The Mathematica Book
Logical and algebraic view of Huzita's origami axioms with applications to computational origami
Proceedings of the 2007 ACM symposium on Applied computing
Computational origami of a morley’s triangle
MKM'05 Proceedings of the 4th international conference on Mathematical Knowledge Management
Computational construction of a maximum equilateral triangle inscribed in an origami
ICMS'06 Proceedings of the Second international conference on Mathematical Software
Computational Origami Construction as Constraint Solving and Rewriting
Electronic Notes in Theoretical Computer Science (ENTCS)
Origami fold as algebraic graph rewriting
Proceedings of the 2009 ACM symposium on Applied Computing
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Computational origami is the computer assisted study of origami as a branch of science of shapes. The origami construction is a countably finite sequence of fold steps, each consisting in folding along a line. In this paper, we formalize origami construction. We model origami paper by a set of faces over which we specify relations of overlay and adjacency. A fold line is determined by a specific fold method. After folding along the fold line, the structure of origami is transformed; some faces are divided and moved, new faces are created and therefore the relations over the faces change. We give a formal method to construct the model origami. The model furthermore induces a graph of layers of faces. We give two origami examples as the application of our model. They exhibit non-trivial aspects of origami which are revealed only by formal modeling. The model is the abstraction of the implemented core of the system of computational origami called Eos (E-origami system).