New algorithm creates sturdy origami patterns for any 3D shape
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The new algorithm - based on an earlier, weaker version - models 3D surfaces as small, flat facets and maps these onto a flat surface to create a complex “crease pattern”.
In 1999, Professor Erik Demaine, a computer scientist at Massachusetts Institute of Technology, published an influential paper in computational origami. This described an algorithm which could, in theory, produce an origami pattern for any 3D shape by winding a long strip of paper. In practice, the resulting shapes were weak, due to a number of “seams” which caused weaknesses throughout the structures.
Nearly 20 years later, Professor Demaine, along with fellow computational origami expert, Professor Tomohiro Tachi of the University of Tokyo, are due to reveal a new, universal algorithm which generates origami patterns with a miminum 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,” said Professor Demaine.
Computer graphics software models 3D shapes – for instance, a beach ball – as polyhedrons of many tiny, triangular sides. The new algorithm creates a pattern by mapping these flat facets onto a flat surface. This surface can then be creased and assembled into the desired shape.
“The new algorithm is supposed to give you much better, more practical foldings,” said Professor Demaine. “We don’t know how to quantify that mathematically, exactly, other than it seems to work much better in practice.”
“But we do have one mathematical property that nicely distinguishes the two methods […] we call this watertightness.”
Creating a pattern with the minimum number of seams means that the “boundaries” of the original paper are preserved. The earlier algorithm, which wraps a thin strip of paper around on itself, is less watertight and less efficient. For instance, creating a mug by wrapping thin strips of paper would result in many tiny boundaries which could leak, whereas creating a mug from one large circle of paper would result in a structure with just one gap: the opening at the top of the mug.
This algorithm could be used in manufacturing to create complex objects from, for instance, flat sheets of plastic.
The researchers are working to implement the algorithm in a new version of Origamizer, software for generating origami patterns developed by Professor Tachi. They will present their new algorithm at the Symposium of Computational Geometry in July.