An additive algorithm for origami design

Abstract

Inspired by the allure of additive fabrication, we pose the problem of origami design from a new 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 four-fold 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 meta-structure design.

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Cited by in corpus (9)

• Inverse design of deployable origami structures that approximate a general surface
• Volumetric-mapping-based inverse design of 3D architected materials and mobility control by topology reconstruction
• An additive framework for kirigami design
• Modelling planar kirigami metamaterials as generalized elastic continua
• Programming bistability in geometrically perturbed mechanical metamaterials
• Roadmap for Animate Matter
• Lagrangian approach to origami vertex analysis: Kinematics
• Totimorphic assemblies from neutrally-stable units
• Explosive rigidity percolation in origami