planar polygons by using kangaroo

Hi all,

I can't find my way out when I try to planarize the polygons by using kangaroo. I was trying to achieve something similar to

How to create planar Honeycomb Shells using Kangaroo.

Seems after applying planarize force, the polygonal faces become very deformed.

And I've also looked at the Daneil Piker's definition here, which helps. However I would like to keep the planar polygons as close to the original overall shape as possible. I've also tried to set a force by pulling the points to the original shape, but seems couldn't help. Is it about setting the right forces?

Please find the attached file.

Thanks for any help!!

Attachments:

planarization.gh, 21 KB
planarization.3dm, 60 KB

Replies to This Discussion

Permalink Reply by hurriarc on December 17, 2013 at 9:38am

anyone could help?

Permalink Reply by Daniel Piker on December 17, 2013 at 10:25am

Making the faces of a polygonal mesh planar is not always possible without dramatically changing the shape of either the polygons or the surface.

When the target surface has only positive Gaussian curvature it makes things somewhat easier, but the surface in your file also has regions of negative Gaussian curvature.

To approximate a surface of negative curvature with a discrete mesh, we need the angles around some of the vertices to sum to less than 360°. This is impossible to do in a mesh with 3 hexagons around each vertex without making some of these hexagons non-convex.

There are a few possible approaches, but I would say how to automatically cover an arbitrary surface with nicely shaped planar hexagons is still an unsolved problem.

Permalink Reply by hurriarc on December 20, 2013 at 11:07am

Hi Daniel,

Thanks for your reply. I see the limitation now. When I modify the surface to only positive Gaussian curvature, the result of the planariztion is better.

Will keep looking into it

Permalink Reply by ng5 Alex on December 17, 2013 at 10:44am

hello hurriarc

you can study this interesting topic http://www.grasshopper3d.com/profiles/blogs/planar-hexagons-on-doub...

Permalink Reply by Rodrigo Medina on December 19, 2013 at 3:24pm

Hello , So I´ve just made a tutorial about this last week you may want to give it a look to see if it helps.

Cheers!!

http://designplaygrounds.com/projects/how-to-create-planar-hexagons...

Permalink Reply by Rodrigo Medina on December 19, 2013 at 3:25pm

However I´m not sure if this is the best way to go if you are looking for double curvature surfaces with convex and concave parts

Permalink Reply by hurriarc on December 20, 2013 at 11:09am

Thanks Rodrigo,

I did looked at your tutorial, but as you aware, i was testing on a double curved surface, which hit the limitation. I'm trying to find a solution still.

Permalink Reply by hurriarc on December 20, 2013 at 12:20pm

Hi Rodrigo,

I followed the tutorial,and understand the principle fully.

I tried the same definition as you set up in the tutorial, on a positive Gaussian curvature surface. However, something still went wrong.

Could you help me out?

Thanks

Attachments: