There are few articles explaining the process of designing new origamis. Hideo Komatsu wrote one in 1999 for Tanteidan Magazine No. 58. Since that issue of the magazine has become difficult to obtain, he was kind enough to publish a new, annotated version on his website in 2016 (in Japanese).
The process he describes allies aesthetic considerations –illustrated with perspective views of his models, with technical considerations –illustrated with Crease Patterns. He details the evolution of a horse model through several iterations. I would like to analyze here the last step of this evolution, using Origami Draw.
In this last step, he takes his previous version of the horse and sets out to increase the size of the hindquarters for a fuller aspect. He starts by reducing his previous CP to a limited portion of the paper (Fig. 8). Here, we will use three quarters of the side:
His previous version (Fig. 7) was made of two interlocking bird bases. The smaller one is encased in a corner of the paper. The size of that corner can be found with a kite base:
If we include the structure in the opposite corner, we can actually see what is called a little bird base (in red):
The larger bird base could have been encased in the square opposite the smaller one, with no overlap. Instead, it is enlarged and encroaches on its neighbor. The easiest way to find its size is from the outside, using the fact that the entire design is based on 22.5-degree lines:
From these elements, we can now draw the entire CP:
That was version P-2.5 of the horse. What he wants to do with the next version is to enlarge the smaller bird base, which forms the hind legs, without modifying the larger one. On his Fig. 9, we see that he mirrors the triangle making up the rump of the horse and builds the smaller bird base around its tip:
This defines the new size of the paper. We can then draw the rest of the CP:
Quite amazingly, the new design is still made of 22.5-degree lines. Moreover, the new bird base occupies exactly a quarter of the new paper size:
This means that it is quite easy to build this new CP on a fresh piece of paper. We start with the smaller bird base and get the size of the larger one using bisectors from its center:
In return, there is no longer a little bird base to define the size of the head. However, there are many different ways we can propagate all the references we need from what we already have. For example, we can start from this line parallel to the diagonal:
From there, we get the whole structure of the CP:
We can complete the CP using perpendiculars, angle sections, and mirror lines:
As Hideo Komatsu says in his conclusion, he couldn’t have designed this model straight with the right proportions. The way the two bird bases interact with each other is pretty complex and it is a little miracle that everything falls in place with only 22.5-degree lines. It is a beautiful design that can only be fully appreciated by deciphering its CP. We are grateful to Komatsu-san for letting us see his design process in action.