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MathGroup Archive 2007

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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


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