Unfolding Polyhedra Method for the Design of Origami Structures with Creased Folds

Abstract

After addressing the kinematics of origami structures with creased folds in the previous chapter, here we present a method for their design to achieve targeted three-dimensional shapes. This chapter addresses the method of unfolding polyhedra. The goal shape is represented in this method as a three-dimensional polygonal mesh, termed as the goal mesh. The objective in unfolding polyhedra is to find the shape and fold pattern of a planar sheet that can be folded towards a configuration that matches the goal mesh. We examine the theory and computational implementation aspects of the unfolding polyhedra method and provide various representative examples. 3.1 Introduction As reviewed in Chap. 1, the potential engineering advantages of origami structures include storage/deployment capabilities and reduction in manufacturing complexity [1-6]. Such advantages lie in the use of folding to form complex three-dimensional shapes from planar sheets and have allowed origami to be utilized in applications ranging from personal fabrication of customized items [7, 8] to biomedical instruments [9-11] and deployable aerospace structures [12-14]. The process of creating an origami structure with desired characteristics (i.e., a desired shape) is known as origami design [15]. Origami design is perhaps the fundamental challenge faced by artists and engineers that apply origami in various fields. Prior to the extensive interest from various research communities seen in the present day, most origami design was performed through trial and error or other heuristic approaches based on the intuition of an experienced artist or designer [16]. With the increase in complexity of origami shapes providing various engineering utilities, computational methods for origami design have become essential [2, 16, 17]. Given the kinematic models for origami on which they are Electronic Supplementary Material The online version of this article (https://doi.org/10.1007/ 978-3-319-91866-2_3) contains supplementary material, which is available to authorized users.