A crease pattern (commonly referred to as a CP)[1] is an origami diagram that consists of all or most of the creases in the final model, rendered into one image. This is useful for diagramming complex and super-complex models, where the model is often not simple enough to diagram efficiently.
The use of crease patterns originated with designers such as Neal Elias, who used them to record how their models were made. This allowed the more prolific designers to keep track of all their models, and soon crease patterns began to be used as a means for communication of ideas between designers. After a few years of this sort of use, designers such as Robert J. Lang, Meguro Toshiyuki, Jun Maekawa and Peter Engel began to design using crease patterns. This allowed them to create with increasing levels of complexity, and the art of origami reached unprecedented levels of realism. Now most higher-level models are accompanied by crease patterns.
Although not intended as a substitute for diagrams, folding from crease patterns is starting to gain in popularity, partly because of the challenge of being able to 'crack' the pattern, and also partly because the crease pattern is often the only resource available to fold a given model, should the designer choose not to produce diagrams. For example, an algorithm for the automatic development of crease patterns for certain polyhedra with discrete rotational symmetry by composing right frusta has been implemented via a CAD program.[2] The program allows users to specify a target polyhedron and generate a crease pattern that folds into it. Still, there are many cases in which designers wish to sequence the steps of their models but lack the means to design clear diagrams. Such origamists occasionally resort to the sequenced crease pattern (SCP) which is a set of crease patterns showing the creases up to each respective fold. The SCP eliminates the need for diagramming programs or artistic ability while maintaining the step-by-step process for other folders to see. Another name for the sequenced crease pattern is the progressive crease pattern (PCP).
Origami is the Japanese art of paper folding. In modern usage, the word "origami" is often used as an inclusive term for all folding practices, regardless of their culture of origin. The goal is to transform a flat square sheet of paper into a finished sculpture through folding and sculpting techniques. Modern origami practitioners generally discourage the use of cuts, glue, or markings on the paper. Origami folders often use the Japanese word kirigami to refer to designs which use cuts.
The Yoshizawa–Randlett system is a diagramming system used to describe the folds of origami models. Many origami books begin with a description of basic origami techniques which are used to construct the models. There are also a number of standard bases which are commonly used as a first step in construction. Models are typically classified as requiring low, intermediate or high skill depending on the complexity of the techniques involved in the construction.
The discipline of origami or paper folding has received a considerable amount of mathematical study. Fields of interest include a given paper model's flat-foldability, and the use of paper folds to solve up-to cubic mathematical equations.
Modular origami or unit origami is a two-stage paper folding technique in which several, or sometimes many, sheets of paper are first folded into individual modules or units and then assembled into an integrated flat shape or three-dimensional structure, usually by inserting flaps into pockets created by the folding process. These insertions create tension or friction that holds the model together.
Fold, folding or foldable may refer to:
Robert James Lang is an American physicist who is also one of the foremost origami artists and theorists in the world. He is known for his complex and elegant designs, most notably of insects and animals. He has studied the mathematics of origami and used computers to study the theories behind origami. He has made great advances in making real-world applications of origami to engineering problems.
The Sonobe module is one of the many units used to build modular origami. The popularity of Sonobe modular origami models derives from the simplicity of folding the modules, the sturdy and easy assembly, and the flexibility of the system.
Satoshi Kamiya is a Japanese origami artist. Kamiya began folding at age two. Kamiya began designing origami models in 1995, and has since published hundreds of creations. Kamiya has drawn inspiration for his designs from Manga, nature, and both eastern and western mythologies.
The Bug Wars were origami contests among members of the Origami Detectives which started when one member made a bug, a horned beetle with outspread wings, from a single sheet of paper: this design provoked other members to design more complex origami in the shape of bugs, such as wasps and praying mantises.
Origami paper is used to fold origami, the art of paper folding. The only real requirement of the folding medium is that it must be able to hold a crease, but should ideally also be thinner than regular paper for convenience when multiple folds over the same small paper area are required.
Kawasaki's theorem or Kawasaki–Justin theorem is a theorem in the mathematics of paper folding that describes the crease patterns with a single vertex that may be folded to form a flat figure. It states that the pattern is flat-foldable if and only if alternatingly adding and subtracting the angles of consecutive folds around the vertex gives an alternating sum of zero. Crease patterns with more than one vertex do not obey such a simple criterion, and are NP-hard to fold.
Paper models, also called card models or papercraft, are models constructed mainly from sheets of heavy paper, paperboard, card stock, or foam.
Nucleic acid design is the process of generating a set of nucleic acid base sequences that will associate into a desired conformation. Nucleic acid design is central to the fields of DNA nanotechnology and DNA computing. It is necessary because there are many possible sequences of nucleic acid strands that will fold into a given secondary structure, but many of these sequences will have undesired additional interactions which must be avoided. In addition, there are many tertiary structure considerations which affect the choice of a secondary structure for a given design.
Rigid origami is a branch of origami which is concerned with folding structures using flat rigid sheets joined by hinges. That is, unlike in traditional origami, the panels of the paper cannot be bent during the folding process; they must remain flat at all times, and the paper only folded along its hinges. A rigid origami model would still be foldable if it was made from glass sheets with hinges in place of its crease lines.
The napkin folding problem is a problem in geometry and the mathematics of paper folding that explores whether folding a square or a rectangular napkin can increase its perimeter. The problem is known under several names, including the Margulis napkin problem, suggesting it is due to Grigory Margulis, and the Arnold's rouble problem referring to Vladimir Arnold and the folding of a Russian ruble bank note. Some versions of the problem were solved by Robert J. Lang, Svetlana Krat, Alexey S. Tarasov, and Ivan Yaschenko. One form of the problem remains open.
DNA nanotechnology is the design and manufacture of artificial nucleic acid structures for technological uses. In this field, nucleic acids are used as non-biological engineering materials for nanotechnology rather than as the carriers of genetic information in living cells. Researchers in the field have created static structures such as two- and three-dimensional crystal lattices, nanotubes, polyhedra, and arbitrary shapes, and functional devices such as molecular machines and DNA computers. The field is beginning to be used as a tool to solve basic science problems in structural biology and biophysics, including applications in X-ray crystallography and nuclear magnetic resonance spectroscopy of proteins to determine structures. Potential applications in molecular scale electronics and nanomedicine are also being investigated.
In mechanical engineering, Yoshimura buckling is a triangular mesh buckling pattern found in thin-walled cylinders under compression along the axis of the cylinder, producing a corrugated shape resembling the Schwarz lantern. The same pattern can be seen on the sleeves of Mona Lisa.
Geometric Folding Algorithms: Linkages, Origami, Polyhedra is a monograph on the mathematics and computational geometry of mechanical linkages, paper folding, and polyhedral nets, by Erik Demaine and Joseph O'Rourke. It was published in 2007 by Cambridge University Press (ISBN 978-0-521-85757-4). A Japanese-language translation by Ryuhei Uehara was published in 2009 by the Modern Science Company (ISBN 978-4-7649-0377-7).
Origami Polyhedra Design is a book on origami designs for constructing polyhedra. It was written by origami artist and mathematician John Montroll, and published in 2009 by A K Peters.
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