Novel Pixelated Multicellular Representation for Origami Structures That Innovates Computational Design and Control

Abstract

Origami is a traditional Asian fine art of creating three-dimensional structures by folding paper. Recently, engineers have started to exploit the functional advantages of foldable structures. Formal representations of origami structures are limited. Most of the origami research describes an origami structure by providing the geometric properties of creases and vertices. This paper proposes a novel representation of an origami structure by describing the faces. An origami sheet is first pixelated with evenly distributed cellular agents, referred to as cells. Pixelization makes the origami structurally analogous to an LED matrix screen, with each of the cells being one LED pixel on the screen. Every cell will possess two key properties that contribute to determine the entire pattern: the cell type, which is analogous to the color of the LED; and the cell size, which is analogous to the light intensity of the LED. Therefore, a collection of cells with the same cell type (color) could represent the rough profile of an origami face, while the sizes of the cells are used to determine the face borders.. Creases and vertices can be subsequently determined by attaining the precise borders among faces. In this paper, we will also propose a crease restoration algorithm to determine the face borders and creases that then enable a fold to the final origami shape. The novel pixelated multicellular representation of origami enables new computational origami design methods as well as new self-folding origami structures.