Unfolding and Flat Layout Design of Non-Manifold 3D Folded Structures

Abstract

There are practical applications in the sheet metal, packaging and various other industries for research into the automatic development of the flat layout or pattern that can be folded into some desired 3D folded structure. The relevant techniques developed in earlier work are based on generating spanning trees of the face adjacency graph (the graph that represents the connectivity among the faces of the folded structure) since any spanning tree is a potential unfolded flat layout of that structure. However, complications in the structure, such as situations where more than two faces are joined at one common edge, pose problems to the spanning tree unfolding methodology that can lead to incorrect results. This work examines these problems through the connectivity and topological representation issues involved when splitting these common edges, and proposes a strategy to handle such complications by developing algorithms to detect topologically invalid spanning trees. These new algorithms are incorporated into a previous procedure developed by the authors, and the overall methodology is implemented on a computer program and applied to unfold four example structures to generate their corresponding flat layouts.

Keywords:

• unfolding
• folded structure
• flat pattern development
• topological representation