Hexagonal planar pattern on Freeform surface - glass structure

Hi guys,

i have a freeformed surface where i want to construct planar hexagonal surfaces on. It dont have to be rigth on the surface but nearly. I divided the surface into several curve and did an anemone loop to project those hexagons along the curve. I did this with every second curve because the other curves have to be a bit different to nearly close the surface. I know, that it is impossible to close the surface with planar ones. There will always be a gap between the curves, but this isnt very important for me.

My problem now is, how to get the right definiton to fit the hexagons in the other curves. I thought that there were two Options. Both options depending on the distance of Point A and B. And the distance depends on the curvature of the curve and on the size of the hexagons. In option 1 the size of the resulting hexagon is always different, but it will stay in a resulting plane of those two side hexagons. And in Option 2 the size of the resulting hexagon will be always the same but the plane will always be different.

However, i will be happy if even one of the two options would bring me to my goal.

Is there someone who can have a look and give me an advice?

Thank you

Hendrik

Attachments:

hexagon on multiple curves_v3 .gh, 45 KB

Replies to This Discussion

Permalink Reply by Sebastien de Wit on October 20, 2016 at 11:54am

I think I have your solution

You need two things;

First a surface, loft or brep.

Second you need a mesh on you surface (UV mesh)

Attachments:

Planarize.gh, 21 KB

Permalink Reply by shuo zhang on October 20, 2016 at 1:07pm

Woah never thought I'd answer a question here lol. But this may help you:

https://www.youtube.com/watch?v=MsbyfC2usUk

you'll need kangaroo and lunchbox installed though. Also note that by this method the resulting hexagonal pattern may be heavily deformed depending on your surface.

Edit: Yeah I guess Sebastien's definition is what the video talks about step by step.

Permalink Reply by Hendrik on October 21, 2016 at 5:12am

Hey Sebastian,

at first, thanks for your help. :)

I had to download the Smart Plug in for GH to test your explanation, and now i didnt really understand for what those components are. Is it for the glass layers or for an analyze?

I put my surface in your file and it works, but the shapes are very ugly and the planar surfaces leave the original surface extremly. Look attached file to know what i mean. (Planarize_v2.gh)

What i actually want to do is to get (nearly) similar hexagon faces on a freeform surface. And i know this is only possible if i make some losses. It is not possible to have same sized, planar, waterthight panels on a freeform. Either i have to deal with ugly faces or with leaky panels. For my structure it is more efficient and architectural better-looking if i deal with gaps as the smithsonian institution. See attached picture.

In the meantime i realized a method to get planar, hexagonal, same-sized panels on a freeform with anemone to get a structure like the smithsonian. See attached File (hexagon on multiple curves v10 Forum.gh). The only thing left is to generate those beams to hold the hexagons (or the glass). Those beams must be generate from the brep points of every single panel depending on the nearest to a target surface.

Maybe you will have an idea to do so.

Thanks,

Hendrik

Attachments:

Planarize_v2.gh, 27 KB

Permalink Reply by Hendrik on October 21, 2016 at 5:25am

See attached file,

i realized one solution to get the nearest point, but unfortunaly they are in a random order to group them.

Attachments:

hexagon on multiple curves_v10_Forum.gh, 48 KB

Permalink Reply by Sebastien de Wit on October 21, 2016 at 6:41am

I did a run with your file. There are some remarks. Like the panel shape actually depends on the Gaussian curvature if you want to do this correctly, see attached paper. If you steel want to keep hexagons in the negative zones you can alter the parameter Hexagon (lunchbox). I was able to get you surface flat but corners which are very angular are problem areas. You probable need 5 to 10 runs to play around with the factor of force and the factor of the Hexagon parameter in order to get a satisfying result.

Attachments:

A Note on Planar Hexagonal Meshes.pdf, 2.3 MB

Permalink Reply by Sebastien de Wit on October 21, 2016 at 6:45am

Or like this

which is more rectangular. By the way that smart plug in is just for visualizing certain things. It is not required for the analysis.

Bewaren

Permalink Reply by Hendrik on October 21, 2016 at 7:13am

Thank you,

i knew the paper and because of it i started some tests, but this isnt very helpful for my main problem, because i wanted the shapes as i explaind (those with the gaps). But for a study your idea is very helpful too, can you attach your GH File please?

Hendrik

Permalink Reply by Sebastien de Wit on October 21, 2016 at 9:07am

Hi Hendrik,

It is the same as above, just with the altered parameters as in the picture.

The problem with the gasp or somewhat twisted/rotated tile I cannot help you.

Perhaps after my planarization you can use a series element (with a pattern) to rotate each tile with a certain amount of degrees. Than you know for sure that they are flat and gasped. This is just an idea anyway.

Sebastien

Permalink Reply by shuo zhang on October 22, 2016 at 10:18am

The thing is that having (nearly) identical panels on a freeform surface is an unsolved problem.. At least not in grasshopper or kangaroo yet. It all depends on the Gaussian curvature of the surface. For positive Gaussian surface it is easier, but for negative ones it's mandatory to have either deformed panels or completely different shapes...

To sum up not every surface can be covered with good looking panels. At least not without advanced mathematical methods.

Permalink Reply by Hendrik on October 24, 2016 at 1:19am

Hi,

i know, regular, same-sized hexagonal panel on a freeform is a geometrical never possible opportunity. If it is a freeform and the need of nearly same sized and planar panels there has to be gaps between those, because of the different Gaussian curvature. One good example is Museo Soumaya. I am trying to copy the method for getting those groups of different panels. It will be possible with GH and Anemone and a k-mean clustering as Mateusz Zwierzycki mentioned here:

http://www.grasshopper3d.com/photo/copycating-the-soumaya-museum-guys

Hendrik

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