Patterning, Polyhedra, and Mapping

Hello, I am a b.arch student trying to expand my horizons. I want to take a custom pattern (which I have created based on the image below) and map it to a sphere. Essentially a 3d/parametric recreation of the image below.

I am really looking for advice on how to proceed. So far I have created a sphere, subdivide it into the hex panels. Get points, for those hex panels. Then I took my pattern, and broke it down into hexagonal modules. So now i think i just need to figure out how to map a group of curves to one/all of the hexagons on my subdivided sphere?

For the moment im rather stuck, so any and all help would be greatly appreciated! My files are attached (and i used the lunchbox plugin for my subdivision).

Thanks G3D!

Attachments:

poolty.PNG, 21 KB
v03b.3dm, 1.1 MB
3b.gh, 14 KB

Replies to This Discussion

Permalink Reply by nikos tzar on December 8, 2014 at 8:29am

Hi David,

I am guessing that you are trying to replicate this project.

In this case my first recommendation would be to leave a comment there, asking for some information on the project.

Having said that, I have a few more comments on what you are trying to do:

1. It is not possible to divide the surface of a sphere with regular hexagons [the most efficient way includes pentagons as well (classic soccer ball)].

So I believe that in the image you posted there is some serious twisting taking place at the back side (you can actually see this starting on the right side of the picture).

Lunchbox's [hexagon cells] component divides the surface in U and V (orange slices for a sphere) and draws hexagons on it. The result is some serious deformation on the 2 poles and many non-planar cells. If you are ok with this, then my only tip would be to use an even number for the U divisions in order to have a clean seam:

instead of:

2. The hexagons you have defined in 2d are wrong as they are overlapping and also leaving gaps between them:

You should define your hexagons so that they form a honeycomb pattern. It could be something like this:

3. There is no direct way for hexagonal mapping, so your best bet would be to draw your pattern inside each cell (good GH data structure understanding is crucial for this). Also, the non-planar cells will probably give you a hard time there...

Hope I cleared some things and didn't cause more confusion!

Nikos

Permalink Reply by Dave Lang on December 8, 2014 at 9:48am

Nikos! My man! Your are amazing! Thank you so much for taking the time to help me I really appreciate it.

I was already thinking I would have to ditch the traditional hex division (due to the warping) and move towards a polyhedra design that integrates pentagon shapes as well. So this just confirms my suspicions.

Your redistribution of the 2d shapes is genious! I thought they should assemble more cleanly, but I couldn't figure it out for the life of me.

And finally, despite having these fundamental issues I have a pretty good grasp of data tree's and think i can pull off the line-work recreation in each cell (with a bit of hard work).

So I will set off on my adventure and post back here with any interesting results.

Thanks again! And any other insights in the meantime are of course still welcome :)

Permalink Reply by nikos tzar on December 8, 2014 at 11:00am

Hi Dave,

Changing your definition to something like a geodesic sphere would solve many problems but it would be something completely different so I didn't go through this in detail.

I believe the main problem now will be the non-planar faces causing trouble with offsets etc.

You can check out this discussion and maybe this tutorial about kangaroo's planarization forces. I haven't tried any of these though so I can't tell if (and how well) they would work on a sphere...

Good luck

Nikos

Permalink Reply by Dave Lang on December 9, 2014 at 2:44pm

Turns out it was a bit of a pain, I decided to build it out as a truncated icosahedron not realizing the pentagon implies a mismatched edge in the pattern.

Other than that, one big messy grasshopper script later I have results! And the extrusion was not challenging, just identifying the center of the overall assembly. If by offsets you mean thickening the geometry that might indeed be problematic. I tried using a mesh based solution through weaverbird that had issues with edge joins. So my next stop (as you suggested) will be with Kangaroo.

Thanks again!