Search results
Results from the WOW.Com Content Network
Let be a metric space with distance function .Let be a set of indices and let () be a tuple (indexed collection) of nonempty subsets (the sites) in the space .The Voronoi cell, or Voronoi region, , associated with the site is the set of all points in whose distance to is not greater than their distance to the other sites , where is any index different from .
The Voronoi cells in a weighted Voronoi diagram are defined in terms of a distance function. The distance function may specify the usual Euclidean distance, or may be some other, special distance function. In weighted Voronoi diagrams, each site has a weight that influences the distance computation.
Worley noise, also 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 outputs a real value at a given coordinate that corresponds to the Distance of the nth nearest seed (usually n=1) and the seeds are distributed evenly through the region.
The Delaunay triangulation of a discrete point set P in general position corresponds to the dual 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 are connected via edges, that can be derived from adjacency-relationships of the Delaunay ...
20 points and their Voronoi cells. The natural element method (NEM) [1] [2] [3] is a meshless method to solve partial differential equation, where the elements do not have a predefined shape as in the finite element method, but depend on the geometry. [4] [5] [6] A Voronoi diagram partitioning the space is used to create each of these elements.
The cell for a given circle C consists of all the points for which the power distance to C is smaller than the power distance to the other circles. The power diagram is a form of generalized Voronoi diagram, and coincides with the Voronoi diagram of the circle centers in the case that all the circles have equal radii. [1] [2] [3] [4]
A Voronoi diagram is a special kind of decomposition of a metric space determined by distances to a specified discrete set of objects in the space, e.g., 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 after Peter Gustav Lejeune ...
Centroidal Voronoi tessellations are useful in data compression, optimal quadrature, optimal quantization, clustering, and optimal mesh generation. [3] A weighted centroidal Voronoi diagrams is a CVT in which each centroid is weighted according to a certain function.