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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 ...
The placement of a point on a curved fold in the pattern may require the solution of elliptic integrals. Curved origami allows the paper to form developable surfaces that are not flat. [41] Wet-folding origami is a technique evolved by Yoshizawa that allows curved folds to create an even greater range of shapes of higher order complexity.
The paper is folded behind itself, this is normally done by turning the paper over, folding a valley fold and then turning the paper back over again. A thin line shows where a previous fold has creased the paper. A dotted line shows a previous fold that's hidden behind other paper, or sometimes shows a fold that's not yet made.
Modular origami or unit origami is a multi-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. [3]
The Miura fold (ミウラ折り, Miura-ori) is a method of folding a flat surface such as a sheet of paper into a smaller area. The fold is named for its inventor, Japanese astrophysicist Kōryō Miura. [1] The crease patterns of the Miura fold form a tessellation of the surface by parallelograms.
For some (multi-vertex) folding patterns, it is necessary to curve or bend the paper while transforming it from a flat sheet to its flat-folded state, rather than keeping the rest of the paper flat and only changing the dihedral angles at each fold. For rigid origami (a type of folding that keeps the surface flat except at its folds, suitable ...
Geometric Origami is a book on the mathematics of paper folding, focusing on the ability to simulate and extend classical straightedge and compass constructions using origami. It was written by Austrian mathematician Robert Geretschläger [ de ] and published by Arbelos Publishing (Shipley, UK) in 2008.
The Huzita–Justin axioms or Huzita–Hatori axioms are a set of rules related to the mathematical principles of origami, describing the operations that can be made when folding a piece of paper. The axioms assume that the operations are completed on a plane (i.e. a perfect piece of paper), and that all folds are linear. These are not a ...