Circle Packing for Origami Design Is Hard

Abstract

Over the past 20 years, the world of origami has been changed by the introduction of design algorithms that bear a close relationship to, if not outright ancestry from, computational geometry. One of the first robust algorithms for origami design was the circle/river method (also called the tree method) developed independently by Lang [Lang 94,Lang 97,Lang 96] and Meguro [Meguro 92,Meguro 94]. This algorithm and its variants provide a systematic method for folding any structure that topologically resembles a graph theoretic weighted tree. Other algorithms followed, notably one by Tachi [Tachi 09] that gives the crease pattern to fold an arbitrary 3D surface.