geodesic grid on the torus

Replies to This Discussion

Permalink Reply by David Rutten on November 20, 2013 at 6:30am

What is a geodesic grid?

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David Rutten

david@mcneel.com

Permalink Reply by Alex on November 20, 2013 at 7:27am

Figure (E) only for the torus

http://www.rwgrayprojects.com/synergetics/s06/figs/f1801.html

http://www.simplydifferently.org/Present/Pics/us-pavilion-1967-mont...

Permalink Reply by Giulio Piacentino on November 20, 2013 at 9:31am

Hi Alex

one simple way would be to start with a simple toroidal 'box model' and then to subdivide it with Weaverbird's Loop subdivision. Finally you can project it again to a torus for precision.

If you want, at this point you could equalize a bit vertex distribution by using Mesh Smooth (in the example), Weaverbird Laplacian, or some other force in Kangaroo, or even some other relaxation algorithms.

Lots of different initial primitives and/or other subdivision schemes will give several different results, and will influence the orientation of the rows that you see.

I've created this original 'primitive' with the ReduceMesh command. If you model it by hand, with a little more thought, you'll get better results.

There are surely other methods, too.
I hope this helps getting started, if you go for this idea,

Giulio

--
Giulio Piacentino
for Robert McNeel & Associates
giulio@mcneel.com

Attachments:

• semiregular-grid-torus.gh, 17 KB
• semiregular-grid-torus.3dm, 296 KB

Permalink Reply by Jesus Galvez on November 20, 2013 at 10:17am

Wouldn't this create a triangular grid on the torus? I think he wants tetrahedrons on the torus. Maybe wb stellate component after what you did would work. 

It's funny I did exactly what you did, but end up with the triangles in a quadrangular grid, instead of an hexagonal grid. In this case stellate doesn't yield the desired result. I guess it's because of the way you created the initial torus. 

Permalink Reply by Alex on November 20, 2013 at 10:45am

Giulio great thanks for help! :)