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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 origami crane diagram, using the Yoshizawa–Randlett system. 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.
Robert Lang folding an origami American flag, which includes 50 stars and 15 white and 13 red stripes, from a single uncut square. Lang was born in Dayton, Ohio, and grew up in Atlanta, Georgia. [1] Lang studied electrical engineering at the California Institute of Technology, where he met his wife-to-be, Diane. [2]
Koshiro Hatori and Robert J. Lang also found axiom 7. The axioms are as follows: Given two distinct points p 1 and p 2, there is a unique fold that passes through both of them. Given two distinct points p 1 and p 2, there is a unique fold that places p 1 onto p 2. Given two lines l 1 and l 2, there is a fold that places l 1 onto l 2.
Computational origami is a recent branch of computer science that is concerned with studying algorithms that solve paper-folding problems. The field of computational origami has also grown significantly since its inception in the 1990s with Robert Lang's TreeMaker algorithm to assist in the precise folding of bases. [2]
Circle packing has become an essential tool in origami design, as each appendage on an origami figure requires a circle of paper. [12] Robert J. Lang has used the mathematics of circle packing to develop computer programs that aid in the design of complex origami figures.
It includes the NP-completeness of testing flat foldability, [2] the problem of map folding (determining whether a pattern of mountain and valley folds forming a square grid can be folded flat), [2] [4] the work of Robert J. Lang using tree structures and circle packing to automate the design of origami folding patterns, [2] [4] the fold-and ...
Robert J. Lang has applied rigid origami to the problem of folding a space telescope. [7] Although paper shopping bags are commonly folded flat and then unfolded open, the standard folding pattern for doing so is not rigid; the sides of the bag bend slightly when it is folded and unfolded. The tension in the paper from this bending causes it to ...