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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 .
By comparison, in a square grid map, the distance from the center of each square cell to the center of the four diagonal adjacent cells it shares a corner with is √ 2 times that of the distance to the center of the four adjacent cells it shares an edge with. This equidistant property of all adjacent hexes is desirable for games in which the ...
The simplest nontrivial cellular automaton would be one-dimensional, with two possible states per cell, and a cell's neighbors defined as the adjacent cells on either side of it. A cell and its two neighbors form a neighborhood of 3 cells, so there are 2 3 = 8 possible patterns for a neighborhood. A rule consists of deciding, for each pattern ...
The Levenshtein distance between two words is the minimum number of single-character edits (insertions, deletions or substitutions) required to change one word into the other. It is named after Soviet mathematician Vladimir Levenshtein, who defined the metric in 1965. [1] Levenshtein distance may also be referred to as edit distance, although ...
A description of linear interpolation can be found in the ancient Chinese mathematical text called The Nine Chapters on the Mathematical Art (九章算術), [1] dated from 200 BC to AD 100 and the Almagest (2nd century AD) by Ptolemy. The basic operation of linear interpolation between two values is commonly used in computer graphics.
The Moore neighbourhood of a cell is the cell itself and the cells at a Chebyshev distance of 1. The concept can be extended to higher dimensions, for example forming a 26-cell cubic neighborhood for a cellular automaton in three dimensions, as used by 3D Life .
The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.
In statistics, probability theory, and information theory, a statistical distance quantifies the distance between two statistical objects, which can be two random variables, or two probability distributions or samples, or the distance can be between an individual sample point and a population or a wider sample of points.