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Tree data structure in which each internal node has exactly eight children, to partition a 3D space

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 octree color quantization algorithm, invented by Gervautz and Purgathofer in 1988, encodes image color data as an octree up to nine levels deep. Octrees are used because and there are three color components in the RGB system. The node index to branch out from at the top level is determined by a formula that uses the most significant bits of the red, green, and blue color components, e. g. 4r + 2g + b. The next lower level uses the next bit significance, and so on. Less significant bits are sometimes ignored to reduce the tree size. The algorithm is highly memory efficient because the tree's size can be limited. The bottom level of the octree consists of leaf nodes that accrue color data not represented in the tree; these nodes initially contain single bits. If much more than the desired number of palette colors are entered into the octree, its size can be continually reduced by seeking out a bottom level node and averaging its bit data up into a leaf node, pruning part of the tree. Once sampling is complete, exploring all routes in the tree down to the leaf nodes, taking note of the bits along the way, will yield approximately the required number of colors.