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A quadtree is a tree data structure in which each internal node has exactly four children. Quadtrees are the two-dimensional analog of octrees and are most often used to partition a two-dimensional space by recursively subdividing it into four quadrants or regions. The data associated with a leaf cell varies by application, but the leaf cell represents a "unit of interesting spatial information". The subdivided regions may be square or rectangular, or may have arbitrary shapes. This data structure was named a quadtree by Raphael Finkel and J.L. Bentley in 1974. A similar partitioning is also known as a Q-tree. All forms of quadtrees share some common features: They decompose space into adaptable cells Each cell (or bucket) has a maximum capacity. When maximum capacity is reached, the bucket splits The tree directory follows the spatial decomposition of the quadtree. A tree-pyramid (T-pyramid) is a "complete" tree; every node of the T-pyramid has four child nodes except leaf nodes; all leaves are on the same level, the level that corresponds to individual pixels in the image. The data in a tree-pyramid can be stored compactly in an array as an implicit data structure similar to the way a complete binary tree can be stored compactly in an array. Quadtrees may be classified according to the type of data they represent, including areas, points, lines and curves. Quadtrees may also be classified by whether the shape of the tree is independent of the order in which data is processed. The following are common types of quadtrees. 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. Each node in the tree either has exactly four children, or has no children (a leaf node). The height of quadtrees that follow this decomposition strategy (i.e. subdividing subquadrants as long as there is interesting data in the subquadrant for which more refinement is desired) is sensitive to and dependent on the spatial distribution of interesting areas in the space being decomposed.

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Octree

An octree is a tree data structure in which each internal node has exactly eight children. Octrees are most often used to partition a three-dimensional space by recursively subdividing it into eight octants. Octrees are the three-dimensional analog of quadtrees. The word is derived from oct (Greek root meaning "eight") + tree. Octrees are often used in 3D graphics and 3D game engines. Each node in an octree subdivides the space it represents into eight octants.

Space partitioning

In geometry, space partitioning is the process of dividing a space (usually a Euclidean space) into two or more disjoint subsets (see also partition of a set). In other words, space partitioning divides a space into non-overlapping regions. Any point in the space can then be identified to lie in exactly one of the regions. Space-partitioning systems are often hierarchical, meaning that a space (or a region of space) is divided into several regions, and then the same space-partitioning system is recursively applied to each of the regions thus created.

K-d tree

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-d trees are a useful data structure for several applications, such as searches involving a multidimensional search key (e.g. range searches and nearest neighbor searches) and creating point clouds. k-d trees are a special case of binary space partitioning trees. The k-d tree is a binary tree in which every node is a k-dimensional point.

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