Origami design process – Part 2


Post is a part of a larger series (Design process):

This blog post is intended to be a sequel to the Origami design process (introduction) blog post. But my true intention was to make a blog post that would serve as a comprehensive guide on the origami design process. You see, I have already written numerous posts on the topics concerning various details important to the process itself. So, for a thorough reader, most of the needed information is already there, readily available.  Nevertheless, I find it necessary to write a blog post that would serve as a guide through all of those posts. 

Simple example

Let’s start with an example.

In this blog post, I chose to demonstrate basic principles using a very simple yet interesting model (figure 1). Model is known as a “Cloud Strife” from Final fantasy VII, but I like to call it a “Little warrior”. Unfortunately, I have to admit that the model is not mine. It was designed by Juanfran Carrillo (@JuanfranCG).

Original post with this model could be found on Twitter: https://twitter.com/JuanfranCG/status/1254667874326712327

"Cloud Strife" from Final fantasy VII (Little warrior)
Figure 1: Little warrior

So, even though the model is not mine, I will use it anyway for various reasons: 

  • First of all, I have to admit I really like this model. 
  • Second, the model itself is exceptionally simple, so even an absolute beginner can fold it in a matter of minutes.
  • Third, the arrangement of various origami elements on its crease pattern is sufficiently out of the ordinary, so even a reader with basic knowledge can find it attractive and worth studying. 
  • Fourth, the model itself is not symmetrical. 
  • Fifth, the model, despite its simplicity, implements various interesting approaches. For example, it employs a central fold opening procedure.
  • Finally, the model is designed using a Box pleating method, which is in line with my firm belief that origami newbies should try to learn this technique first.

In figure 1, you can see a final result –  a “little warrior”. It is obvious that like any other human figure, the “little warrior” poses a head, two legs and hands and a body. It also has a long sword.  Above that as a special feature, the “little warrior” has recognizable hair. And that is more or less it.

Stick figure

Ok, let’s start with a stick figure, since most origami design processes start with a stick figure. This statement is not entirely correct since this is not true for various 3D origami models (e.g. Voronoi origami, architecture origami, so-called rigid models or tessellations). But for the classical models having a tree-like structure (humans, animals, bugs etc.) this statement holds.

So, “little warrior’s” stick figure is shown in figure 2. As you can see, the stick figure is simple. It has only nine flaps and only one river.

"Cloud Strife" from Final fantasy VII (Little warrior) - Stick figure
Figure 2

On the left side, you can see a stick figure that is rearranged in a way that better resembles a human figure. On the right side is the same stick figure, but this time it is stretched in all directions to simplify further analysis.

Crease pattern

Next step is to develop a crease pattern.

But before we start, it would be wise to say a few words about the connection between flaps and circles. You see, every flap on a stick figure, and in this case we have nine of them,  must be represented by a corresponding circle on the crease pattern. In other words, how many flaps we need, that many circles of appropriate size we have to pack on a square piece of paper.

In figure 3, you can see such an arrangement. On a square piece of paper, there are nine circles. Larger circles represent larger flaps that will form legs, arms or a sword, while shorter ones represent flaps that will form strands of hair.  Here I would like to point out that the sword is quite long, and as such, it is made out of two parts. In other words, two circles are needed to form the sword.

Of course, these circles must be next to each other on a crease pattern (figure 3), since both sword’s parts obviously must be connected on the final model.

Further reading: Origami and circles.

Please, be aware that Box pleating method assumes that polygons do not overlap. Again, this is not completely true since only circles inside the polygons are not allowed to overlap, while polygons itself can overlap, but in that case, a quite advanced technique known as Pythagorean stretch must be used. But do not worry, our simple example does not use a Pythagorean stretch technique, meaning there are no polygons that overlap, making this example a classical one. 

But, if you want to know more and to learn what is a Pythagorean stretch technique, and how to implement it, feel free to read a blog post on Pythagorean stretch.

"Cloud Strife" from Final fantasy VII (Little warrior) - Circles and polygons
Figure 3

If we analyse a crease pattern in figure 3, we will see that the circles’ arrangement is a really interesting one, since it is not symmetrical. But on the other hand, if we compare this arrangement with a stick figure (figure 2B), it is not hard to see that all of these long flaps originate from the single point (point A). Meaning, all of them must be next to each other on a crease pattern. And they are next to each other for sure. Look at figure 2.

What is also interesting to realise, is that the head and the upper part of the body are represented by the river. What’s more, the river separates the circles that represent hair from the rest of the model. But then again, this is perfectly OK, since the hair should be on the head. Or, in other words, the head should separate the hair from the rest of the model. Won’t you agree?

For those who want to learn more on this topic, I would recommend reading the following blog post: Relationships between basic elements of an origami model

Now that we know where the polygons are, we can proceed further and develop a complete crease pattern. That means that we have to define positions of all basic creases as well as their orientation. That means that first, we have to define the positions of all hinge, ridge and axial creases (figure 4). With this in mind, I would strongly advise you to read the following blog posts:

Further reading:  

Hinge crease,

Ridge crease,

Axial crease

"Cloud Strife" from Final fantasy VII (Little warrior) - Crease pattern (Phase I)
Figure 4

What we have to do now is to define the orientation of all creases. In other words, we have to define if a crease is a mountain or a valley. 

Remark: There is some kind of an unwritten rule that all mountains are marked in red, and all valleys are marked in blue. So, here we will stick to that convention.

