An additive algorithm for origami design.
| Autor: | Dudte LH; John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138., Choi GPT; John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138.; Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139., Mahadevan L; John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138; lmahadev@g.harvard.edu.; Department of Physics, Harvard University, Cambridge, MA 02138.; Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138. |
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| Jazyk: | angličtina |
| Zdroj: | Proceedings of the National Academy of Sciences of the United States of America [Proc Natl Acad Sci U S A] 2021 May 25; Vol. 118 (21). |
| DOI: | 10.1073/pnas.2019241118 |
| Abstrakt: | 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. Competing Interests: Competing interest statement: L.H.D. and L.M. have filed a patent on the proposed algorithm for origami design. |
| Databáze: | MEDLINE |
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