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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.
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