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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.
Edges of the Voronoi diagram going to infinity are not defined by this relation in case of a finite set P. If the Delaunay triangulation is calculated using the Bowyer–Watson algorithm then the circumcenters of triangles having a common vertex with the "super" triangle should be ignored. Edges going to infinity start from a circumcenter and ...
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 ...
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 purple-shaded region is the new Voronoi cell, after inserting the point to be interpolated (black dot). The weights represent the intersection areas of the purple-cell with each of the seven surrounding cells. Natural-neighbor interpolation or Sibson interpolation is a method of spatial interpolation, developed by Robin Sibson. [1]
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 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 ...
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 ]