P-Hex mesh starting from mesh (instead of a surface)

Hi,

I am looking to designing something like this where the hexagons are planar:

I did this one in the crudest way by using the project component with an hexagonal grid as the curves to project, and a mesh (the bubbly things) as the brep to project onto.

I have been able to create a Planar Hexagonal Mesh (P-Hex mesh) by starting from an initial surface component and doing iterative processes in Kangaroo. But here the initial component is a mesh, so my definition to create planar hexagons doesn't work.

Any ideas on how to procede? Thanks!

Replies to This Discussion

Permalink Reply by Daniel Piker on April 10, 2013 at 4:14pm

As your surface has some anticlastic curvature, it is impossible to cover it with hexagonal panels that meet the 3 requirements of being watertight, convex, and planar. You can choose any 2 !

If you choose to let the hexagons be non-convex there are some interesting shape possibilities, though I do wonder about the practicalities of fabricating and joining such panels in many materials.

(See this thread for some more on this : http://www.grasshopper3d.com/xn/detail/2985220:Comment:242949)

Permalink Reply by Jesus Galvez on April 11, 2013 at 1:54am

Thank you Daniel, I wasn't aware of that. But I still have the same problem. You see the problem is that usually definitions that have to do with creating 3d meshes, start from a Surface component. Whereas my initial component is a mesh; so any 3d meshing definition I would apply wouldn't work.

I don't know if first I have to convert the bubbly mesh into a single surface (or to that matter if that's even possible), or if it's possible to apply a 3d meshing definition to an initial mesh instead of a surface.

Bellow is the wireframe display of the bubbly mesh, and the definition I did to planarize polygonal grids starting from a surface.

Permalink Reply by Daniel Piker on April 11, 2013 at 5:06am

http://www.nieser-berlin.de/research/bib/2010_NieserPalaciosPolthie...

Here's a description of an approach to hexagonal parametrization, developing from the work with quads I was mentioning here (http://www.grasshopper3d.com/forum/topics/nurbs-quads?xg_source=act...)
However, your problem is essentially one of remeshing, and if you are okay with the occasional pentagon and heptagon, you don't need to find a full parametrization. You can work on getting a nice triangulation, then take the dual.
However, this still doesn't solve the planarity issue...

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