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BSP trees

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I am trying to understand bsp trees, I think I have it, I just want to make sure. In 2d, you would take a line and fin the normal and divde by left or right, recursivly for all lines right, building a tree. But for the viwer, would you test each frutsum line in the tree to seee what lines were to the inside of the frutsum? So you would traverse the tree twice per line in the frutsum?

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