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Origamic architecture is a form of kirigami that involves the three-dimensional reproduction of architecture and monuments, on various scales, using cut-out and folded paper, usually thin paperboard. Visually, these creations are comparable to intricate 'pop-ups', indeed, some works are deliberately engineered to possess 'pop-up'-like properties.
2-dimensional section of Reeb foliation 3-dimensional model of Reeb foliation. In mathematics (differential geometry), a foliation is an equivalence relation on an n-manifold, the equivalence classes being connected, injectively immersed submanifolds, all of the same dimension p, modeled on the decomposition of the real coordinate space R n into the cosets x + R p of the standardly embedded ...
The DSP implementation in the folding algorithm is a Data flow graph(DFG), which is a graph composed of functional nodes and delay edges.. Another input for folding algorithm is folding set which is the function maps an operation unit of original DFG to an operation of transformed DFG with the number n <= N indicated the order of reused operation.
In mathematics, the Reeb foliation is a particular foliation of the 3-sphere, introduced by the French mathematician Georges Reeb (1920–1993). It is based on dividing the sphere into two solid tori , along a 2- torus : see Clifford torus .
Intersection lineations are measured in relation to the two structures which intersect to form them. For instance, according to the measurement conventions of structural geology, original bedding, S 0 intersected by a fold's axial plane foliation, forms an intersection lineation L 0-1, with an azimuth and
A geodesic lamination of a 2-dimensional hyperbolic manifold is a closed subset together with a foliation of this closed subset by geodesics. [3] These are used in Thurston's classification of elements of the mapping class group and in his theory of earthquake maps. Quadratic laminations, which remain invariant under the angle doubling map. [4]
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.