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The fundamentals of hierarchical data structures are reviewed and it is shown how they are used in the implementation of some basic operations in computer graphics. The properties of hierarchical structures are discussed, focusing on quadtrees and octrees. The latter are defined, some of the more common ways in which they are implemented are examined, and an explanation of the quadtree/octree complexity theorem is provided. Vector quadtrees and vector octrees are discussed. The performance of basic operations using quadtrees is considered.>
Samet et al. (Sun,) studied this question.