how to create Equilateral Trangle Panels

Replies to This Discussion

Permalink Reply by Martin Siegrist on October 26, 2016 at 9:23am

check out Kangaroo, there are useful simple examples around

Permalink Reply by Andy Watts on October 27, 2016 at 5:41am

Hi Yutaka,

I'm afraid you may be going down a dead end on this. 

Equilateral triangles will only have internal angles of 60deg. No more, no less. So when they are attempting to accommodate a curve surface, they will either overlap or diverge and leave gaps in your surface. Unless your surface is extremely regular, or planar.

I would recommend that for this exercise you introduce a tolerance to the angles of the triangles - so that they approximate your curved surface whilst remaining as close to equilateral as possible (say a tolerance of 1 or 2 degrees).

Andy

Permalink Reply by Yutaka takenochi on October 29, 2016 at 3:36am

Hi Andy

Thanks for your tips.

Actually yes my base surface is in planar and modular modes and can fit in the triangles , say 3 or four eq. Triangles in one module rather like many pyramids.
Multiply these pyramids and rotating them  will form a spaced fame like structure.
This can be done easily manually using card board but I just wonder if there's a method to populate them in Rhino.

Warm Regards
Yutaka

Permalink Reply by Romain Mesnil on October 27, 2016 at 6:35am

Hi Yutaka,

some precisions: it is not possible to mesh a doubly-curved surface with equilateral triangular panels only. What you can achieve it the meshing of singly-curved surfaces (like cylinders) when 6 triangles meet at a vertex. You can create double curvature by having a valence 5 (positive curvature, like a sphere), or 7 (negative curvature "saddle shape").

Such meshes were studied by Alain Lobel in the 1980's (maybe even before that). There is a paper mentioning them in the proceedings of AAG2014. Repetition of panels is also studied here, with the use of clustering, which can be very efficient.

You can look at the SMART Clustering plug-in developped by Buro Happold, I've never tried it, but it looks interesting and maybe suited for what you're aiming for.

Best,

Romain

P.S: If you are interested in repetition, you can also look at repetition of members (e.g. constant length) or repetition of nodes. Most of the research deals with repetition of panels, but repetition of nodes could be also interesting because they are much more difficult to fabricate than panels. Two references about node repetition: one for a specific family of shapes with high node congruence , and the other on the use of hyperbolic geometry for 3-valent meshes.

Permalink Reply by Yutaka takenochi on October 29, 2016 at 3:34am

Hi Romain

Extremely thanks to your views. The Advance Architectural Geometry is very interesting while the second link did not work.

I also looked at the Smart cluster demo and very interesting too. It looks similar to the Paneling Tool, or maybe it is more advanced in optimizing the panels?

Kindest regards

Yutaka