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# Voronoi Script Mobius Bracelet

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Voronoi Script Mobius Bracelet
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Voronoi Script Mobius Bracelet
\$0.00
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Voronoi Script Mobius Bracelet _Designed by nauseum ( http://www.thingiverse.com/thing:364744 ) __In mathematics, a Voronoi diagram is a partitioning of a plane into regions based on 'closeness' to points in a specific subset of the plane. That set of points (called seeds, sites, or generators) is specified beforehand, and for each seed there is a corresponding region consisting of all points closer to that seed than to any other. These regions are called Voronoi cells. The Voronoi diagram of a set of points is dual to its Delaunay triangulation.It is named after Georgy Voronoy, and is also called a Voronoi tessellation, a Voronoi decomposition, a Voronoi partition, or a Dirichlet tessellation (after Peter Gustav Lejeune Dirichlet). Voronoi diagrams have practical and theoretical applications to a large number of fields, mainly in science and technology but even including visual art. _In the simplest and most familiar case (shown in the first picture), we are given a finite set of points {p1, …, pn} in the Euclidean plane. In this case each site pk is simply a point and its corresponding Voronoi cell (also called Voronoi region or Dirichlet cell) Rk consisting of every point whose distance to pk is less than or equal to its distance to any other site. Each such cell is obtained from the intersection of half-spaces, and hence it is a convex polygon. The segments of the Voronoi diagram are all the points in the plane that are equidistant to the two nearest sites. The Voronoi vertices (nodes) are the points equidistant to three (or more) sites. _Voronoi diagrams are also related to other geometric structures such as the medial axis (which has found applications in image segmentation, optical character recognition, and other computational applications), straight skeleton, and zone diagrams. Besides points, such diagrams use lines and polygons as seeds. By augmenting the diagram with line segments that connect to nearest points on the seeds, a planar subdivision of the environment is obtained.This structure can be used as a navigation mesh for path-finding through large spaces. The navigation mesh has been generalized to support 3D multi-layered environments, such as an airport or a multi-storey building. _ Voronoi diagrams find widespread applications in areas such as computer graphics, epidemiology, geophysics, and meteorology. __The Möbius strip or Möbius band , also Mobius or Moebius, is a surface with only one side and only one boundary component. The Möbius strip has the mathematical property of being non-orientable. It can be realized as a ruled surface. It was discovered independently by the German mathematicians August Ferdinand Möbius and Johann Benedict Listing in 1858. _A model can easily be created by taking a paper strip and giving it a half-twist, and then joining the ends of the strip together to form a loop. However, the Möbius strip is not a surface of only one geometry (i.e., of only one exact size and shape), such as the half-twisted paper strip depicted in the illustration to the right. Rather, mathematicians refer to the (closed) Möbius band as any surface that is homeomorphic to this strip. Its boundary is a simple closed curve, i.e., homeomorphic to a circle. This allows for a very wide variety of geometric versions of the Möbius band as surfaces each having a definite size and shape. _A half-twist clockwise will give a different embedding of the Möbius strip than a half-twist counterclockwise – that is, as an embedded object in Euclidean space the Möbius strip is a chiral object with "handedness" (right-handed or left-handed). However, the underlying topological spaces within the Möbius strip are homeomorphic in each case. There are an infinite number of topologically different embeddings of the same topological space into three-dimensional space, as the Möbius strip can also be formed by twisting the strip an odd number of times greater than one, or by knotting and twisting the strip, before joining its ends. The complete open Möbius band (see section Open Möbius band below) is an example of a topological surface that is closely related to the standard Möbius strip but that is not homeomorphic to it. _It is straightforward to find algebraic equations the solutions of which have the topology of a Möbius strip, but in general these equations do not describe the same geometric shape that one gets from the twisted paper model described above. In particular, the twisted paper model is a developable surface (it has zero Gaussian curvature). A system of differential-algebraic equations that describes models of this type was published in 2007 together with its numerical solution.