Inventing Models

[TheUnChosenOne]

How about Treemaker? Maybe it's just for noobs but still, it's useful. maybe

[TheUnChosenOne]

And it's good with circle-packing with all those nodes and all.

And I was just wondering, what's "river-packing" or whatever it's called? I don't get those at all.

[Baltorigamist]

Circle/river packing is essentially the same thing as circle packing, but there are "rivers" between the circles that represent gaps between the flaps. For another schematic:( )( )| |( )( ) The circles are flaps, and the gap between them is the river between the flaps. (The base would look like this: >-<.)

[TheUnChosenOne]

Oh I see. I thought they were something that had to do with a different type of flap or something.

[Baltorigamist]

In a way, it does have to do with a different type of flap: one that has a separation between the tree nodes and the leaf nodes in the tree. It's kind of hard to explain it, but say you have two flaps coming from the same point (e.g., a bird base). Take the root of the point (the hinge crease between the flaps) and pull it out a la Frog Base. The aforementioned points are now shorter (by a factor of 1:1+sqrt2), but there's a 1-unit river between them and the rest of the model.

(I think I have the math somewhat right, correct me if I'm wrong. I'm doing it mentally.)

[TheUnChosenOne]

I'm sorry, but I had no idea what you were talking about starting from the root of the point part.

Anyways, how would you strip-graft a frog base on a corner of a square? Because there's only one side, so you only have 2 or 4 flaps, depending on how you look at it.

[Harpseal]

I do, allthough i don't think i could apply it to anything. Also, i've made great progress with the silver surfer!

[dragon]

Can you post picture of the cp you were trying to make? I may be able to help you

Sorry,
I can't post pics yet, but what happened was that I radiated creases running at 22.5 degree intervals, and when I got to the hands and wings, the flaps weren't the lengths that I had assigned to them with the circle packing. They were meant to be different lengths, but turned out to be the same length. I tried to rearrange the creases so that they were approximately the right length, but then I started to have ~5 degree creases and the cp looked like a tree-maker designed cp.

[Baltorigamist]

Dragon -> There's no concrete way to help you without seeing what you're working on. All I can say is to make sure all the circles and rivers are at a constant width throughout the CP.

I assume a "Treemaker-designed" CP is one that has many different angles of creases and different molecules (arrowhead, gusset, etc.) If so, you're unlikely to have a proportional CP with references that lie on the 4x4 grid I think you mentioned earlier.

(And, just to let you know, 22.5deg angles don't fit on a grid. When you have a crease 22.5deg from horizontal, the elevation is always 1+sqrt2 units across for every unit upward, approximately 1:2.4143 ratio.)

[TheUnChosenOne]

Ok then. But what kind of thing would someone use a river "flap" for? I don't see any crease patterns of models with circle packing use the rivers at all!

[cowburger13]

A river in not a flap, but a space between two flaps. ex: http://langorigami.com/art/gallery/gall ... e=longneck For this design, there is a space between the head and the body. That space is called a river. Hope this helped!

[Harpseal]

Would that be like the bits that have the small flaps on on the frog base, or like the bits that support the two types of flap in the frog base? I'm guessing there must be a really good example in the frog base from what i get about circle packing......?

[Baltorigamist]

There are no rivers in a Frog Base, only circles. The corner and middle flaps have a relative length of 1+sqrt2, and the edge flaps have a length of 1. They're all fixed on the same point, though; there's no separation between the flaps.

[Falcifer]

This shows a simple CP based on a frog base which has circles and rivers.

The tree on the left shows the tree I made in TreeMaker. The relative lengths are shown at the bottom. The resulting crease pattern (drawn in ORIPA and overlaid with circles and rivers) is also shown, along with the folded form and an attempt to show the actual flaps and rivers, along with a more scaled tree (imagine it as a side view).

The basic point is that circles, which have a radius equal to the relative length of the flap, indicate flaps. From a "tree" point of view, they are branches; they terminate. 1, 2, 3, 5, 7, 8, and 9 are flaps/circles. They only contact other parts of the tree at one end of the branch.

Rivers, which have a width equal to the length of the flap/gap, indicate where flaps are separated. They are the trunk(s) of the tree. 4, and 6 are gaps/rivers. They contact other parts of the tree at both ends.
Each river is a constant width. In this case, they are the same width but, like flaps, you can have rivers of different widths.

On the tree, you can see that flaps 1, 2, and 3 are joined, but they are all separated from flap 5 by gap 4.
The river, #4, touches circles 1, 2, and 3. Although circles 1 and 2 aren't touching, the fact that they both contact the same river means that they are connected to each other.

Circle 5 touches both rivers, but no other circles, so it's a flap on its own, branching off 4 and 6.

The two rivers are touching, so they meet as well.

You can fill in the left and right middles with flaps, equal to flaps 3 and 7, which would give you the frog base. The river would now encircle flap 5.

I suggest folding the base and seeing how things compare. Mark on the paper where the flaps are and where the rivers are, then switch it to a frog base and see how the flap 5 transforms. You can see how the "river" still exists, since it separates the original flap 5 from the rest of the flaps. But flap 5 is the only flap branching off the river, so you don't see it as a river anymore, just a longer flap.

[Harpseal]

Wow. I can understand this! I could probably use circle packing in a design now (maybe? Possibly? A bit?)
That was a brilliant explanation! (Well done)
Thanks for putting up with my ignorance!