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. In a point region (PR) octree, the node stores an explicit three-dimensional point, which is the "center" of the subdivision for that node; the point defines one of the corners for each of the eight children. In a matrix-based (MX) octree, the subdivision point is implicitly the center of the space the node represents. 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 point. Also k-d trees are always binary, which is not the case for octrees. By using a depth-first search the nodes are to be traversed and only required surfaces are to be viewed. The use of octrees for 3D computer graphics was pioneered by Donald Meagher at Rensselaer Polytechnic Institute, described in a 1980 report "Octree Encoding: A New Technique for the Representation, Manipulation and Display of Arbitrary 3-D Objects by Computer", for which he holds a 1995 patent (with a 1984 priority date) "High-speed image generation of complex solid objects using octree encoding" Level of detail rendering in 3D computer graphics Spatial indexing Nearest neighbor search Efficient collision detection in three dimensions View frustum culling Fast multipole method Unstructured grid Finite element analysis Sparse voxel octree State estimation Set estimation The octree color quantization algorithm, invented by Gervautz and Purgathofer in 1988, encodes image color data as an octree up to nine levels deep.