1. collect wisely
2. explode simply
3. plot nicely
Borrowed from the live forum "W Truss from Ioan"

Jean

Utilities XY [Draw Truss].sm (17kb) downloaded 159 time(s).

Probably i am wrong or I have misunderstood something .. but to reach the result of Jean it is necessary to put in a proper sequence the extremes of each beam of the truss , reversing their original order if necessary and so on ...so is something that must be done in a manual way observing the Truss or the structure that is necessary to handle ... sincerely i don't see room for big automation with an algorithm.
It is a solution to develop on each specific case ..at least is what looks to me.

Best regards

Franco

Hi Joan,
prior to go ahead to address your request I would like to summarize the different approaches used till now.
I will start from the worst one till what I consider the best ...if I was you.

-My way: In my method I do not consider your input for drawing in term of beams ( or segments if we consider the Truss just a set of segments to tie together based on a reference Model you have supplied to us ).
For me the focal point are just the nodes ( or points ) that I need to link in a continuous sequence because otherwise the X-Y graph method can't be used.
So starting from the ends of each segment (beam) I have:

1-defined which are the single point to connect.
2-defined a continuous path to connect them all

In your case this path is the following 1->2->4->6->7->5->3->1(external border of the truss completed, so I start to draw the missing link with this other sequence linked to the previous one ..)->2->3->4->5->6 ( completed)
Each number in the sequence is a node as reported in your initial Sd matrix.
To tell the truth the sequence can be optimized/shortened just for drawing purposes in the following one :
1->4->7->5->3->1->2->3->4->5->6 ..but is just cosmetics

-Jean Method: In his method , that is better than my one, I guess that Jean has thought in terms of segment consecutive to link together. So he has kept your Input closer to the original structure of the Sd matrix in term of 11 segments to link ..the only permission that he allowed to himself is to define the sequence of the segments and where necessary reverse their extremes so that in the sequence the end of one segment matches the beginning of the next one.
Then after this MANUAL reassemble of the 11 segments he ha built the V matrix automatically and sketched the truss.
-Davide and Ber7 : their method id similar and starts from a deep knowledge of the ins of the X-Y graph features and limitations ..trying to turn the limitations in something useful to address your request.
In particular the Ber7 method is the most elegant and the best in my modest opinion ( not easy to understand at first sight ) but in this case they don't care to draw a consecutive path but isolated segments and with their method there is no manual arrangement of point or sequence of segments to solve the problem. They do not touch and alter the initial info's that you have supplied the Sd matrix.

Hope that with this e-mail I have not bothered/disappointed anyone because this was not the aim and that with my poor English was able to explain what I desired.

Best regards

Franco

P.S: my method could be automated using method of Operational Research ( Graph Theory ) building from the beams list the adjacency matrix ..but I guess that the effort is too much ..even if feasible.

I'm not sure to understand about W truus that it would be a waste of time.
If your original grouping is always the same, the adjacency matrix is unique.
It will follow any new coordinates per new design. If you have more members,
the grouping will be different, it will rquire to redetermine the transitional
"prover" [see the attached work sheet], determined manually again but unique again.
No software can do, proof: Chemists use the Polyhedron family ... immense...
to represent the flat coordinates of the molecules. Each "Polyhedron molecule" is
done manually, that keeps many brains busy.

The adjacency of W was no sweat at all compared to the "prover", but that was
pretty new for me like teaching a parrot to sing "La Marseillaise".
Please, let me know that you are still on gear.

Salut Ioan and all

Jean

Utilities W Truss Adjacency.sm (27kb) downloaded 25 time(s).

... past W adjacency that plots clean the Truss,
I have added a module for re-nesting the plotting W.
Works well as expected.

Jean

Utilities W Truss Adjacency.sm (49kb) downloaded 37 time(s).

Salut Ioan,

If I may express an opinion, it's that:
When (and if) I have a choice, I prefer to navigate in the real life problems, not in dreams, nor in nightmares, ... nor to catch a fly with the canon...

BTW,
Do you have a Platonean's and a Archimedean's polyhedral coordinate generator in 3d?

For the Platonean & Archimedean, you have better chance with Robert Fereol

http://www.mathcurve.com/courbes2d/courbes2d.shtml

next visit:

http://www.mathcurve.com...medien/archimedien.shtml

Your Isocahedron is made from Mathematica. I rcognise their horror
colormap. We have lot of 3D in Mathcad "Creating Amazing Images"
but not the Carbon 60 Buckyball. Anyway it wouldn't render in Smath
that does have "conventional" 3D plot.

The Mathcad Buckyball is via Matlab "sparse matrix". Mathcad does not
generate Buckyball by itself. Thanks for zipping file and attach.

I must admit: lost in those "....hedrons"
That's all what I have about Buckyball

Buckyball.sm (130kb) downloaded 35 time(s).

If you plot: augment(col(Coord,1),col(Coord,2))
You get a very scary parrot plot ! Dare

Jean

Ioan,

my approach is similar to the Jean one , the only difference is that I am trying to develop an automatic procedure that starting from a description of the structure as a graph (i.e through an Adjacency matrix ) draw automatically the structure with one color.
For what concern the original phyisical problem ...it has no relation with the manipulation that it is necessary to accomplish on the graph to make it Eulerian if it is't.
This means that the addition of further edges at nodes that have an odd degree to allow the forth and back on these edges is just an artifacts and is needed to avoid that we lift the pen from the paper while drawing the graph ( and use just one pen color ..from a practical standpoint ) ...so these doesn't mean that we go on the real structure/truss to add further beams.

Hope that I have understood your 2nd point with my answer.( Sometime what we feel is different from what is meant )

...Then I will move to 3-d structure and in that case I'll need to project the 3-d structure on a plane using a isometric-like projection and then associate to this 2-d graph the usual Adjacency matrix..but the journey is still long.


Best regards

Franco