Computational Origami

Computerworld - Robert Lang, a laser physicist and origami artist for more than 30 years, continues to be amazed at the potential applications of the centuries-old art of paper folding. "You would think that there is not much you can do with origami as an art form that has not been already figured out," he says.
But, Lang adds, origami artists continue to "demonstrate new structures and realize new levels of beauty," a statement well supported by his own origami renderings of subjects such as cows, fish, blue herons and owls.
Origami was purely a hobby for Lang until he decided to apply the kind of mathematical modeling he used in laser physics to paper folding.
Lang, who is based in Alamo, Calif., now considers himself a full-time artist. He says computational origami helped him automate the process by which he determined how to make the precise kinds of folds needed to produce a multilegged insect and its antennae.
After he did that, he realized that the theory and equations he developed to make better origami figures could also be applied to engineering problems in which a large surface needs to be folded to fit into a flat space without cutting.
Today, while concentrating on his art, Lang also works as an industrial consultant, applying his computational origami expertise to the design of a range of products, including consumer electronics and medical equipment.
From Birds to Air Bags
EASi Engineering GmbH in Alzenau, Germany, asked Lang to help determine how to squeeze a very large object -- an automobile air bag -- into a tiny compartment inside a steering wheel. Lang had already developed algorithms to flatten a set of polygons, and he applied them to a computer simulation of how to flatten the 3-D polyhedron shape of an inflated air bag. This process saved time and eliminated the expensive requirement of crashing real cars to determine if an air-bag design would really work, Lang says.
The air-bag design was based on an algorithm Lang calls the "universal molecule," which flattens a set of polygons so their edges remain aligned to one another.
Lang sees a definite future for computational origami in engineering and design work, but he acknowledges that the field is relatively esoteric and requires artistic as well as computational, mathematical and engineering skills.
"You have to be able to fold paper" before proceeding to computational origami, he says.
Lang developed software called TreeMaker that runs on Apple Macintosh computers and helps automate origami design. The program, which Lang said