Circle packing question

[cowburger13]

Hi there,
I understand the way circle packing works, and the molecules and stuff, and I can draw a rough sketch of the packing, but I don't know how to 'finalize' it and get an exact packing and not just a rough sketch. Please help me

-Justin

[Baltorigamist]

From what I understand of circle-packing, finalizing the packing is the hardest part. There's really no way to help you without a picture of what you're doing, but the first step would be to make sure the packing is tight, i.e., no circles can move around. You should be able to get the axial and/or hinge polygons from there, and then fill in those polygons with molecules.

[cowburger13]

Well, I read ODS and can sketch a packing to make a beetle, but I don't know how to make it EXACT. Is there some hard math involved or what?

[Rickygami]

I've never done this myself, but i'd imagine for exact exactness you're going to need some algebra/trig to define the precise reference points

[cowburger13]

Darn.... I fail horribly at math.

[yevgen]

you can make a precise circle packing using a compass but you will need knowledge of trigonometry and algebra to find the exact size of the circle.

[cowburger13]

Yes! That's what I mean. I don't know how you find out the exact size of the circle, but that's what I meant. I know the basics of trig, but not a lot of algebra. Can someone with an understanding of this help me? (bugfolder,anermak,falcifer....)

[ftangdude55]

To find the exact sizes of the circles, I think the best way to do it if you're just using a paper and pencil would be to just draw up the pattern real big, and then measure the radius of each circle with a ruler, being as exact as you can be. Then just divide the radius by the side length of the square, and you've got the circle radius relative to the square size.

In terms of finalizing the CP, it's really quite arbitrary; you pretty much just have to choose what circle sizes you want, and then just go with it.

I don't think my advice will be much help, but from my limited experience with circle-packing it's just a lot of trial and error

[Baltorigamist]

Depending on how complex of a pattern you're willing to go, the bead-and-string method described in ODS should work pretty well as long as you contain it to a square. If you can get the optimal lengths from Treemaker, pin the string to the square, and that'll give you the vertices. From there, fill in the axial creases, and fill the axial polygons with molecules.

[cowburger13]

bead and string method? Which chapter is that in?

[cowburger13]

Here is an example of what I'm talking about. The author draws a sketch of the packing, and if he like it, then he does 'math' to get the packing exact. He actually commented: "I draw circle packings alot but I only do the math when the circle packings look promising." What is this math?