Quadtrees are everywhere spatial data exists. Mapping services use quadtree-like tile pyramids to serve map tiles at different zoom levels (Bing's quadkey system, for example, addresses tiles as base-4 paths). Game engines use them for collision detection and visibility culling. Geographic information systems use spatial indexes to store and query spatial datasets. PostGIS uses GiST indexes (R-tree-style) for spatial queries on geometries, while PostgreSQL's core supports quadtree-like SP-GiST indexes for certain data types like points.
The algorithm walks the tree recursively. At each node, it checks: does this node's bounding box overlap with the query rectangle? If not, the entire subtree gets pruned (skipped). If it does overlap, it tests the node's points against the query and recurses into the children.
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