Graph Rewriting in Computational Origami

We formalize paper fold (origami) by graph rewriting. Origami tion is abstractly described by a rewrite system (O, ), where set of abstract origami’s and is a binary relation on O, called abstract origami is a triplet (Π, , ), where Π is a set of faces constituting an origami, and and are binary relations on Π, each representing adjacency and superposition relations of the faces. Origami tion is modeled as a rewrite sequence of abstract origami’s. We then address the problems of representation and transformation of abstract origami’s and of reasoning about the construction for computational purposes. We present a hypergraph of origami and define origami fold as algebraic graph transformation. The algebraic graph theoretic formalism enables us to reason origami in two separate domains of discourse, i.e. pure combinatoric domain and geometric domain R×R, and thus helps us to further tackle challenging problems in origami research.

• Type: Conference
• Year: 2008
• Where: SYNASC
• Authors: Tetsuo Ida
• Keywords: Abstract Origami, Algorithms, Binary Relations, Origami Tion, SYNASC 2008