Designing with circle packing

[satoshifan]

How is it done? I can design models based on box pleating, but that doesn't seem to be working for everything. For one thing, I can't make those many-pointed heads like kamiya's dragons/pheonix, and models like a griffin have horrid-looking pleats running down the sides. So once I've packed in all the circles, how do I devise a crease pattern from there?
From people who have designed their own models by circle packing before, please give examples and explain the thought process that went into it. Thanks in advance.

Satoshifan

[origamipete]

if you have the circles in place, mark their centres, connect those points together and this should give you a pattern of polygon shapes. then you make angle bisectors in these polygons and that gives you the basic structure of the crease pattern. then you are free to fold. when you collapse your crease pattern, you may want to sink certain areas to get narrower legs/neck/tail for example, but that's simple to do for someone whi has experience with boxpleating already =)
I haven't done many models using circle packing, boxpleating works fine for me, but I can show you something in regards of circle packing here:'
http://palaeorigamipete.deviantart.com/ ... -294621329
http://palaeorigamipete.deviantart.com/ ... -295112429

[satoshifan]

Wow thanks for the quick reply!

So what I did was I went through my collection of origami books, and as I expected, I had a copy of R. J. Lang's design secrets book (second edition) which I had, like an idiot, folded all the instructions and most of the crease patterns, but read nothing. Going through it I read the chapters on circle packing, molecules, and tree theory. So from what you said, I could have worked it out. But what happens when some of those quadrilaterals don't meet some specific requirements? Simply bisecting won't work. If it did, that would be a "waterbomb" molecule. (If a river goes through it, it's a sawhorse molecule, but really the same thing) When "waterbomb" molecules won't work, it has to be changed to either an arrowhead or gusset molecule. The arrowhead molecule is mostly asymmetric (on it's own), however, if you have two of them, it's technically symmetrical. Generally a gusset molecule, which seems to be generally the best (like elimination for solving for x and y given two constraining equations with both variables), will work, but in some cases, like R. J. Lang's Silverfish, you want the arrowhead because it gives narrower flaps. Triangle flaps will always just work with a rabbit ear.

Now I know I started by asking for help, but I figure that since the thread is now effectively over and it was missing the previous information, I might as well add it for any aspiring designers who come here to find out how to circle pack and run into a dead wall when the fold that "water bomb" molecule that will fold flat, but won't line up the tangent points (meaning that when you try and manipulate the flaps, one or more of them will react differently and may restrict you from doing what you want with it).

So good luck to anyone who wants to use circle packing, check out my gallery to see what I've done (once I get a chance). Thanks for reading this!