ABSTRACT
Demaine et al. [6,7] have proposed a solution to this cut-out problem, based on propagating paths of folds out to the boundary of the rectangle R. Here we give a more “local” solution, based on disk-packing. Our strategy is to pack disks on R so that disk centers induce a mixed triangulation/quadrangulation respecting the boundary of polygon P. We fold each triangle or quadrilateral interior (exterior) to P upwards (respectively, downwards) from the plane of
the paper, taking care that neighboring polygons agree on crease orientations. A cut through the plane of the paper now separates interior from exterior.