The easiest way to initiate the whole process is to start with the axial creases. In this particular case, the decision to start with axial creases is obvious. You see, in this model, there are no advanced elements such as level shifters, so we can be pretty sure that every other axial crease has to be a valley or a mountain. In other words, we only have to decide the orientation of the first axial crease. The rest should be easy since every other axial crease has to be differently oriented (look at figure 5).

"Cloud Strife" from Final fantasy VII (Little warrior) - Crease pattern (Phase II)
Figure 5

Next step is to define the orientation of all ridge creases. Again, since the model is a simple one, the process is a simple one as well.. You see, since there are no level shifters or Pythagorean stretch elements, all ridge creases run at a 45-degree angle.

Now, before we start with ridge crease orientation assignment, few rules or guidelines are in order. I have used the word “guidelines” on purpose because if you apply these rules or guidelines, you will get a proper ridge crease orientation. But be aware that the orientation you are about to get is by no means the only possible. It is possible to orient the ridge creases differently and still get a feasible crease pattern. But, for those who just started to learn origami, I would strongly advise you to stick to these rules since it will make your life easier. Later, when you gain more experience, you could try different approaches.

So the guidelines are as followers: 

  • Whenever a ridge crease intersects an axial crease, it changes orientation;  meaning, on one side of the axial crease the ridge crease has to be a valley and on the other side a mountain. 
  • Whenever a ridge crease changes direction, it’s orientation stays the same. 
  • Two ridge creases cannot intersect. If they encounter one another, they have to bounce into the opposite direction. This rule is important because it will force the ridge crease to change direction in the centre of a circle and as a consequence ridge crease orientation in the middle of the circle will stay the same.

If we implement all these rules, we will get the crease pattern as one shown in figure 6.

"Cloud Strife" from Final fantasy VII (Little warrior) - Crease pattern (Phase III)
Figure 6

Finally, what is left, is to define the orientation of all hinge creases. Unfortunately, the theory behind hinge crease orientation is substantially more complex. Problems arise from the fact that not all hinge creases are present on a crease pattern since crease pattern definition is for the most part governed by the flat-foldability rules. But do not worry, quite extensive explanations are available in the following posts:

Crease pattern and

Maekawa-Justin and Kawasaki-Justin theorems are not enough.

Also, I strongly recommend you to read a blog post on Hinge crease again. Believe me, you will find it useful.

Ok, let’s assume that now you know how to define an orientation of all creases on a crease pattern (Figure 7). It is not that hard.

"Cloud Strife" from Final fantasy VII (Little warrior) - Crease pattern
Figure 7

Collapsing

Now, the fun part. Collapsing the crease pattern and folding the final model. 

I would suggest trying to fold this model on your own. It is sufficiently simple, so even if you are an absolute beginner, you should be able to do it in no time. But if you feel you need help, feel free to read the blog post on How to Collapse Box Pleated Crease Pattern? This particular post is quite long, but I believe it will give you a good insight into the whole collapsing process.

But before you begin, let me give you a tip. You see, if you analyse a crease pattern in figure 7, you will see that the central horizontal crease is missing. The reason is a simple one. It is missing only to facilitate the collapsing process. You see, this simple model has two central flaps (represented on the crease pattern with two central circles), that according to the collapsing theory, should be folded first. But the problem with central flaps is that they are hardly ever free. In other words, if we want to free them, and we certainly want, then we have to open the central crease that connects them. I am aware that the last few sentences sound a bit vague, but if you read the post Can central flaps be free? everything will be much more understandable.

Ok, I hope you are going to make it. I hope that you will be able to collapse the crease pattern in figure 7. The final result should look like the one in figure 8.

"Cloud Strife" from Final fantasy VII (Little warrior) - folded base
Figure 8

Next step is the interesting one. What we have to do is to close the central horizontal crease, while at the same time we have to open the central vertical crease. When we open this new central crease, the model will start to take a final shape (look at figure 9).

"Cloud Strife" from Final fantasy VII (Little warrior) - folded base
Figure 9

I can almost hear you wondering: how am I supposed to know that? Well, the truth is that this comes with the experience. The problem with the crease pattern is that it represents a base, not a final model. What’s more, in this particular case, the author of the “little warrior” has decided to show some kind of middle phase in the model base development (figure 7). If for some reason he had decided to provide the crease pattern that represents a more advanced stage of the base development, specifically to show a crease pattern that is the result of central vertical fold opening, the crease pattern would look quite differently (figure 10).

"Cloud Strife" from Final fantasy VII (Little warrior) - Crease pattern and stick figure.
Figure 10

As you can see, an additional river appears, effectively making legs shorter but in some time making the body longer. But, what is particularly interesting is that as many as three additional short flaps in the middle appear as a consequence of this move. Fortunately, all these three small flaps are buried deep inside the model virtually becoming invisible. Nevertheless, they are there.

Why this crease pattern rearrangement, due to the central fold opening, has accrued is explained in detail in the blog post Why is central fold opening so popular?

Now, only what is left is to make a few additional folds to get the final model (figure 11). I believe you are going to be able to do this on your own.

"Cloud Strife" from Final fantasy VII (Little warrior)
Figure 11

Conclusion

I hope I have managed to shed additional light on the origami development process. But if you are an absolute beginner and if you need more in-depth explanations of the whole process, I would suggest enrolling into the Origami introduction course on Teachable learning platform (first four lessons are free).

Note: The official name of a course is Origami – Polygon packing method. But, don’t be mistaken, Polygon packing method is just another name for Box pleating method.

https://abrashi-origami.teachable.com/p/origami-polygon-packing-method