Geometric design of flat layout of 3D folded structures

This thesis describes three progressively enhanced methodologies that were developed for unfolding 3D folded structures so as to generate all possible flat layouts that can be folded back to the original 3D shapes. The key to the first methodology is a computer representation of the topology/connectivity of the faces of the 3D folded structure by a graph-theoretic model, and an algorithm to operate on this model to unfold and enumerate the topology and geometry of the planar layout. Building upon the first methodology, a topological recognition method is proposed in the second methodology for handling more complex structures (like those containing common edges that are shared by more than two faces) and improving enumeration efficiency.DOCTOR OF PHILOSOPHY (MPE