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A power diagram is a type of Voronoi diagram defined from a set of circles using the power distance; it can also be thought of as a weighted Voronoi diagram in which a weight defined from the radius of each circle is added to the squared Euclidean distance from the circle's center.
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 ...
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.
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 ...
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 ...
In electrical engineering and computer science, Lloyd's algorithm, also known as Voronoi iteration or relaxation, is an algorithm named after Stuart P. Lloyd for finding evenly spaced sets of points in subsets of Euclidean spaces and partitions of these subsets into well-shaped and uniformly sized convex cells. [1]
For a given set of points in space, a Voronoi diagram is a decomposition of space into cells, one for each given point, so that anywhere in space, the closest given point is inside the cell. This is equivalent to nearest neighbor interpolation, by assigning the function value at the given point to all the points inside the cell. [ 3 ]
This diagram arises, e.g., as a model of crystal growth, where crystals from different points may grow with different speed. Since crystals may grow in empty space only and are continuous objects, a natural variation is the crystal Voronoi diagram, in which the cells are defined somewhat differently. In an additively weighted Voronoi diagram ...