Regular triangle panel

Hi there,

I am trying to make a triangle panel on this surface, but i wanted to make it more regular, is there anyway i don’t get those little nested forms at the top?

dome.3dm (8.0 MB) domed.gh (7.3 KB)

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I doubt that there is a singular solution. Most “automatic” tessellation would depend on your surface topology. Looks like you do have a convergence at the peak. It may have to be non uniform panels like the one on the Gherkin (first image). Even without a convergence, it’s likely you’ll have to use quite a few different type of panels, like on the court roof (second image)

There are people here much more savvy than me on geometries and tessellation but i think you’ll need to provide more constraints. For example, should all nodes align? Can surface be rebuild/refitted? etc…

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Yes, there is a way to get more regular patterns, but it takes a few design iterations and some balancing between competing mathematical realities.

The approach I would take to solve this is:

  1. Roughly sketch the ideal organization to get a good idea of the goal. That will help in later steps.
  2. Use PanelingTools plugin for Grasshopper. This will give the control needed as you refine the design. It can get complicated, but the problem here is definitely not automatic and may not be easy on arbitrary shapes.
  3. Keep posting your progress here and there are people that can help guide you.

Here are a couple threads that might help.

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This old chestnut. You can look into MeshMachine which is also via Scott’s very useful references. Here is another thread on a similar topic: Convert Mesh into equilateral triangles.

I have tried it with your surface, but I can’t seem to get as fair a triangulation as to just repel some points on the surface and then join them up with closest neighbours (with a little post-production). I wrote a component that did that a while ago which you can try (see gha file below), it does this:

Repulsion2

With a little bit of editting it looks ok, but you’re always going to get something funky at the singularities:

dome_edit.3dm (5.8 MB) RepulsionExample.gh (15.8 KB) AgentSystem.gha (13 KB)

John.

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RCDUtilities plugin (Repulsion timer component error in this definition).

Can you elaborate @ajarindia?

The AgentSystem.gha should give the Repulsion component, located in Extra:

Unrelated, but the previous file referenced the dome from the original Rhino file, so I’ve instead internalised it here:
RepulsionExample2.gh (96.0 KB)

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Sorry John, first I installed the plugin which you provided above. That time it didn’t worked now it’s working well. Some weird behavior by GH. Now I’m getting it in extras. Even I checked those unblock option too before putting it into the components folder I don’t know why it didn’t turn up for the first time when I opened the file. GH cheated me: wink: Thanks & Regards.

Just looking at this again @Leonardo_G_Pate, the nature of the shape means you might get a good triangulation by projecting part of a geodesic sphere onto the surface. Indeed, this does seem to work quite well. You can see below the result of the projection (a) and the reformed triangular mesh, however of course the issue now lies with the boundary conditions.

One option that seems to work ok is to use Kangaroo 2 in order to pull the mesh to the boundary curve of the surface. The result for this is shown (b). A small improvement can be made by culling any vertices with valence < 4 (i.e. less than 4 connected nodes). The result is I think cleaner than the earlier repulsion example I gave. You can try different positions of the surface in relation to the geodesic sphere to get different results of course (and different triangle sizes). By all means have a play with it!

Triangulate.gh (104.0 KB)

… and the version with a little more culling that seems to work better:

Triangulate (more culling).gh (103.0 KB)

Best wishes,

John.

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I think I’d approach this first by stretching a simple subdivided 2 triangle mesh:
triangles_wedge_mesh.gh (102.4 KB)

alternatively - 3 triangles gives more even edge lengths along the top, but a bit more squeezing at the base:


triangles_wedge_3tris.gh (109.0 KB)

It might even give a better fit here to use ‘2 and a half’ triangles - so you get those 2 valence 4 vertices on the lower boundary that can line up with the rounded corners, and the triangles meeting the top left edge are closer to 30-60-90 triangles than equilateral.
That’s a bit more work to set up though.
Doing this really well takes time - getting a good grid for an actual building can take weeks or months of refinement.

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… and as a final thought, if you’re not bothered by smallish triangles but just want to relieve the bunching at the top, you can use the same methods on the original triangulation which does help a little. You might want to try adjusting the strength of some of the forces to get different results, although the mesh is prone to folding in on itself at the top:

NodeRepelAgain3

domed_edit.gh (108.1 KB)

John.

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Hi Daniel,

Since its a triangle panel’s query, all you folks focused on implementing triangular pattern here. Is there any limitation’s that we can’t use some different patterns other than these regular Triangle, Diamond, Honeycomb for paneling. Because when it comes to real life architecture I heard people saying that these paneling shapes are more efficient, economical, easy to fabricate etc… so they are using and only these conditions restricting all major architectural firms to follow these paneling approaches for their projects. Thanks & Regards.

Eg: Studio Fuksas, Zaha Hadid, F&P, many others.

As more requirements are put on the panels to improve the economics, there becomes a set of tradeoffs. The companies you mention can take months in design iteration trying to balance the issues.

This post talks about some of the challenges:

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Hi @ajarindia,

There are some cases of architectural paneling and grid structures which don’t use regular grids.
Here’s one nice example, where the panels are a mix of irregular triangles, quads and pentagons, and the nodes have many different valences:


I think there does need to be a good reason to use something irregular like this for structure though, since keeping things at least topologically regular simplifies design, fabrication and construction considerably.
There are only 3 fully regular polygonal tilings possible. https://en.wikipedia.org/wiki/Euclidean_tilings_by_convex_regular_polygons
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Holy cow! That tiling wiki is pretty eye-boggling. Thanks for that link, could be really really useful for laying stones out in crazy pave arrays on jewelry.

it seems superb, but this is too complicated to be build so what i was seeking was something more practicle, so i became trying to repeat a triangle with panneling tools, but couldn’t get the geometry following the surface properly… i wish to do the same in all 3 surfaces and try to match them at the joints.orient.gh (17.5 KB) marina dome.3dm (10.1 MB)

Hi @Leonardo_G_Pate,

If you just need something triangular with that type of pattern, you can consider the M+ tools and Weaverbird for the extrusions. Unfortunately I don’t have panelling tools installed on my system.

That’s the best I can do I’m afraid. I think Daniel’s projection even without doing any Kangaroo still looks better than your original result, but it sounds like the design problem might have changed.

Take care,

John.

thanks man! In fact it does, the problem is that the triangles in that situation doesnt have the same weight and is a huge problem in order to be build, is way easier to make an all the same measures parts.

This one you made look exactly what i seek! Thanks

No probs. You can try and match up the elements and do a little editting and trimming in Rhino I guess, probably the fastest way.

J.

orient_edit.gh (33.4 KB)