How to change a flat hexagonal grid's density with an attractor ?

Replies to This Discussion

Permalink Reply by Arthur Mamou-Mani on January 27, 2011 at 3:40am

Actually any idea about how to locally change/deform a grid density while keeping the edges of the grid as they are and the grid flat would be helpful :)

Cheers,

Arthur

 

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Permalink Reply by manu on January 27, 2011 at 7:06am

A quick anwser could be use a packing circle box ( like this http://www.grasshopper3d.com/forum/topics/packing-circles-on-curved), and then put inside the hexagon.

 

The other option, (that I think you are looking for) would be starting from a very little and constant grid of triangles, and then changing the number of points that build the hexagon, depending on the distance of the point

Attachments:

• circle with hexagons.3dm, 50 KB
• circle with hexagons.ghx, 90 KB

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Permalink Reply by Arthur Mamou-Mani on January 27, 2011 at 7:48am

Thanks a lot Manu,

 

This is amazing! 

 

 

Do you think there would be a way to connect the centres of these circles together into a grid? I am trying to make a continuous pattern based on the drawing hereafter and when placing the hexagon inside the circle they are all disconnected:

 

 

 

Cheers,

 

Arthur

 

 

 

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Permalink Reply by manu on January 27, 2011 at 8:41am

To conect the circles by lines, is easy using "delanauy edges" (in mesh components), mades the more natural grid. The problem is to group the lines into hexagons, I don`t know now how is possible to done....

Suerte!

Attachments:

• circle conects.ghx, 102 KB

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Permalink Reply by Arthur Mamou-Mani on January 27, 2011 at 8:45am

Muchas Gracias Manu !

 

I have no idea how to organize delauney edges into a hexagonal pattern.

This might deserve a question on its own!

 

Cheers,

Arthur

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Permalink Reply by manu on January 27, 2011 at 9:02am

Hehehe, Also in my project I was looking for something like you ask with the hexagons, but after a lot I looked, I decided to change the design into  circles, it is easier. I sugest you start to work with the triangular grid, and the order to asocieted points to draw hexagons.

Good Luck! :D

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Permalink Reply by Daniel Piker on January 27, 2011 at 9:29am

If your Delaunay triangulation has 6 triangles around each vertex, then the Voronoi decomposition of the vertices will be made up of hexagons.

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Permalink Reply by Arthur Mamou-Mani on January 28, 2011 at 10:40am

Thanks Daniel

 

Actually the points do always have 6 triangles around each vertex :)

The hexagons are really hardly recognisable though:

 

 

I have found a cool definition from Co-de-it doing what I wanted, but when using several attractors there is a weird separation between the cells, not sure how to fix that:

 

 

I also found a great applet by n-e-r-v-o-u-s which uses springs from "traer.physics" to stretch the hexagonal grid, would you know if the same is possible with the Kangaroo's spring component? 

 

Exciting :)

Cheers,

 

Arthur

 

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Permalink Reply by Daniel Piker on January 28, 2011 at 6:48pm

Look again at your first picture - definitely not all 6 triangles per vertex - several pentagons and heptagons in there, and this is a limitation of that approach to circle packing.

 

and here's my Kangaroo take on Nervous System's applet. I think it works rather well :)

(definition attached)

Attachments:

• nervsys.3dm, 66 KB
• nervsys.ghx, 300 KB

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Permalink Reply by Arthur Mamou-Mani on January 28, 2011 at 7:01pm

Daniel,

 

You are awesome, thanks so much!

It looks even better when animated...

 

I'll start placing the pattern from the grid and will post the results.

 

 

 

Permalink Reply by Arthur Mamou-Mani on January 31, 2011 at 1:04pm

Hi Daniel,

 

Would you have a trick to bring these single lines back to hexagonal cells after the Kangaroo component? It'd be great if the lines removed from the "remove duplicate lines" could be brought back. Sounds difficult though.

 

Cheers,

 

Arthur

 

 

Permalink Reply by Daniel Piker on January 31, 2011 at 2:24pm

Rebuilding the cells is no trouble at all - that's what the Geometry Input and Output of Kangaroo is there for. Just connect the vertices from the explode component to the input, and it will be output deformed by the physics simulation but with path and list structure still intact, so you can make closed polyline cells from it

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