Re: drawing polygon diagonals

*To*: mathgroup at smc.vnet.net*Subject*: [mg123961] Re: drawing polygon diagonals*From*: Ralph Dratman <ralph.dratman at gmail.com>*Date*: Mon, 2 Jan 2012 02:47:59 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <i6755n$873$1@smc.vnet.net>

How about CompleteGraph[6] Would that serve your purpose? Ralph On Sun, Jan 1, 2012 at 2:30 AM, Chris Young <cy56 at comcast.net> wrote: > 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} > ] > >