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# Shatter Vase-Voronoi Style

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Shatter Vase-Voronoi Style
\$0.00

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Shatter Vase-Voronoi Style
\$0.00
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Shatter Vase-Voronoi Style _Designed by AK_Eric ( http://www.thingiverse.com/thing:74172 ) _Comments written by designer :"I've been interested in Voronoi diagrams for a long time: I really like the organic cellular structure they create. I ran across a set of pluigins for Maya called SOuP that allow for the 'shattering' of 3d mesh via a Voronoi algorithm. I set about to writing a Python script I could apply to any volumetric polygonal solid in Maya to apply this shatter, and this vase was the first usable version I came up with: I modeled the smooth "interior" section of the vase first, and then generated a slightly larger version which I 'shattered', and booleaned the two together. It is now a trendy art-piece in my bathroom window. For the pics with the blue-glow, I just dropped a small LED in there .Note, it is not water-tight: Just for fun I filled it with water: There's still some sloshing around now inside the print..." ***_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.