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I don't often play with it, but today I was trying to really nail down the functionality of the Honeycomb Array Mode of the Cloner object.


So I started by creating a hexagon of a nice even size (disc primitive, with axis rotated 30 degrees, although I also tried it without that adjustment). Here it is before it went in the cloner.




So then I put that in my cloner, set my modes up and wondered what sort of numbers I'd need to get a square grid of them perfectly aligned in a honeycomb, like this. 'It'll be some multiple of 10 or 20, or maybe half that value', I mused to myself...




.... some time later I chanced upon the correct numbers, which were this...




My question is, what is the relationship between the physical dimensions of my hexagon, and the Size Width / Size Height parameters required to produce perfect tiling ? I mean I know we can get there by patiently moving the values until they are vaguely right and weld them later if needed, but isn't there some formula we can apply to say the width of our cloned object to find out what exact numbers we will need here. Or perhaps I am basing stuff on the wrong measurements ?


Apologies if I am being thick, or missing something obvious, but if that is the case, I will be delighted if someone would point out what !

Or are you all setting up your honeycombs by just fiddling with numbers until it looks OK ?  :)








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Ok guys, thanks for all input so far.  I have made some progress too, and now perhaps understand what the relationships are, if not why. As it goes, the why doesn't matter so much to me. But @kingcoma was right to get me to measure the other distance, which I did below...




And now I can see a relationship between the numbers !


Check this out - Size Width is exactly half the 17.321 measurement, and Size Height is exactly x1.5 of the other (20 cm) dimension !

For some reason they are the wrong way round from what I would expect (17.321 is the height isn't it ?), but at least the numbers sort of make sense.




Or do they ? Is that right ? :) I'd better go try that on some other sizes...



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There's 2 radius


R = length of side

r = R * sqrt(3) / 2 = R * 0.866 approx


in one direction the step is 1.5 * R

other direction step is r * 2


for your obj with length 10, this equates to 15 and 17.32




square root of 3 is not an exact number



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Excellent, thanks @jed that's much clearer :) We'll call that one solved then...



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A bit more on that pesky root 3





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I know this topic is marked as solved, but you could also look into explanations of the Unit Circle, I've seen used to used to calculate a position along the circumference of a circle using divisions of Pi * Radians. 


Tim Clapham from HelloLuxx gave an interesting talk using this technique to contract a honeycomb with some Xpresso and Math nodes a few years back.


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Phil Richards, www.fugidesign.co.uk

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