Fundamentals of Algebraic Graph Transformation (Monographs in Theoretical Computer Science. An EATCS Series)
Computational Origami Construction as Constraint Solving and Rewriting
Electronic Notes in Theoretical Computer Science (ENTCS)
Modeling origami for computational construction and beyond
ICCSA'07 Proceedings of the 2007 international conference on Computational science and Its applications - Volume Part II
Computational construction of a maximum equilateral triangle inscribed in an origami
ICMS'06 Proceedings of the Second international conference on Mathematical Software
Symbolic and algebraic methods in computational origami: invited talk
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
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We formalize paper fold (origami) by graph rewriting. Origami construction is abstractly described by a rewriting system (O, ↬), where O is the set of abstract origami's and ↬ is a binary 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 x R, and thus helps us to further tackle challenging problems in computational origami research.