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Re: need help with surface polygons

• To: mathgroup at smc.vnet.net
• Subject: [mg7939] Re: need help with surface polygons
• From: Eckhard Hennig <hennig at itwm.uni-kl.de>
• Date: Fri, 25 Jul 1997 02:40:18 -0400
• Organization: ITWM
• Sender: owner-wri-mathgroup at wolfram.com

ericf at uidaho.edu wrote:
> 
> I can't seem to figure out how to get the nifty polygons used on the
> surface in the solving the quintic poster.
> 
> the best that i can seem to do is to rotate the rectangles 45 degrees
> and reduce them by half, to get a partial see-thru object:
> 
> rot = Polygon[x_] :-> Polygon[1/2(x+RotateRight[x])]
> 
> but what i really want is the one used on the surfaces of the solving th
> quintic poster.

Eric,

below my sig I quoted a message which appeared in this newsgroup this April.
This seems to be what you need.

-- Eckhard

----------------------------------------------------------------------------
Eckhard Hennig                                  mailto:hennig at itwm.uni-kl.de
         Institut fuer Techno- und Wirtschaftsmathematik e.V. (ITWM)
         Erwin-Schroedinger-Strasse,  67663 Kaiserslautern,  Germany
            Voice: +49-(0)631-205-3126   Fax: +49-(0)631-205-3616
http://www.e-technik.uni-kl.de/organizations/itwm/people/Hennig/Eckhard.html
----------------------------------------------------------------------------

Quote from comp.soft-sys.math.mathematica, April 4, 1997:

> Does anyone have a good Mathematica algorithm for converting a Polygon
> expression (where the polygon has three dimensions and is known to be
> convex) into one or more Polygon expressions which, when displayed with a
> Graphics3D wrapper, look like the exterior skeleton of the original
> polygon. Put differently, I want an attractive  "wire frame" of the Polygon
> where the "wires" are themselves polygons and not lines.

Hi Seth,

suppose You have a graphics 3d object gr and You want replace
all polygons with hollow polygons and the hole corners are
fac times closer to the center of the polygon than the
following works:


fac=0.8;
Show[gr /. Polygon[pnts_] :>
             ( cntr=(Plus @@ pnts)/Length[pnts];
               sp=(fac*(#- cntr)+cntr) & /@ pnts;
               Polygon /@ Transpose[
                            {pnts,RotateLeft[pnts],RotateLeft[sp],sp}
                           ]
              )
  ];
  
  Hope that helps 
  Jens