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...

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

electrical engineering and computer science, Lloyd's algorithm, also known as Voronoi iteration or relaxation, is an algorithm named after Stuart P. Lloyd for...

positive and negative Voronoi poles of a cell in a Voronoi diagram are certain vertices of the diagram. Let V {\displaystyle V} be the Voronoi diagram for a set...

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...

centroidal Voronoi tessellations of five points in a square In geometry, a centroidal Voronoi tessellation (CVT) is a special type of Voronoi tessellation...

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...

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...

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

color 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...

Voronoi deformation density (VDD) is a method employed in computational chemistry to compute the atomic charge distribution of a molecule in order to...

) The Voronoi cell for each defining point is a convex polygon. The Delaunay triangulation is a tessellation that is the dual graph of a Voronoi tessellation...

In mathematics, a Voronoi formula is an equality involving Fourier coefficients of automorphic forms, with the coefficients twisted by additive characters...

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...

set of points. This diagram is named after Georgy Voronoi, also called a Voronoi tessellation, a Voronoi decomposition, or a Dirichlet tessellation after...

Frederick Seitz, is a primitive cell which has been constructed by applying Voronoi decomposition to a crystal lattice. It is used in the study of crystalline...

describe the normal distributions exactly, while k-means splits the data in Voronoi-cells. The cluster center is indicated by the lighter, bigger symbol....

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

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

regions that are obtained through simple procedures such as thresholding. Voronoi tesselation can be used to define their spatial relationships—divisions...

Lattice based Point based Worley noise (Voronoi/Cellular noise)...

of the cluster. This results in a partitioning of the data space into Voronoi cells. k-means clustering minimizes within-cluster variances (squared Euclidean...

because the shape makes efficient use of space and building materials. The Voronoi diagram of a regular triangular lattice is the honeycomb tessellation of...

correspond to rays rather than line segments of the Voronoi diagram. This duality between Voronoi diagrams and Delaunay triangulations can be turned into...

in 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...

Brunn–Minkowski inequality. Two elementary proofs due to H. S. M. Coxeter and Voronoi will be presented here. Coxeter's proof proceeds by assuming that there...

continuous space that minimize distance and/or other location dependent costs. Voronoi diagram, also known as Thiessen polygons, an algorithm for partitioning...

} This effectively decomposes the color cube into a Voronoi diagram, where the palette entries are the points and a cell contains all...

1 + 3 ≈ 2.73 {\displaystyle 1+{\sqrt {3}}\approx 2.73} . Voronoi Treemaps based on Voronoi diagram calculations. The algorithm is iterative and does...