Grasshopper

algorithmic modeling for Rhino

# Uniform tiling of a circle

Been googling on this for a bit to find that most packing problems are concerned with getting as many circles as possible into given shapes.

I'd like to do the reverse and pack triangles (polygons) into a circle. I need:

- the edges to be the same lengths as much as possible
- a symmetry, either axial or radial (latter preferred)

I need to be able to set circle diameter and edge lengths with sliders.

I'm using Daniel's MeshMachine and tend to get results like these:

The bottom one has some symmetry I suppose, but what I want is more like this, the only positive result I have managed to achieve:

I struggle to make Kangaroo help me produce several possible solutions to choose from.

How would you do it?

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### Replies to This Discussion

Hi Duncan

small mesh but correct topology> subdivide>pull naked vertices to circle

Then you can play whether you want 7-valence vertices or not, and where do you want them.

the file

Attachments:

Many thanks.

Results tend to be extremly hexagonal looking. To remedy, I've been trying to do this not on a disc but on a fifth or third pizza slice, and then array polarly. Not too successful.

Do I HAVE to use anchor points? Why can't I just tell Kangaroo to use only the circle to pull to, and increase faces dynamically depending on the edge length slider I give it?

It's not clear what you're trying to accomplish. It sounds like you are looking for a periodic tiling that can be perfectly inscribe in a circle? Mathematically I don't think this is possible with a single triangular tiling.

You can create a repeating pattern and test for inclusion within a region...

Here's some more of my own attempts that I hope will make clear what I'm after.

All of these have a 'hole' in the middle which I don't want, and the edge lengths are too different.

You can also see the anchor points I had to give. Using just a boundary curve doesn't work and the mesh is sucked up immediately. Why is that?

Ideally, I would not want to use anchor points. I want Kangaroo to choose their position and number for me. How?

From a regularized grid you can see the deformation required to conform to a circle. Below is a K2 setup but the results are similar to what enrique has already produced...

by June Lee

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