Folding and Cutting Paper
نویسندگان
چکیده
We present an algorithm to nd a at folding of a piece of paper, so that one complete straight cut on the folding creates any desired plane graph of cuts. The folds are based on the straight skeleton, which lines up the desired edges by folding along various bisectors; and a collection of perpendiculars that make the crease pattern foldable. We prove that the crease pattern is at foldable by demonstrating a family of folded states with the desired properties.
منابع مشابه
Making the cut: lattice kirigami rules.
In this Letter we explore and develop a simple set of rules that apply to cutting, pasting, and folding honeycomb lattices. We consider origami-like structures that are extrinsically flat away from zero-dimensional sources of Gaussian curvature and one-dimensional sources of mean curvature, and our cutting and pasting rules maintain the intrinsic bond lengths on both the lattice and its dual la...
متن کاملThe concept of cutting lines in carbon nanotube science.
A review is presented of one-dimensional cutting lines that are utilized to obtain the physical properties of carbon nanotubes from the corresponding properties of graphite by the zone-folding scheme. Quantization effects in general low-dimensional systems are briefly discussed, followed by a more detailed consideration of one-dimensional single-wall carbon nanotubes. The geometrical structure ...
متن کاملContinuous Flattening of Orthogonal Polyhedra
Can we flatten the surface of any 3-dimensional polyhedron P without cutting or stretching? Such continuous flat folding motions are known when P is convex, but the question remains open for nonconvex polyhedra. In this paper, we give a continuous flat folding motion when the polyhedron P is an orthogonal polyhedron, i.e., when every face is orthogonal to a coordinate axis (x, y, or z). More ge...
متن کاملFoldable Composite Structures
This paper presents a study of the folding of a new self-powered, self-latching tube hinge for deployable structures. This hinge is made by cutting three parallel slots in a thinwalled carbon fibre reinforced plastic (CFRP) tube, thus leaving three tape springs connecting the two ends of the tube.
متن کاملUniversal Hinge Patterns for Folding Orthogonal Shapes
Polycube Ruby Implementation Cutting Plotter (Graphtec/CraftROBO) Folded Model PostScript Figure 8: The process by which paper origami can be constructed using the described algorithms. square was inserted as part of a row or column), and does not take into account any non-orthogonal creases made as a result of later steps. The PostScript file can be sent to a cutting plotter, which can etch th...
متن کامل