Tiling circle pattern

[RealNum]

Hi all,

I'm trying to tile a pattern of circles arranged at each corner of a hexagon. Except that a hexagon does not have the same width as height, and I find myself with a ratio of  cos(pi/6)≈0.866 that I can not tile properly. I stretched the pattern using a Transform 2D node with the above expression in a scale matrix, so it is perfectly tileable, but i don't have circles anymore. How can i achieve the desired effect ?






My client want me to create a substance where he only have to tell a number of holes in X and Y, the percentage of perforation and he gets the right result in one click, i got a headache !

[Nicolas Wirrmann]

here is a test:


It's basically a Tile Sampler node where the pattern size is driven by the number of pattern (to avoid stretching).
The circle scale could also be exposed.

[michael_11]

nice

[RealNum]

Thanks for the reply,

That's a good start, but the thing is that i need an equilateral pattern, like below



My first thought is to find some X and Y amounts that approach the 0.866 ratio, but i need to find an expression to drive let's say the Y amount according to the X one and to keep that ratio with integers. It will not be perfect, but well, that's just for imagery, not production.

[Nicolas Wirrmann]

You need to find the best X/Y ratio that corresponds to 0.866 but the Y number must be even in order to keep the tiling aspect of the pattern.

Given this restriction, it appears it does not make sense to expose the number of pattern because very few pair of X/Y correspond to the constrain. 14 * 16 is a good candidate.

Edit: 26 / 30 = 0.8666

[RealNum]

Yeah i think i will go with those numbers. It makes a bunch of disks but it fits the best.