MIT researchers develop universal algorithm to provide origami designs for any 3D shape

Erik Demaine, an MIT professor and Tomohiro Tachi of the University of Tokyo have developed an algorithm that can determine how to fold a piece of paper into any 3D shape. The new algorithm is an advance version of an approach described by Demaine in a scientific paper in 1999. The algorithm will be implemented in an updated version of  Origamizer , a free software for generating origami patterns first released by Tachi in 2008.

The new algorithm is a more efficient version, that minimises the number of creases. Demaine says “It’s efficient if your initial piece of paper is super-long and skinny. But if you were going to start with a square piece of paper, then that old method would basically fold the square paper down to a thin strip, wasting almost all the material. The new result promises to be much more efficient. It’s a totally different strategy for thinking about how to make a polyhedron.”

The difference can be explained with a paper cup. According to the original method, the algorithm would use a long thin sheet of paper to coil around to make a cup. If you poured water in the cup, it would probably leak. The new algorithm provides watertight designs, for example using a circular sheet of paper, and then folding the edges in a pleated pattern. Some manufacturers actually use this design to make paper cups.

The new method allows the boundries on the paper to match up with the boundries of the shape. If the shape is something like a sphere, then the user can specify the location of a seam where the boundries can meet. Once Origamizer is updated with the new algorithm, users can generate designs for paper folding by feeding in a any 3D shape to the software.