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MathGroup Archive 2007

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Anomolous behaviour of Penrose Triangle Demonstration

  • To: mathgroup at smc.vnet.net
  • Subject: [mg81085] Anomolous behaviour of Penrose Triangle Demonstration
  • From: Syd Geraghty <sydgeraghty at mac.com>
  • Date: Tue, 11 Sep 2007 05:23:52 -0400 (EDT)

I would appreciate some insight regarding the Penrose Triangle  
Demonstration which can be found at:-

		http://demonstrations.wolfram.com/PenroseTriangle/

The original source I downloaded when run on my machine displayed a  
blank panel!
(The demonstration ran fine on my machine in "watch web preview" mode!)


$Version    Out[1]= "6.0 for Mac OS X x86 (32-bit) (June 19, 2007)"

The demonstration source was;-

Manipulate[
  cu[x_, y_, z_, d_] :=
   Cuboid[ {x - d/2, y - d/2, z - d/2}, {x + d/2, y + d/2, z + d/2} ];
  Graphics3D[
   {Opacity[o],
    cu[0, 15, 30, 7.5], cu[15, 45, 0, 7.5],
    Table[cu[0, 0, 15 n, 7.5], {n, 0, 3}],
    Table[cu[0, 15 n, 0, 7.5], {n, 3}]
    } ,
         ViewPoint -> 200 {-1, -1, 1},
         Boxed -> False,
         PlotRange -> 50 {{-1, 0.8}, {-0.6, 1}, {-0.08, 1}},
         ImageSize -> {400, 400}
   ],
        {{o, 1, "opacity"}, 0, 1}, TrackedSymbols :> Manipulate]


I changed the "viewpoint factor" in  ViewPoint -> 200 {-1, -1, 1}  
above to 100{-1, -1, 1} on a hunch and the panel
displayed correctly.

After failing to find any documentation for the use of the "viewpoint  
factor" I tried setting a range for vp and generating a slider in
addition to opacity to see the effects.

Manipulate[
  cu[x_, y_, z_, d_] :=
   Cuboid[ {x - d/2, y - d/2, z - d/2}, {x + d/2, y + d/2, z + d/2} ];
  Graphics3D[
   {Opacity[o],
    cu[0, 15, 30, 7.5], cu[15, 45, 0, 7.5],
    Table[cu[0, 0, 15 n, 7.5], {n, 0, 3}],
    Table[cu[0, 15 n, 0, 7.5], {n, 3}]
    } ,
         ViewPoint -> vp {-1, -1, 1},
         Boxed -> False,
         PlotRange -> 50 {{-1, 0.8}, {-0.6, 1}, {-0.08, 1}},
         ImageSize -> {400, 400}
   ],
        {{o, 1, "opacity"}, 0, 1}, {{vp, 10, "ViewPoint Factor"}, 10,  
200, 10},
   TrackedSymbols :> Manipulate]

The effects of using the vp slider are very odd. Bits of the graphic  
start disappearing!

Any clues as to what is happening here would be appreciated.


Yet another strange "feature" showed up when I tried to "Save As" the  
modified demonstration code.

I cannot successfully save the modified demonstration.

I suspect that is a WRI safeguard for protecting the integrity of the
Demonstrations Project (which is fine by me).

I can of course save the modified code in a new blank notebook.

Syd Geraghty


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