This is not the latest version of this item. The latest version can be found here.
Origamizer: A practical algorithm for folding any polyhedron
Name
LIPIcs-SoCG-2017-34.pdf
Description
Published version
Size
8.04 MB
Format
Adobe PDF
Checksum (MD5)
5e3547edcfe6e5ea6d61fe3cde0d9f75
Author(s)
Demaine, Erik
Tachi, Tomohiro
Date Issued
2017
Citation
Demaine, Erik and Tachi, Tomohiro. 2017. "Origamizer: A practical algorithm for folding any polyhedron."
Version
Final published version
Abstract
© Erik D. Demaine and Tomohiro Tachi. It was established at SoCG'99 that every polyhedral complex can be folded from a sufficiently large square of paper, but the known algorithms are extremely impractical, wasting most of the material and making folds through many layers of paper. At a deeper level, these foldings get the topology wrong, introducing many gaps (boundaries) in the surface, which results in flimsy foldings in practice. We develop a new algorithm designed specifically for the practical folding of real paper into complicated polyhedral models. We prove that the algorithm correctly folds any oriented polyhedral manifold, plus an arbitrarily small amount of additional structure on one side of the surface (so for closed manifolds, inside the model). This algorithm is the first to attain the watertight property: for a specified cutting of the manifold into a topological disk with boundary, the folding maps the boundary of the paper to within ϵ of the specified boundary of the surface (in Fréchet distance). Our foldings also have the geometric feature that every convex face is folded seamlessly, i.e., as one unfolded convex polygon of the piece of paper. This work provides the theoretical underpinnings for Origamizer, freely available software written by the second author, which has enabled practical folding of many complex polyhedral models such as the Stanford bunny.
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
10.4230/LIPIcs.SoCG.2017.34
