An algorithm for transitive reduction of an acyclic graph
Science of Computer Programming
Geometric Folding Algorithms: Linkages, Origami, Polyhedra
Geometric Folding Algorithms: Linkages, Origami, Polyhedra
Computational Origami Construction as Constraint Solving and Rewriting
Electronic Notes in Theoretical Computer Science (ENTCS)
A virtual computational paper folding environment based on computer algebraic system
Edutainment'11 Proceedings of the 6th international conference on E-learning and games, edutainment technologies
Computer Graphics Forum
| Hi-index | 0.00 |
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 origamis and @? is a binary relation on O, that models fold. An abstract origami is a structure (@P,@?,@?), where @P is a set of faces constituting an origami, and @? and @? are binary relations on @P, each representing adjacency and superposition relations between the faces. We 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 RxR. 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.