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

Jean

Utilities XY [Draw Truss].sm (16 KiB) downloaded 187 time(s).

Wonderful algorithm.
Now I will use it instead of my. Thank you, Jean!

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

... [suite], Ioan ,,,,
I tried to add the content of the attached work sheet in your "pour Jean ..."
After few play, it crashed Smath. For the 2d XY plot, you can have only
mirror, flip left, rotate ± 90° [typical Paint rotation] and preserve the "view".
Angular rotation preserves the afinities, but the eye does not recognise.
How does it look from a graphic package ?

I didn't understand Davide algorithm completely.

An X Y matrix is a surface matrix [a terrain level, a grayscale image ...].
The truss is flat, the level matrix is 0's. There is nothing to rotate to
view from different angle. Maybe it's possible to rotate around the Y or
around the X. I have not explored that yet in Smath.

That project is most interesting, but there are some missing links.

Please don't abandon.
Cheers all champions.

Jean

Ioan_Jean_2020160225 bis2 (1).sm (113 KiB) downloaded 67 time(s).

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.

Ioan, Franco:

Let's leave the 3D on the ice, for now. Talk about the "parrot plot".
From what you are saying, both of you, the W Truss has 9 members, for
an 11 set of coordinates. Ioan initial nested set of coordinates is
the one that "plots parrot", and you want an adjacency matrix that
would convert "parrot => graph". If that's what you want, it looks
easy. So, Ioan designs W truss for JoBlo with JoBlo "parrot coordinates",
Then Ioan desgns W truss for ArtBlue with ArtBlue "parrot coordinates"
... and so on, Ioan designs W truss for SueZan with SueZan "parrot coordinates"
I suspect, Ioan would like to deliver to each client the product on paper
but this time not "parrot plot" ...
Let me work in that understanding of skinning the parrot via "adjacency matrix".

Jean

Wrote

@Jean,

Thanks!
If you think on solving only the first particular case (W Truss), from my viewpoint, it's a waste of time.
I worked a little to offer more examples. All must fit to the solution if there is one.
Never mind rotations; they do not influence the colors; they are only to facilitate the view of 3d models.

A
Ioan

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 (26 KiB) downloaded 45 time(s).

... W Truss compactum as a finished product.
Specific to this particular member collection.

Jean

... 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 (48 KiB) downloaded 58 time(s).

Wrote

In this context I appreciate that you have no solution; all your development is simply cosmetics and "witchcraft"... Your "adjacency matrix" is a kind of smoke...

In some way you are right if you plot member by member, but if you plot "no pen lifting",
it's were a connectivity [adjacency] is needed. It may turn not simple like in the "Buckyball".
In the attached revised work sheet, the Carbon 60 "Buckyball" connectivity [adjacency] can
be plotted . The 2 col vector is 180 length. It is saved in file, this file is attached. Just
plug it in your file system and you should get the "Bucky" plot. I can't show a 3D display
because my unregistered Mathcad 11 does not access the Matlab component.

A interesting project. Thanks for sharing.

Jean

Utilities W Truss Adjacency.sm (105 KiB) downloaded 53 time(s).

Bad luck: Forum does not attach Smath data from file.
If wanted, please let me know to explode in work sheet.

Jean

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/polyedres/archimedien/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 (129 KiB) downloaded 52 time(s).

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

Jean

Hi, a voice from the desert is speaking ...

In this period I have decided to study again Operational Research and Graph Theory .
The initial result is the attached file .CinesePostmanProblem_1stPart.sm (51 KiB) downloaded 37 time(s).
This study has been done mainly for educational purposes, my modest opinion is that this approach for solving the Ioan issue is like Jean says " ..Shouting a fly with a cannon ".

The problem to solve ( one of its enunciates ) is the drawing of a path without lifting the pen from the paper, when this is not possible minimize however the forth and back on some segments of this path.
This problem can be brought back to the Chinese Postman Problem i.e to find the shortest route in a network that uses every arc (undirected edge) and gets back to where they started (closed problem-Eulerian graph ) or doesn't go back (open problem Semi-Eulerian graph).

To use this method it is necessary to turn the structure/truss in a graph and build the corresponding Adjacency Matrix...but I guess that this should not be an issue.
Having this matrix in the case of Eulerian or semi-Eulerian graph it is possible to find a sequence of traversed Nodes that solves the problem.

Next step will be to solve the problem in a case of non Eulerian graph , it is necessary to make other intermediate steps ..but soon or later I will be able to complete this part too.

@Davide
--------
During this journey I have found in Internet this library for graph/network study http://igraph.org/ , because it is available for several packages and languages ..make me wonder if it would be possible to wrap it for Smath , it would be really beneficial and it would open new applications area for Smath ..avoiding to reinvent the wheel.


Best regards

Franco

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