2021-09-27T04:09:53Zhttps://tsukuba.repo.nii.ac.jp/oaioai:tsukuba.repo.nii.ac.jp:000192612021-03-01T20:42:05ZOrigami fold as algebraic graph rewriting井田, 哲雄Ida, TetsuoTakahashi, Hidekazu© 2009 Elsevier Ltd.We formalize paper fold (origami) by graph rewriting. Origami construction is abstractly described by a rewriting system View the MathML source, where View the MathML source is the set of abstract origamis and right arrow-looped is a binary relation on View the MathML source, that models fold. An abstract origami is a structure (Π,reverse similar,succeeds), where Π is a set of faces constituting an origami, and reverse similar and succeeds are binary relations on Π, each representing adjacency and superposition relations between the faces.\n\nWe then address representation and transformation of abstract origamis and further reasoning about the construction for computational purposes. We present a labeled hypergraph of origami and define 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 combinatorial domain where symbolic computation plays the main role and geometrical domain View the MathML source. We detail the program language for the algebraic graph rewriting and graph rewriting algorithms for the fold, and show how fold is expressed by a set of graph rewrite rules.Elsevier Ltd2010-04engjournal articlehttp://hdl.handle.net/2241/105148https://tsukuba.repo.nii.ac.jp/records/1926110.1016/j.jsc.2009.10.0020747-7171AA10460294Journal of symbolic computation454393413https://tsukuba.repo.nii.ac.jp/record/19261/files/JSC_45-4.pdfapplication/pdf526.7 kB2013-12-20