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Re: drawing polygon diagonals

• To: mathgroup at smc.vnet.net
• Subject: [mg123949] Re: drawing polygon diagonals
• From: Chris Young <cy56 at comcast.net>
• Date: Sun, 1 Jan 2012 02:30:08 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <i6755n$873$1@smc.vnet.net>

On 2010-09-08 04:58:31 +0000, MH said:

> Hi,
> 
> This seems basic but it has me stumped.  I'm trying to illustrate the
> idea of the "handshake problem", where small circles represent people
> and the lines between the circles represent handshakes.  With the code
> below, I'm able to show (and manipulate) any number of circles, and
> I'm also able to show the lines between adjacent circles.  This just
> generates a polygon whose vertices are all connected, as it should.
> But how can I update my code to show the diagonals, too, and not just
> the sides of the polygon?  I'm not sure what to add.

To get some practice with GraphicsComplex, I spent some time figuring 
out how to distinguish the diagonals from the other line segments. 
Thanks very much to the others who explained GraphicsComplex. It looks 
like a big time-saver. It must also help when figuring out shared 
borders of polygons, since the indices are just integers, rather than 
the real numbers you'd need to match up vertices.

There's a screen shot at
http://home.comcast.net/~cy56/DiagonalsOfPolygon.png
and a notebook at
http://home.comcast.net/~cy56/DiagonalsOfPolygon.nb

I use short horizontal lines, via the keyboard shortcut esc-hline-esc 
(where "esc" stands for the Escape key) to distinguish any names I use 
starting with a capital letter from Mathematica's functions. I use two 
of them in a row to separate words in a Boolean flag, such as 
"show_border", since we can't use the underscore character, which is 
reserved for pattern matching. Apparently, Mathematica will allow a lot 
of these special characters in names, which is very handy.


Manipulate[
 Module[
  {P = \[HorizontalLine]CrcPts[n]},
  Graphics[
   GraphicsComplex[
    P,
    {
     PointSize[Large],

     If[show\[HorizontalLine]\[HorizontalLine]points,
      Table[{Hue[(k - 1)/n], Point[k], Black,
        Text[k, P[[k]], -2.5*P[[k]]]}, {k, 1, n}]
      ],

     If[show\[HorizontalLine]\[HorizontalLine]border,
      {Thick, Line[Range[1, n]~Append~1]}
      ],

     If[show\[HorizontalLine]\[HorizontalLine]diagonals,
      {Thin, Dashed,
       Line[Select[
         Subsets[Range[1, n], {2}], #[[2]] - #[[1]] > 1 &]]}
      ]
     }
    ]]],
 {{show\[HorizontalLine]\[HorizontalLine]points, True}, {True, False}},
 {{show\[HorizontalLine]\[HorizontalLine]border, True}, {True, False}},
 {{show\[HorizontalLine]\[HorizontalLine]diagonals, True}, {True,
   False}},

 {{n, 6}, 2, 12, 1}
 ]