Planarity in polygons with more than 4 vertices

Hi there,

I'm currently trying to make a relaxation process for plate structures (polygons), using different kinds of forces. But one important thing is keeping all polygons planar, no matter how many vertices they have.

For hexagons, I tried using three planarity components, which worked but looks kind of ugly. I also know that in maya I once saw pentagons, which automatically stayed planar by applying springs between opposing vertices, maybe that's another method.

Replies to This Discussion

Permalink Reply by Daniel Piker on March 23, 2011 at 2:31pm

Hi Oliver,

I've just recently added planarization for polygons of any number of edges, and it is working nicely.

I will post the public release soon.

Permalink Reply by Oliver David on March 23, 2011 at 2:46pm

Awesome! Thanks Daniel!

Another idea: What about being able to set the bending restrain to a specific angle?

Cheers,

Oliver

Permalink Reply by Mårten Nettelbladt on March 23, 2011 at 3:31pm

Hi Oliver,

I believe this is also added in the next version:

http://smartgeometry.org/index.php?option=com_community&view=gr...

Mårten

Permalink Reply by Oliver David on March 24, 2011 at 5:43am

thats just amazing! I'm so much looking forward to the next release!

Permalink Reply by taz on May 15, 2011 at 11:03am

Hi Daniel,

Is this on the street yet?

I think with a dualized tri mesh it would be fun to planarize the hexes to model this...

Although from the looks of it there's still a bit of fishscaling going on. I believe the panelization was done by GT.

Viva la mexico!

http://www.dezeen.com/2011/04/28/museo-soumaya-by-free-fernando-rom...

Museo Soumaya by FREE Fernando Romero EnterprisE

Permalink Reply by Daniel Piker on May 16, 2011 at 2:49am

Hi Taz,

I'll try and get a release of this out in the next few days.

By the way, Daniel Davis recently shed some interesting light on that project:

http://www.grasshopper3d.com/forum/topics/kmeans-1?commentId=298522...

From the little I've played around with it so far, it seems that the surfaces which can be tiled watertight by planar convex hexagons are quite tightly constrained. I believe more interesting things are possible if you allow the hexagons to become non-convex in regions of negative gaussian curvature, but I've not tried this yet.

To tile surfaces with genus≠1 also needs some non hexagonal faces (heptagons, pentagons etc) and how best to place these is a really challenging question. As you suggest though, it is sometimes easier to tackle this issue of the singular vertices on the triangular mesh and then dualize it.

Permalink Reply by taz on May 16, 2011 at 10:44am

I'll have to see what Daniel was up to... Thanks for the link.

By "non-convex" do you mean "concave"?

This is a link with some construction images and GT screenshots. I think that's where I figured they were using a triangular base mesh since the substructure is all triangulated.

http://www.designboom.com/weblog/cat/9/view/11789/soumaya-museum-by...

Permalink Reply by Daniel Piker on May 16, 2011 at 11:15am

Non-convex like this:

From Wenping Wang and Yang Liu's paper:

http://research.microsoft.com/en-us/um/people/yangliu/publication/a...

Permalink Reply by taz on May 16, 2011 at 5:50pm

Ah yes, they work with Pottmann...

Permalink Reply by Iain Blampied on September 6, 2011 at 1:00am

Hi Daniel,

I’m also really interested in using the Planarity component with hexagons, did you get a chance to release an example of this? I can’t seem to work it out myself.

Cheers

Iain

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