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The k-d tree is a binary tree in which every node is a k-dimensional point. [2] Every non-leaf node can be thought of as implicitly generating a splitting hyperplane that divides the space into two parts, known as half-spaces.
Simple example of an R-tree for 2D rectangles Visualization of an R*-tree for 3D points using ELKI (the cubes are directory pages). R-trees are tree data structures used for spatial access methods, i.e., for indexing multi-dimensional information such as geographical coordinates, rectangles or polygons.
Hilbert R-tree, an R-tree variant, is an index for multidimensional objects such as lines, regions, 3-D objects, or high-dimensional feature-based parametric objects. It can be thought of as an extension to B+-tree for multidimensional objects.
In data processing R*-trees are a variant of R-trees used for indexing spatial information. R*-trees have slightly higher construction cost than standard R-trees, as the data may need to be reinserted; but the resulting tree will usually have a better query performance.
The terms "min/max k-d tree" and "implicit k-d tree" are sometimes mixed up.This is because the first publication using the term "implicit k-d tree" [1] did actually use explicit min/max k-d trees but referred to them as "implicit k-d trees" to indicate that they may be used to ray trace implicitly given iso surfaces.
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.
The region quadtree represents a partition of space in two dimensions by decomposing the region into four equal quadrants, subquadrants, and so on with each leaf node containing data corresponding to a specific subregion.
The Priority R-tree is a worst-case asymptotically optimal alternative to the spatial tree R-tree.It was first proposed by Arge, De Berg, Haverkort and Yi, K. in an article from 2004. [1]