Origami, paper folding, is a traditional Japanese art of folding paper into representation of 3-D figures. In general, it is quite difficult to learn origami from 2-D images such as diagrams and videos, because it requires inference of 3-D models from 2-D images. We are developing a system for folding origami over the Web, by designing a model of an origami folding process and by implementing a...

This paper presents the fundamentals of Origami engineering and its application in nowadays as well as future industry. Several main cores of mathematical approaches such as HuzitaHatori axioms, Maekawa and Kawasaki’s theorems are introduced briefly. Meanwhile flaps and circle packing by Robert Lang is explained to make understood the underlying principles in designing crease pattern. Rigid ori...

REVIEW ARTICLE Masayuki Endo, Hiroshi Sugiyama et al. DNA origami technology for biomaterials applications Biomaterials Science REVIEW DNA origami is an emerging technology for designing and constructing defined multidimensional nanostructures. This technology is now expanding to materials science. This article introduces the basics of DNA origami, the design of various two-dimensional and thre...

Origami (paper folding) has a long tradition in Japan’s culture and education. We are developing a computational origami system, based on symbolic computation system Mathematica, for performing and reasoning about origami on the computer. This system is based on the implementation of the six fundamental origami folding steps (origami axioms) formulated by Huzita. In this paper, we show how our ...

In this paper, we address a method for supporting origami folding process on origami. We focus on a folding operation with a view to understanding the state of origami. We estimate the folding operations by using one camera. The folding operation can be estimated by comparing origami shapes of before and after a folding operation. A silhouette model is introduced to grasp the correspondence of ...

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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 specifi...

A proof document for origami theorem proving is a record of entire process of reasoning about origami construction and theorem proving. It is produced at the completion of origami theorem proving as a kind of proof certificate. It describes in detail how the whole process of an origami construction and the subsequent theorem proving are carried out in our computational origami system. In partic...

An origami manifold is a manifold equipped with a closed 2-form which is symplectic except on a hypersurface where it is like the pullback of a symplectic form by a folding map and its kernel fibrates with oriented circle fibers over a compact base. We can move back and forth between origami and symplectic manifolds using cutting (unfolding) and radial blow-up (folding), modulo compatibility co...

Artificial DNA nanostructures, such as DNA origami, have great potential as templates for the bottom-up fabrication of both biological and nonbiological nanodevices at a resolution unachievable by conventional top-down approaches. However, because origami are synthesized in solution, origami-templated devices cannot easily be studied or integrated into larger on-chip architectures. Electrostati...