Hexagonal Tessellation on a Trimmed 3D Surface

hello!! I am trying to make a hexagonal tessellation on a trimmed 3D surface, but here is the problem. All hexagons must have the same size. (or almost the same(?))

I tried using Lunchbox, but it doesn't seem to work.

I am using attractors later on to define the radius of circles inside the hexagons, as you can see in the definition, so it would be good to control the size of the hexagons.

Attachments:

hex.3dm, 709 KB
hex-circles.gh, 68 KB

Replies to This Discussion

Permalink Reply by peter fotiadis on January 8, 2016 at 5:15am

BTW: Most people believe that "equal" panels means less cost. But the real cost of something (in real-life) is hidden in the ultra expensive aluminum system that can "follow" different dihedral angles per edge (the angle defined by the adjacent faces normals).

As always I have systems in mind that don't leak (but have an umbrella ready when in the building and cost could be considerably lower).

Speaking about leaks: what is the most convincing case these days? (famous building + famous Architect > Armageddon)

I can't mention the building for obvious reasons ... but if you follow that type of gossip ...

Permalink Reply by Rémy Maurcot on January 8, 2016 at 5:46am

Hey guys,

I have a same project, I tried with PanelingTools or Evolute Tools Lite but I have not managed to do it.

It is really important fo rme to rationalize(make it identical) a maximum number of hexagon.

I will test your approach.

Best,

Permalink Reply by Rémy Maurcot on January 8, 2016 at 5:51am

@Peter it's possible to you to send me your Surface for a Relax_Hexagons_V1AStatic (related to thispost)

Thanks.

Permalink Reply by peter fotiadis on January 8, 2016 at 6:04am

Remy,

What surface? You mean the underlying thingy? But this is "included" in the def posted provided that GH memorized the (internalized) Brep.

Or you mean that GH failed to do the internalize task? (it happens rather frequently).

If so get them all (hexagons, brep and the donor surface).

So the Moral is clear:

create the most "easy" surface possible.
make some hexagons.
cull them (that's a bit tricky AND slow) VS the desired trim.
use the def provided.
ACCEPT that equality means in fact: deviating from the trimmed boundaries (the brep) but the good news are that hexagons they DO "follow"the surface.

Attachments:

Relax_Hexagons_V1A-Static.3dm, 291 KB

Permalink Reply by Rémy Maurcot on January 8, 2016 at 6:15am

Your hexagons is internalize but not your Surface.

Thanks for this.

For you it's impossible to receive all same hexagons ?

Permalink Reply by peter fotiadis on January 8, 2016 at 7:07am

Oops GH did it (again).

If same means "exactly" the same (within some "smallish" engineering tolerance) ... well ... it's rather ... unlikely.

On the other hand achieving the "same" is doable (if you have stand alone panels in mind) IF you get the "average" hexagon (or better the smallest) and replace all (the relaxed) ones with this (pay attention to the coordinate systems [planes] for the orient "this to these" process): exactly what we do in real-life in similar projects.

If you do that take some realistic provision (offset inwards) for obvious reasons .

If you want some MERO KK System type of truss out of the hexagons > provide to the Germans the "unequal" nodes (this is not an issue for them) and make the envelope panels as above (be prepared for the hideous aluminum system price). A MERO from hexagons to triangles is like that (this is done solely via C#):

If you want hex planarity ... well...that's another totally different animal.

Permalink Reply by Rémy Maurcot on January 8, 2016 at 7:56am

Thanks Peter,I do not completely able to follow you, but thank you very much for your explanations.

In your definition: Relax_Hexagons_V1AStatic

If i understand all:

Your modify hexagons but your hexagons it's not same !

This is consistent but not exact approach.

Your hexagons are on a surface, their points are exactly on the surface.

For another approach would not it be possible to modify slightly these points in order to obtain identical hexagons ?

Permalink Reply by peter fotiadis on January 8, 2016 at 8:41am

Well ... literally speaking ...I don't do anything actually > blame Daniel for all that, he he. In this occasion I'm just a passenger.

The "live" report at the rightmost part tells you what is the min/max and average length. Notice that the more the engine "loops" the more the max-min diff is minimized (not becoming zero, mind): this is rather expected.

Pts "exactly" (meaning distance to surf < tolerance) on the surface ... well that's also hard to claim since K does an all-overall "optimization" (that "narrows" the "error" the more "loops" are performed).

Thus the critical part is to understand what K actually does: IT'S not a fire once and forget thingy ... it's just "satisfies" your goals "better" the more it "loops" (but if garbage in > garbage out).

Modify the points? (per hex I do hope) You mean finding the min distance (from any hex node to center) and then moving the nodes?

You can do that but ... then ... the ex "coincident" hexagons they would separate each other ... thus > use the min hex method suggested above.

All in all: a physics engine is actually like dating a super-model: it's not a bad thing ... provided that you have reasonable expectations AND you are willing to "optimize" some goals of yours.

Permalink Reply by dimitris skom on January 8, 2016 at 9:13am

@Peter it's not about the money the hexagons must be almost equal so i can inscribe circles.

the only way this can be made is to smooth the surface mecause it is too wavy

btw the hexagons are not hexagons anymore :P how can i make this surface wavy but not too much?

Permalink Reply by peter fotiadis on January 8, 2016 at 9:38am

Hmm ... Karma my friend what else? he he.

BTW: for hexagons staying hexagons play with the def provided elsewhere in this thread (load the rhino file [posted later] as well ... since Remy reported that GH failed to memorize the internalized brep > chaos) named:

"Relax_Hexagons_V1A-Static"

There (see comments on top) a classic method is used in order to force hexagons to behave properly.

BTW: Interactively (on the fly) "managing" items in collections (in this occasion: nurbs control points) > the holly grail of Engineering > we must spend some time on the phone for that one ... since it's doable only via code (lot's of cases available - but you need some "training" : volatile VS persistent data VS design variants [ A MUST] VS slider control VS events VS Karma, he he).

Permalink Reply by peter fotiadis on January 8, 2016 at 9:47am

BTW: There's always (a bit extreme, mind) a Plan B for a "wavy" surface > let's allow God to decide: have fun with this combo attached.

Attachments: