >> cylinders, >> and so I should mention Cylinder[] and the Method->{"CylinderPoints"} >> option. >> "CylinderPoints" is documented right at the end of this tutorial... > > Thanks for point me to Cylinder[]. I had been constructing everything > with ParametricPlot3D, and didn't know about the knew Cylinder[] > graphics primitive. Cylinder[] works quite well, and I now have some > lovely illustrations of approximating volumes with disks (a Table of > stacked, opaque cylinders) and with cylindrical shells (a Table of > transparent, nested cylinders). They look great, render in a reasonable > time even on my old PC, and rotate easily with the mouse, without having > to use the Method->{"CylinderPoints"} option. > > The one graphic that's been causing the most trouble is the following. > The idea is to illustrate the use of washers (stacked on top of each > other) to approximate the volume of a solid of revolution. For example : > > f[y_]=1/12(18-y+9y^2-3y^4); > g[y_]=1-y/12-(y^2)/8; > RevolutionPlot3D[{{f[y], y}, {g[y], y}}, {y, -2, 2}] > > Because of the "hole" in the middle of each washer, I was unable to come > up with a way to do what I needed with Cylinder[]. (I tried concentric > cylinders, with the idea of having the inner cylinder acting as negative > space -- the hole -- but after much fiddling around with Opacity, Color, > etc., I couldn't find a way to make it look right.) So here's what I > have instead. > > n=10; > dy=4/n; > Show[Table[RegionPlot3D[g[-2+(k+1/2)dy]^2 <= x^2+y^2 <= > f[-2+(k+1/2)dy]^2,{x,-3,3},{y,-3,3},{z,-2+k*dy,-2+(k+1)dy}, > PlotPoints->25,Mesh->False],PlotRange->Automatic] > > Until I tried setting Mesh->False, this thing would freeze up my PC > completely if I tried to rotate it with the mouse. With Mesh->False it's > a lot better -- it's still a bit sluggish, but it will rotate with the > mouse as long as n (and the number of PlotPoints) isn't too large. I > think it will be fine on the newer computers in the classroom, but if > you can think of a way to make it a little less sluggish and still look > OK, let me know. > > -- > Helen Read > University of Vermont > > > -- DrMajorBob at bigfoot.com