Using Direct and Contructive Methods for the Existence of Origami Models with Given Boundary Conditions

Abstract

Whenever a unit square is folded to create an origami model in threedimensional space, the edge of the paper forms a closed curve in space with a total length equal to four units. In this paper, some of the restrictions applicable to such resulting closed curves are derived in the case of classic origami models, in which none of the sections of the folded paper is curved
in any way. This allows us to restrict the methods applied to those of classic euclidean geometry. Noting that it is of interest to determine origami models whose edges coincide with a polyline fullling the required conditions, we then proceed to show some methods for reconstructing the origami model if the boundary is known. Finally, some concrete reconstructions are demonstrated.