GH Tesselation Challenge

[Simon_Vorhammer]

Dear Grasshopper Community,

Does anyone have an idea how to create this type of tessellation in Grasshopper? It’s probably a simple one - or at least it looks like it should be!

I’m starting from a hexagonal grid (either NGons or polylines) and would like to transform it into this tessellated pattern. I think it might be related to Doo-Sabin subdivision, but I’m not entirely sure.

There’s a component in Mesh+ that seems relevant, but I haven’t managed to get it working as intended.

Any tips or guidance would be greatly appreciated!

[Joseph_Oster]

@Simon_Vorhammer

It’s probably a simple one

You lost me right there. And didn’t post a GH file.

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[laurent_delrieu]

Hello
you can look at these discussions
Blending Delaunay and Voronoi : Lines
Crochet-blending-between-delaunay-and-voronoi, Idea from Entagma Crochet – Blending between Delaunay and Voronoi – Entagma
and
Blending between Mesh and DualMesh

I implemented something quite similar in Nautilus.

Require Nautilus plugin and License
triangles to hexagon quad tri.gh (13.3 KB)
To be placed in LDLIB.dll directory or one folder upper
NautilusLicencesEvaluation.xml (22.8 KB)

[martinsiegrist]

Weaverbird has a bevel mesh edges component which could be used as a start…

[Joseph_Oster]

This isn’t correct (yet) and definitely isn’t “simple”

[leopoldomonzani]

tesselation.gh (20.9 KB)

[leopoldomonzani]

tesselation a.gh (28.9 KB)

[dk2079]

I am not sure what exactly your plan for applying this pattern is from your posting.

why not draw this by hand and array it, and remap it from 2d to whatever target 2d/3d geometry you want to apply it to?

I could imagine you want to use a ‘3d’ hexagonal grid structure as input and generate the tesselation ‘on the fly’ in 3d space.

maybe this helps.. I believe this should work with any hexagonal pattern as long as it has shared(identical) points.
tesselate.gh (35.6 KB)

(the polyline node in GH closes even lines (i think it shouldn’t), so you get duplicates when you bake. can be filtered out with more code. see .gh file)

[Joseph_Oster]

Oh, look, it’s so simple