Origami fold as algebraic graph rewriting

We formalize paper fold (origami) by graph rewriting. Origami construction is abstractly described by a rewriting sys), where O is the set of abstract origami’s and ary relation on O, called fold. An 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 between the faces. We then address representation and transformation of abstract origami’s and further 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 about 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 computational origami research. Categories and Subject Descriptors G.2.2 [Mathematics of Computing]: Discrete Mathematic...

• Type: Conference
• Year: 2009
• Where: SAC
• Authors: Tetsuo Ida, Hidekazu Takahashi
• Keywords: Abstract Origami, Applied Computing, Graph Rewriting, Origami Construction, SAC 2009