An additive algorithm for origami design

Inspired by the allure of additive fabrication, we pose the problem of origami design from a different perspective: How can we grow a folded surface in three dimensions from a seed so that it is guaranteed to be isometric to the plane? We solve this problem in two steps: by first identifying the geo...

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Bibliographic Details
Published in:Proceedings of the National Academy of Sciences - PNAS 2021-05, Vol.118 (21), p.1-7
Main Authors: Dudte, Levi H., Choi, Gary P. T., Mahadevan, L.
Format: Article
Language:English
Subjects:
Algorithms
Curve fitting
Fabrication
Inverse design
Isometric
Physical Sciences
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Summary:Inspired by the allure of additive fabrication, we pose the problem of origami design from a different perspective: How can we grow a folded surface in three dimensions from a seed so that it is guaranteed to be isometric to the plane? We solve this problem in two steps: by first identifying the geometric conditions for the compatible completion of two separate folds into a single developable fourfold vertex, and then showing how this foundation allows us to grow a geometrically compatible front at the boundary of a given folded seed. This yields a complete marching, or additive, algorithm for the inverse design of the complete space of developable quad origami patterns that can be folded from flat sheets. We illustrate the flexibility of our approach by growing ordered, disordered, straight, and curved-folded origami and fitting surfaces of given curvature with folded approximants. Overall, our simple shift in perspective from a global search to a local rule has the potential to transform origami-based metastructure design.
ISSN:0027-8424
1091-6490
DOI:10.1073/pnas.2019241118