20 points and their Voronoi cells (larger version below)
In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. It can be classified also as a tessellation. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites, or generators). For each seed there is a corresponding region, called a Voronoi cell, consisting of all points of the plane closer to that seed than to any other. The Voronoi diagram of a set of points is dual to that set's Delaunay triangulation.
The Voronoi diagram is named after mathematician 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 cells are also known as Thiessen polygons, after Alfred H. Thiessen.[1][2][3] Voronoi diagrams have practical and theoretical applications in many fields, mainly in science and technology, but also in visual art.[4][5]
^Burrough, Peter A.; McDonnell, Rachael; McDonnell, Rachael A.; Lloyd, Christopher D. (2015). "8.11 Nearest neighbours: Thiessen (Dirichlet/Voroni) polygons". Principles of Geographical Information Systems. Oxford University Press. pp. 160–. ISBN 978-0-19-874284-5.
^Longley, Paul A.; Goodchild, Michael F.; Maguire, David J.; Rhind, David W. (2005). "14.4.4.1 Thiessen polygons". Geographic Information Systems and Science. Wiley. pp. 333–. ISBN 978-0-470-87001-3.
^Sen, Zekai (2016). "2.8.1 Delaney, Varoni, and Thiessen Polygons". Spatial Modeling Principles in Earth Sciences. Springer. pp. 57–. ISBN 978-3-319-41758-5.
^Aurenhammer, Franz (1991). "Voronoi Diagrams – A Survey of a Fundamental Geometric Data Structure". ACM Computing Surveys. 23 (3): 345–405. doi:10.1145/116873.116880. S2CID 4613674.
^Okabe, Atsuyuki; Boots, Barry; Sugihara, Kokichi; Chiu, Sung Nok (2000). Spatial Tessellations – Concepts and Applications of Voronoi Diagrams (2nd ed.). John Wiley. ISBN 978-0-471-98635-5.
In mathematics, a Voronoidiagram is a partition of a plane into regions close to each of a given set of objects. It can be classified also as a tessellation...
mathematics, a weighted Voronoidiagram in n dimensions is a generalization of a Voronoidiagram. The Voronoi cells in a weighted Voronoidiagram are defined in...
by a discrete set of points. This diagram is named after Georgy Voronoi, also called a Voronoi tessellation, a Voronoi decomposition, or a Dirichlet tessellation...
graph of the Voronoidiagram for P. The circumcenters of Delaunay triangles are the vertices of the Voronoidiagram. In the 2D case, the Voronoi vertices...
Ukrainian mathematician Voronoidiagram Weighted VoronoidiagramVoronoi deformation density Voronoi formula Voronoi pole Centroidal Voronoi tessellation This...
Russian mathematician of Ukrainian descent noted for defining the Voronoidiagram. Voronyi was born in the village of Zhuravka, Pyriatyn, in the Poltava...
A diagram is a symbolic representation of information using visualization techniques. Diagrams have been used since prehistoric times on walls of caves...
computational geometry, a power diagram, also called a Laguerre–Voronoidiagram, Dirichlet cell complex, radical Voronoi tesselation or a sectional Dirichlet...
called Voronoi noise and cellular noise, is a noise function introduced by Steven Worley in 1996. Worley noise is an extension of the Voronoidiagram that...
infinity to the Voronoidiagram, to serve as the other endpoint for all of its rays, or by treating the bounded part of the Voronoidiagram as the weak dual...
intersections between a given set of line segments. Delaunay triangulation Voronoidiagram: Given a set of points, partition the space according to which points...
method generates a Voronoidiagram composed of polygons each with a unique grade; in three dimensions this method generates a Voronoidiagram composed of polyhedra...
space-filling tessellation (or honeycomb) in Euclidean 3-space. It is the Voronoidiagram of the face-centered cubic sphere-packing, which has the densest possible...
problems in computational geometry, such as the construction of the Voronoidiagram (Fortune's algorithm) and the Delaunay triangulation or boolean operations...
algorithm (JFA) is a flooding algorithm used in the construction of Voronoidiagrams and distance transforms. The JFA was introduced by Rong Guodong at...
the shape makes efficient use of space and building materials. The Voronoidiagram of a regular triangular lattice is the honeycomb tessellation of hexagons...
A zone diagram is a certain geometric object which a variation on the notion of Voronoidiagram. It was introduced by Tetsuo Asano, Jiří Matoušek, and...
measure of the interface between the cells linked to x and xi in the Voronoidiagram (length in 2D, surface in 3D) and d(xi), the distance between x and...
a fundamental domain.) This is an example of a Dirichlet domain or Voronoidiagram: since complex translations form an Abelian group, so commute with...
{\displaystyle S} . The Voronoidiagram of any set S {\displaystyle S} of points partitions space into regions called Voronoi cells that are nearer to...
Ornament (folio ed.). Bernard Quaritch. Aurenhammer, Franz (1991). "VoronoiDiagrams – A Survey of a Fundamental Geometric Data Structure". ACM Computing...
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