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best way to handle volumes in a kd-tree?

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Everything I've read about kd-trees involved adding points to the tree. Of course, 3D objects are not points. What's the standard way of adding bounding volumes to 3d-trees? I have an octree in which I add volumes that lie across the edge of a node to that node. This actually works pretty well although its not ideal. I was hoping to switch to a 3d-tree to get slightly better results.

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