Godidody
Godidody
When drawing a tree to design a model, you might notice that there are flaps attached to one vertex, but there are also flaps attached on both vertexes (both ends of the flap are attached to other flaps). When one flap is attached to another flap on both ends, it is called a river. The more you start drawing crease patterns and trees, the more you will realize how common rivers are. They appear almost everywhere, most commonly from bodies, all the way to necks and even arms and legs.
As an example, you'll commonly see rivers that look just like flaps, but instead hold two or more flaps, like this:
Too implement rivers, you'll first need to understand some basics about rivers. On a crease pattern, a river is just like a real life river. They snake around on the paper, and do not cut off. Rivers must either enter and exit the paper from the edges, or it must flow back into itself. Rivers are always a certain width, and it cannot change. Rivers only can turn at 90 degree angles. That said, if I wanted to implement a 6 unit river into a crease pattern, it will look like so: (the river will be highlighted in yellow)
The river, in this case, flows straight. Any crease lines would just run straight through it. However, if I wanted the river to bend and go down and exit the paper that way, it should look like this: (the arrow represents the direction of the river)
As you can see, a new diagonal crease appears whenever it changes direction. You're probably starting to see where this is going; rivers can bend and start in different places to accommodate for the shape of different flaps packed in a crease pattern. Here's what it would look like if I were to put a river in the middle of a crease pattern to separate two sides of a paper. The tree is shown on the right.
Initially, this concept may seem difficult to grasp, but with enough examples, you'll probably be able to see the patterns between the crease patterns. Here are a few other examples:
