The spatial view (the grid of rectangles) and the tree view (the hierarchy of nodes) represent the same structure. Searching for a point means walking down the tree: at each node, you check which of the four children contains your target coordinate and recurse into that child. You never visit the other three.
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The objects have been taken to Cardiff University's lab. Conservator Nicola Emmerson is painstakingly removing the dirt of the dig from an ornate copper brooch.