Re: Fast interactive graphics

*To*: mathgroup at smc.vnet.net*Subject*: [mg78024] Re: Fast interactive graphics*From*: Helen Read <read at math.uvm.edu>*Date*: Thu, 21 Jun 2007 05:53:18 -0400 (EDT)*References*: <f58d3p$8cl$1@smc.vnet.net> <f5at1i$adm$1@smc.vnet.net>

Helen Read wrote: > > 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] Let's try that again. This is what I meant: 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],{k,0,n-1}],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.