It's quite a read, but I hope this helps.
You can use circle-packing and box-pleating to make designs but it's not the only way to go.
Let me explain. For me there are actually three ways to designs:
- Design first
- Fold first
- Combination of the previous two.
Some people exist that can draw up a crease pattern, fold it. If it doesn't look okay they will draw up a new pattern, if it is okay, there you go a new design. For me this is the first category.
Then you have the people that start with folding and rely on a vast experience of folding to achieve what they want. This is the second category.
The third is a combination of both, they draw up a pattern to see if it works. If it doesn't work they apply folds to make changes. Unfold the model, redraw the crease pattern. See where it can be improved again. Fold again. Keep repeating until satisfied.
The first category is really rare in my opinion and it's usually the third one you will end up with if you start with drawing up a pattern and then folding it.
The second one is stand alone. There are some great designers that just fold, they don't care about all of the mathematics that can be applied or anything like that.
So where should you start designing? That depends entirely on the person that is designing.
I would advise to at least know some fundamentals on the following things:
- How does one create a flap? (a nice talk by Robert Lang about this can be found here:
https://www.youtube.com/watch?v=NYKcOFQCeno)
- What is an origami base?
What fundamental bases exist? (Kite-Base, Fish-Base, Bird-Base, Frog-Base, Windmill-Base etc). How can I utilize them to create a subject I want to create?
- How does my pattern change when I apply this fold here, and this fold there?
- How would I split a flap into multiple flaps? This is called "Point Splitting".
- How can I add some extra paper to a part of my design so that I can create more details? This is called "Grafting".
- I have this nice folded shape, how can I incorporate this in my model? You can graft this part on your model for example. A technique that will come up here as well is "Tiling".
These are just some techniques to build upon something that already exists.
For example: I want to create a bird. It has one head, two wings, two legs and a tail. For that one would need: 6 flaps of various sizes. But you don't care about the legs, so that leaves us 4 flaps. Do we know of a four flap base?
Yes the Bird-Base. (it isn't called that for nothing
, it's actually 4 big flaps and 1 little flap, but it comes the most close). So we would start with that and we start folding and apply techniques and knowledge we have. For example the head of some birds is a bit smaller, so would need to shorten one of the "big flaps". We could try to split it to create a beak with a top and bottom part. Thus we try to apply techniques for splitting up points. Now we have a beak. Up next we might want to make the wings a bit bigger and add some more detail on the tail. (the other three flaps). How would one add extra paper to this? Add a graft, hence the grafting tecchnique mentioned before. Eventually with enough playing around will get something you will like.
At this point you are building upon a part that you know, just from folding experience, and you experience some new things. If you would go directly to circle-packing, or box pleating you will get into fairly unknown territory, but it is not impossible. You will come into contact with some of the following techniques:
- Circle Packing - I need 6 flaps. Since every flap can be represented by a circle, how would I pack them in my square?
- Circle-River Packing- A more general approach on Circle-Packing, with the addition of rivers. For example when you pack circles they closely connect to each other. But a human really doesn't consists of 4 closely connected flaps. We have a torso, which we can represent with a river. It's basically answering the question how can I separate these flaps with a distance X?
In both of the above techniques one would usually create a stick figure, with a length for each stick and then you try to map that stick figure to points on your paper. There are some ways for that, but that would put a lot of more text here, which I'm not gonna do.(there are books for that and some info on the internet)
The biggest drawback of the above methods is that they are really exact. You will get problems like: How should I fold this 78.4423434 degree angle. That's why usually people use techniques that derive from the above. The theory is exactly the same, but we use approximations instead, think of:
- Box Pleating - When using this technique you are restricting yourself to 45 and 90 degrees angles in your crease pattern. Flaps usually are represented by squares, but also by rectangles (a flap can consume more paper). A river is represented by a rectangular piece of paper, that can change direction. (for example an L shape is a river with a 90 degree angle change).
- Hex Pleating - Restriction to 30,60 and 90 degree angle. Crease patterns usually consist of Hexagons and Triangles or other shapes you can create with 30,60 and 90 degree angles. Rivers are a bit trickier here, but the general idea is the same.
- 22.5 Degree design - Not sure if there is an exact name for this. But usually angles are restricted to 22.5, 45 and 90 degree angles. Think of Fish-Base, Frog-Base and Bird-Base. Flaps look like Octagons, Squares and everything you can create from the before mentiond angles. These are alle bases that fall into this category.
- 11.25 Degree design - Similair to the 22.5 Degree design, but will also have degrees that are halve of 22.5.
- Mixed Pleating - Combining techniques with each other. For example one could combine box pleating with 22.5 degree design.
People can even go crazy with pentagons, dodecagons and other polygons, but the main idea is that approximations to a circle are being used. Nothing more, nothing less.
You will find quite some information about almost anything mentioned above in books or the internet, with a really big part in ODS.
I hope this gives a quick and brief overview what you can do, but the most important thing is to find the way you are most comfortable with, since there is no "BEST" way to design.