Point quadtree
Insert point. Subdivide leaf when it holds > threshold points. Sparse regions have shallow trees.
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Region quadtree
Recursively subdivide space (not points). Used for image compression, terrain LOD, collision.
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Octree in 3D graphics
Ray tracing acceleration. Voxel storage (Minecraft-like games). 3D collision detection.
Complexity
Search + insert: O(log N) expected. Worst case: O(N) if degenerate.