Curved Creased Origami

I love curved creased origami and will be writing more about it over time, albiet mostly with an eye towards architecture scale work. Today I just want to highlight the work of Fynn Jackson. An example of what he can do below. All of his designs can be bought from here: and he has a youtube tutorial for folding them all:

Let’s look at a fragment of the crease pattern for the mask above. Sorry it is a bit faint, I don’t want to use more or trace it as this is the man’s livelihood. Note how he is breaking the mathematical rules of origami. It’s a bulk buy discount as they work together, you break one you break a few, but to be specific:

1. You can’t colour his pattern with only two colours without them meeting.
2. At some vertexes (meetings of creases), the number of valley/mountain folds does not differ by two.
3. Rule kept: The sheet DOES not not penetrate itself during folding. (more of an issue in computer design, to be honest)
4. He does break every other angle around a vertice must add to 180 degrees

And yet it folds!, what is happening? The answer is he is using curved creases. Sometimes obviously, like the eyebrow, sometime subtly, like that crease going across the bottom of the pattern. These curves induce curvature in the paper. A tiny square drawn on the paper can only be curving in one direction at a time (think of a cylinder or cone), and the direction it is NOT curving in (where you can put a ruler against it), is called the ‘rulings’. These rulings act as secret creases. You can simplify his patterns to turn the curve creases into a series of straight lines with intermediate vertices, and when you fold it you’ll find

1. that away from the creases the paper stays flat
2. that you will have a a series of new creases appear at the new verticies those vertexes
3. The paper still won’t penetrate itself
4. and the rules above will work for the new crease pattern.

It will be COMPLICATED to work out where these rulings and creases will be on the final shape from the crease pattern alone. It’s one of the hard problems, I’ve written on it previously, and I’ll post some of my work on it later. So how does he do it?

He goes more into his design process in this video: https://www.youtube.com/watch?v=8l-WJM5ligU It is largely iterative, adding creases and shifting creases to folded and refolded designs, marking with a coloured pen as he goes. That way, the crease pattern is ‘found’ on the 3d shape and is always compatible with existing panel curvature and rulings emergent from the paper. It’s a nice approach.