Oktree

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. This process is repeated for each octant that contains data, until some stopping criterion is met. This criterion might be the presence of a certain number of points in an octant, the size of an octant, or the level of recursion.

The primary advantage of using an octree is its ability to efficiently represent sparse data in three-dimensional space. Instead of storing every single point or voxel, an octree can represent empty space by simply not storing nodes for those regions. This makes it very useful for applications where data is not uniformly distributed.

Octrees find applications in various fields. In computer graphics, they are used for collision detection, ray tracing, and rendering of large scenes. They can accelerate queries by quickly identifying which parts of the scene are relevant to a particular operation. In geographic information systems (GIS), octrees can be employed to store and query spatial data, such as terrain models or satellite imagery. Furthermore, they are utilized in computational geometry for tasks like nearest neighbor searches and spatial indexing. The recursive subdivision nature of octrees allows for logarithmic time complexity for many spatial queries, making them a powerful tool for managing and analyzing 3D data.