Computational Construction of a Maximum Equilateral Triangle Inscribed in an Origami

Front. Comput. Sci. China

2008

Self Cite

We present a computing environment for origami on the web. The environment consists of the computational origami engine EOS for origami construction, visualization, and geometrical reasoning, WEBEOS for providing web interface to the functionalities of EOS, and web service system SCORUM for symbolic computing web services. WEBEOS is developed using Web2.0 technologies, and provides a graphical interactive web interface for origami construction and proving. In SCORUM, we are preparing web services for a wide range of symbolic computing systems, and are using these services in our origami environment. We explain the functionalities of this environment, and discuss its architectural and technological features.

Section: Using Scorum To Reason About Origami Constructionsmentioning

confidence: 99%

Computational origami environment on the web

Kasem

Front. Comput. Sci. China

2008

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“…As part of our research efforts in computational origami, we have developed a computational origami system called Eos [9]. In brief, it is an e-origami system which allows us to do virtual origami.…”

Section: Introductionmentioning

confidence: 99%

Logical and algebraic view of Huzita's origami axioms with applications to computational origami

Ghourabi

Proceedings of the 2007 ACM Symposium on Applied Computing

Takahashi

et al. 2007

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We describe Huzita's origami axioms from the logical and algebraic points of view. Observing that Huzita's axioms are statements about the existence of certain origami constructions, we can generate basic origami constructions from those axioms. Origami construction is performed by repeated application of Huzita's axioms. We give the logical specification of Huzita's axioms as constraints among geometric objects of origami in the language of the firstorder predicate logic. The logical specification is then translated into logical combinations of algebraic forms, i.e. polynomial equalities, disequalities and inequalities, and further into polynomial ideals (if inequalities are not involved). By constraint solving, we obtain solutions that satisfy the logical specification of the origami construction problem. The solutions include fold lines along which origami paper has to be folded. The obtained solutions both in numeric and symbolic forms make origami computationally tractable for further treatments, such as visualization and automated theorem proving of the correctness of the origami construction.

“…By giving geometrical interpretation to the triple, we are able to define a model of origami. The model is further concretized to be used to implement a computational origami system [3].…”

Section: Introductionmentioning

confidence: 99%

Graph Rewriting in Computational Origami

2008 10th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing

2008

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We give graph-theoretic formalization of origami, the art of paper folding. Starting from the abstract origami system, we model origami construction as a rewrite sequence of abstract origami's. To reason about the entire origami construction for the computational purposes, we define a labeled hypergraph for origami and give the abstraction of origami fold as a set of algebraic graph rewrite rules. We give detailed description of the fold operation in terms of graph rewriting. The graph-theoretic formalism enables us to reason in two separate domains of discourse, i.e. pure combinatoric domain and geometrical domain R 2 .