ABSTRACT
Three-dimensional origami represents the surface of a 3D shape with a sheet of paper, so the first step for designing the crease pattern (an unfolded pattern for origami with fold lines) is to unfold the 3D shape onto a 2D plane by figuratively cutting it along some subset of its edges and unfolding the result to lie flat. When we unfold a 3D shape, we usually cannot avoid the existence of empty spaces between the unfolded pieces. If we cut away the paper from the 2D pattern in those empty spaces, the result is no longer
origami; instead, we call it papercraft. To make the unfolded pattern work for origami, we have to lay out the unfolded pieces appropriately and add fold lines in the empty spaces to fill the gaps between the facets of the 3D shape.
