Treemaker Troubles

I spent the last two weeks studying the Mathematics of Origami at Harvard. There, I made many great friends, saw many new things, and learned about concepts that I had never heard about before. However, this post will be about my final project.

Treemaker is very helpful because it does all the math for you—until it does not. For my final project, I wanted to use treemaker to help me design an evangelion (eva) [1.0] from the anime “Neon Genesis Evangelion.” Basically, a giant robot. I was ultimately unsuccessful, but the project taught me a great deal about the challenges and conveniences of applying math to artistic design.

1.0 an Evangelion

I started this project knowing a little background about treemaker. I knew that people rarely use treemaker to design origami models, but use it to do “rapid prototyping” instead. Rapid prototyping is exactly what it sounds like: rapidly going through different prototypes to see what works and what doesn’t. I was unsure of why treemaker was so unpopular for artistic design, but after a series of not-so-rapid prototyping, I understood why.

I also knew that treemaker was terrible for box pleats, so details like fingers and the face would be difficult. However, I could get around that by using strip grafts after the basic structure was created in treemaker. Strip grafting is a technique that inserts detail without affecting the rest of the model’s structure. The diagram [2] below shows an example of how strip grafting is done.

2.0 a strip graft example from Robert Lang’s Origami Design Secrets (ODS)

My decision to use strip grafting to create fingers have two weak conditions (these conditions can be ignored, but you will be ignoring elegance as well):

1. the arm flaps are on the edge/corner of the paper
2. there is few other flaps blocking the path connecting the arm flaps. (only applies if arms aren’t made from corners) [2.1]

2.1 Node 4 is bad because it is in between the arm flaps, which interferes with strip grafting

After going through a series of not-so-rapid prototypes, I understood why treemaker is limited to prototyping. After burning through eight different prototypes, I found only one pattern that I liked [3.0]. The rest were discarded due to paper inefficiency (circles do not cover much of the paper), inconvenient arrangement of flaps (, inelegant molecules, strip graft conditions, etc.), and inappropriate width of flaps (translates to extreme thickness in folded version.

3.0 attempt #4

Although the flap lengths and arrangement is what I wanted, the angles between folds are irregular. This means that the flaps will not line up in the folded result, and that the folding process is difficult because you must first locate all the points. However, I noticed that all the angles were very close to multiples of 30o, so I decided to try that [3.1].

3.1 More equations than variables? Uh oh..

Treemaker seems to struggle when I ask it to use nice angles, so I decided to create the nice angles by hand in another program: Oripa [4.0]. Oripa doesn’t do any complicated math for me, but provides me with tools to draw crease patterns like angle bisector and orthogonal measurements.

Oripa is nice

That’s a really clean crease pattern! What happens when we fold it?

side view

front view

The result is very close to the structure we want. However, the model has no torso. I decided to strip graft on paper for the torso. This however, proved difficult, because there were flaps in the way of the area I wanted to strip graft.

That is all that I managed to finish. After all my experiments with treemaker, I have come to the conclusion that it is unwieldy because it is only good at dealing with flap lengths and locations. Other variables such as symmetry and angle measures add too much complexity for treemaker to solve nicely. This makes it very nice to quickly confirm or reject a prototype, but less so when trying to create an aesthetically pleasing model.