Computational Geometric Modeling and Unfolding of 3-D Folded Structures

Abstract

Due to environmental considerations, corrugated paperboard folded into appropriate 3-D structural shapes are increasingly being used as packaging cushions, as a substitute for those traditionally made of polymer foams. However, since paperboards are manufactured in the form of sheets, 3-D structures have to be created from these boards by folding. The design of the necessary flat layout pattern of a board that can be folded into a reasonably complex and intricate shape is a process requiring a lot of costly trial-and-error and creativity on the part of the designer. This paper describes a methodology developed to aid the designer by automatically and systematically generating many possible flat layouts that can be folded into a specified 3-D folded structure. The key to such a method is a computer representation of the topology/connectivity of the faces of the 3-D folded structure by a graph-theoretic model, and an algorithm to operate on this model to unfold and generate the geometry of the planar layout. The procedure is implemented on a computer and resulting flat layout designs have been generated for four example structures. Some of the issues concerning the types of folded structures that can and cannot be easily unfolded and the types of layouts that can and cannot be generated by the current methodology are discussed.