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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:
The root node of a PR octree can represent infinite space; the root node of an MX octree must represent a finite bounded space so that the implicit centers are well-defined. Note that octrees are not the same as k-d trees: k-d trees split along a dimension and octrees split around a
A BSP tree is traversed in a linear time, in an order determined by the particular function of the tree. Again using the example of rendering double-sided polygons using the painter's algorithm, to draw a polygon P correctly requires that all polygons behind the plane P lies in must be drawn first, then polygon P , then finally the polygons in ...
The key feature of the BIH is the storage of 2 planes per node (as opposed to 1 for the kd tree and 6 for an axis aligned bounding box hierarchy), which allows for overlapping children (just like a BVH), but at the same time featuring an order on the children along one dimension/axis (as it is the case for kd trees).
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.
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.
A 1-dimensional range tree on a set of n points is a binary search tree, which can be constructed in () time. Range trees in higher dimensions are constructed recursively by constructing a balanced binary search tree on the first coordinate of the points, and then, for each vertex v in this tree, constructing a (d−1)-dimensional range tree on the points contained in the subtree of v.
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