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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).
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In many applications, one needs to determine the location of several different points with respect to the same partition of the space. To solve this problem efficiently, it is useful to build a data structure that, given a query point, quickly determines which region contains the query point (e.g. Voronoi Diagram).
As Fortune describes in ref., [1] a modified version of the sweep line algorithm can be used to construct an additively weighted Voronoi diagram, in which the distance to each site is offset by the weight of the site; this may equivalently be viewed as a Voronoi diagram of a set of disks, centered at the sites with radius equal to the weight of the site. the algorithm is found to have ...
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.
Let be the Voronoi diagram for a set of sites , and let be the Voronoi cell of corresponding to a site . If V p {\displaystyle V_{p}} is bounded, then its positive pole is the vertex of the boundary of V p {\displaystyle V_{p}} that has maximal distance to the point p {\displaystyle p} .
The jump flooding algorithm (JFA) is a flooding algorithm used in the construction of Voronoi diagrams and distance transforms. The JFA was introduced by Rong Guodong at an ACM symposium in 2006. [1] The JFA has desirable attributes in GPU computation, notably for its efficient performance. However, it is only an approximate algorithm and does ...
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 ...