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# Moai - Voronoi Style

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Moai - Voronoi Style
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Moai - Voronoi Style
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Moai - Voronoi Style _Designed by roman_hegglin ( http://www.thingiverse.com/thing:171059 ) __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. ***_Moai figure, small wooden statue of uncertain religious significance, carved on Easter Island. The figures, thought to be representations of ancestors who live on in the form of skeletons, are of two types, moai kavakava (male) and moai paepae (female). They were sometimes used for fertility rites but were more often used for harvest celebrations, during which the first picking of fruits was heaped around them as offerings. During the time between these public festivals, the statues were wrapped in bark cloth and kept in private homes, where it is possible that they served decorative or private ritualistic purposes. It has been reported, for example, that from time to time the islanders picked the figures up like dolls and executed slight dancing motions with them.The moai kavakava were fashioned as slumping human figures that displayed the rib cage and spinal cord through decaying flesh. The head is of a standard type, in which circular eyes are placed under bushy, protruding eyebrows and often filled with shells. A large, blunted beak nose dominates the facial profile, and the downward-curving nostrils direct attention to the open mouth and bared teeth. A goatee always ornaments the chin of the moai kavakava, and a fantasy animal or human is sometimes incised on the crown of the head. _The moai paepae, which appear to have been executed at a later date, had a flat, relieflike quality resulting from a shallow demarcation of the breasts, torso, limbs, and genitals. The long face with huge, staring eyes gives the female figure a haunting expression that makes it an appropriate pendant to its male counterpart.