In a 1999 paper, Erik Demaine—now an MIT professor of electrical engineering and computer science, but then an 18-year-old PhD student at the University of Waterloo, in Canada—described an algorithm that could determine how to fold a piece of paper into any conceivable 3-D shape.
It was a milestone paper in the field of computational origami, but the algorithm didn't yield very practical folding patterns. Essentially, it took a very long strip of paper and wound it into the desired shape. The resulting structures tended to have lots of seams where the strip doubled back on itself, so they weren't very sturdy.
At the Symposium on Computational Geometry in July, Demaine and Tomohiro Tachi of the University of Tokyo will announce the completion of a quest that began with that 1999 paper: a universal algorithm for folding origami shapes that guarantees a minimum number of seams.
"In 1999, we proved that you could fold any polyhedron, but the way that we showed how to do it was very inefficient," 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."
Demaine and Tachi are also working to implement the algorithm in a new version of Origamizer, the free software for generating origami crease patterns whose first version Tachi released in 2008.
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