triangulation using only equilateral triangles?

Hi,

I'm trying to figure out a way to model objects using only equilateral triangles, with triangle edges touching (no gaps.) Ideally I'd like to be able to manipulate the shape by moving vertices and having the entire surface adjust while maintaining equilateral triangles. The closest solutions I've come across are the equilateralize and shell and plate examples for Kangaroo (images below), but I don't think the definition in the equilateralize demo will work because I don't always want 6 triangles around each vertex (I want a range from 4 to 7.) The shell and plate example seems more promising, but when I open it in rhino/GH it says the C# component is old, and the code is missing. Also, the shapes I'm trying to model are much less spherical than the mesh in the demo, so I'm not sure if that method will work anyway. I'm also posting an image of some physical models that show what I'm going for.

Any advice would be much appreciated!

Replies to This Discussion

Permalink Reply by Rebecca Rusinow on March 16, 2014 at 7:07pm

by the way, here are the demo files:

Attachments:

Permalink Reply by Rebecca Rusinow on March 16, 2014 at 7:11pm

last demo file:

Attachments:

shell_and_plate_example.gh, 9 KB

Permalink Reply by martyn hogg on March 17, 2014 at 2:04pm

Similar threads have appeared on this forum looking for ways of panelling surfaces using only hexagons and pentagons but trying to keep the hexagons and pentagons regular.

I'm not sure, but this seems to be impossible for many surfaces because constraining the solution to only regular hexagons, pentagons or, in your case, equilateral triangles restricts the possible curvature and change of curvature too much.

It works for geodesic domes sort of... the base shape of a geodesic dome is an icosohedron - a 20 sided shape made up of 20 equilateral triangles. When you sub-divide these triangles and project the points out onto a sphere, they are no longer equilateral triangles.

How important is it that your triangles are equilateral? Can they be nearly equilateral? You might be able to use something like the hexagrid techniques that project hexagons onto a surface but I think this is not going to be good enough for what you want to do.

Are you trying to manufacture your models and simplifying the process by only using identical equilateral triangles?

Permalink Reply by Daniel Piker on March 17, 2014 at 2:10pm

This looks very much like the recent question answered here:

http://www.grasshopper3d.com/forum/topics/folded-plane-subdivided-i...

Permalink Reply by martyn hogg on March 17, 2014 at 2:58pm

so, in order to answer all the hexagon surface requests, can kangaroo remove mesh triangles to leave hexagons and pentagons? :)

Permalink Reply by Daniel Piker on March 17, 2014 at 3:31pm

do you mean like this:

http://www.grasshopper3d.com/forum/topics/skeletal-mesh?commentId=2...

Permalink Reply by martyn hogg on March 17, 2014 at 3:42pm

maybe

Permalink Reply by Firat Aydin on January 9, 2018 at 6:51am

Hello All;

I am trying to divide a single curvature surface into equal sized triangles.

There are projection curves over the surface - they are my purlins actually. and baseline of the triangles must follow the purlin curves and they must be equal siezed.

can any body help me with it?

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