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...

mathematics, a weighted Voronoi diagram in n dimensions is a generalization of a Voronoi diagram. The Voronoi cells in a weighted Voronoi diagram 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...

Russian mathematician of Ukrainian descent noted for defining the Voronoi diagram. Voronyi was born in the village of Zhuravka, Pyriatyn, in the Poltava...

Ukrainian mathematician Voronoi diagram Weighted Voronoi diagram Voronoi deformation density Voronoi formula Voronoi pole Centroidal Voronoi tessellation This...

graph of the Voronoi diagram for P. The circumcenters of Delaunay triangles are the vertices of the Voronoi diagram. In the 2D case, the Voronoi vertices...

algorithm. The Voronoi diagram of the current site positions (red) at each iteration is shown. The gray circles denote the centroids of the Voronoi cells. The...

computational geometry, a power diagram, also called a Laguerre–Voronoi diagram, Dirichlet cell complex, radical Voronoi tesselation or a sectional Dirichlet...

Fortune's algorithm is a sweep line algorithm for generating a Voronoi diagram from a set of points in a plane using O(n log n) time and O(n) space. It...

A diagram is a symbolic representation of information using visualization techniques. Diagrams have been used since prehistoric times on walls of caves...

called Voronoi noise and cellular noise, is a noise function introduced by Steven Worley in 1996. Worley noise is an extension of the Voronoi diagram that...

values for a textured surface. For a given set of points in space, a Voronoi diagram is a decomposition of space into cells, one for each given point, so...

infinity to the Voronoi diagram, to serve as the other endpoint for all of its rays, or by treating the bounded part of the Voronoi diagram as the weak dual...

and negative Voronoi poles of a cell in a Voronoi diagram are certain vertices of the diagram, chosen in pairs in each cell of the diagram to be far from...

(Mathematically, this means partitioning the observations according to the Voronoi diagram generated by the means.) S i ( t ) = { x p : ‖ x p − m i ( t ) ‖ 2...

any number of dimensions. The algorithm can be also used to obtain a Voronoi diagram of the points, which is the dual graph of the Delaunay triangulation...

intersections between a given set of line segments. Delaunay triangulation Voronoi diagram: Given a set of points, partition the space according to which points...

space-filling tessellation (or honeycomb) in Euclidean 3-space. It is the Voronoi diagram of the face-centered cubic sphere-packing, which has the densest possible...

sufficient layer of profiles. Voronoi diagram approach: In voronoi diagram approach, the pocket boundary is segmented and voronoi diagram is constructed for the...

quantization, clustering, and optimal mesh generation. A weighted centroidal Voronoi diagrams is a CVT in which each centroid is weighted according to a certain...

{\displaystyle S} . The Voronoi diagram of any set S {\displaystyle S} of points partitions space into regions called Voronoi cells that are nearer to...

method generates a Voronoi diagram composed of polygons each with a unique grade; in three dimensions this method generates a Voronoi diagram composed of polyhedra...

problems in computational geometry, such as the construction of the Voronoi diagram (Fortune's algorithm) and the Delaunay triangulation or boolean operations...

measure of the interface between the cells linked to x and xi in the Voronoi diagram (length in 2D, surface in 3D) and d(xi), the distance between x and...

A zone diagram is a certain geometric object which a variation on the notion of Voronoi diagram. It was introduced by Tetsuo Asano, Jiří Matoušek, and...

orthogonal convex hull, convex layers, Delaunay triangulation and Voronoi diagram, and convex skull. A set of points in a Euclidean space is defined...

always lie on a vertex of the Voronoi diagram of the already selected points, or at a point where an edge of the Voronoi diagram crosses the domain boundary...

algorithm (JFA) is a flooding algorithm used in the construction of Voronoi diagrams and distance transforms. The JFA was introduced by Rong Guodong at...

Ornament (folio ed.). Bernard Quaritch. Aurenhammer, Franz (1991). "Voronoi Diagrams – A Survey of a Fundamental Geometric Data Structure". ACM Computing...

a fundamental domain.) This is an example of a Dirichlet domain or Voronoi diagram: since complex translations form an Abelian group, so commute with...