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I know there's separating axis theorem for intersection checks, but is there any more efficient way to do this than that?


Would the way to check whether the boxes intersect be to check the four sides?


Are the sizes or the placements of these small blocks chosen with cache coherence in mind? I'm thinking it could be possible a block spans across conflicting cache lines so when we traverse a small block incrementally it may cause unnecessary evictions


Does varying the size of these blocks change efficiency?


To check if a big box is completely inside/outside a triangle, even if we check the four sides/four corners, we can still have issues. For example, if we check only the edges, a very small triangle inside the box would not have intersection with the sides of the box. So I'm wondering a better way?


How are edge cases usually considered? For example, if a point on the grid was on the edge of the triangle, and one of the coarse blocks with that as its corner was completely inside the triangle and the direct opposite one completely outside (besides the one corner), would this hybrid approach result in both of the coarse blocks having to be tested?


How do we determine if a large block is entirely in or out of a triangle? Do we just see if the 4 corners of that block is in the triangle?


What are the edge cases in this approach?


Are we always using the center of the block as the sample point? What if the center is not in the triangle but part of the block is in, do we still consider this case as having coverage?


If each edge has a corner of the box that is outside its half-plane, can we say the triangle is wholly inside the box?


What if the triangle size is less than early in block?


What would be an efficient approach to determine the optimal box size?