An additive algorithm for origami design

Abstract

Significance Origami, the art of paper folding, is an emerging platform for mechanical metamaterials. Prior work on the design of origami-based structures has focused on simple geometric constructions for limited spaces of origami typologies or global constrained optimization problems that are difficult to solve. Here, we reverse the mathematical, computational, and physical paradigm of origami design by proposing a simple local marching approach that leads to a constructive theorem on the geometry of compatible growth directions at the boundary of a given folded seed. We show how this discovery yields a simple algorithm for the additive design of all developable quadrilateral surfaces, enabling the design of novel foldable metastructures from flat sheets at any scale.