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In computer science, a k-d tree (short for k-dimensional tree) is a space-partitioning data structure for organizing points in a k-dimensional space. K-dimensional is that which concerns exactly k orthogonal axes or a space of any number of dimensions. [1] k-d trees are a useful data structure for several applications, such as:
A relaxed K-d tree or relaxed K-dimensional tree is a data structure which is a variant of K-d trees. Like K-dimensional trees, a relaxed K-dimensional tree stores a set of n-multidimensional records, each one having a unique K-dimensional key x=(x 0,... ,x K−1). Unlike K-d trees, in a relaxed K-d tree, the discriminants in each node are ...
In computer science, a K-D-B-tree (k-dimensional B-tree) is a tree data structure for subdividing a k-dimensional search space. The aim of the K-D-B-tree is to provide the search efficiency of a balanced k-d tree, while providing the block-oriented storage of a B-tree for optimizing external memory accesses. [1]
The regions can be organized into a tree, called a space-partitioning tree. Most space-partitioning systems use planes (or, in higher dimensions, hyperplanes) to divide space: points on one side of the plane form one region, and points on the other side form another. Points exactly on the plane are usually arbitrarily assigned to one or the ...
Another type of sphere arises from a 4-ball, whose three-dimensional surface is the 3-sphere: points equidistant to the origin of the euclidean space R 4. If a point has coordinates, P ( x , y , z , w ) , then x 2 + y 2 + z 2 + w 2 = 1 characterizes those points on the unit 3-sphere centered at the origin.
The corresponding implicit k-d trees are complete implicit k-d trees. A complete splitting function is for example the grid median splitting-function. It creates fairly balanced implicit k-d trees by using k-dimensional integer hyperrectangles hyprec[2][k] belonging to each node of the implicit k-d tree. The hyperrectangles define which ...
Let H = {h 1, h 2, ..., h k} be the convex hull of P; then the farthest-point Voronoi diagram is a subdivision of the plane into k cells, one for each point in H, with the property that a point q lies in the cell corresponding to a site h i if and only if d(q, h i) > d(q, p j) for each p j ∈ S with h i ≠ p j, where d(p, q) is the Euclidean ...
An adaptive k-d tree is a tree for multidimensional points where successive levels may be split along different dimensions. References. Samet, Hanan (2006).