If you need to think about it try to do it on the outside
Specified by pminand pmax.
Center c = (pmin+pmax)/2.
Size s = pmax - pmin.
Closest point to AABB
The point is p and the closest point will be q.
For each axis in p check if value is below min then set that axis in q it to min and if above max set it to max. This will push p along each axis towards the box.
If any axis position is inside the box it will remain in the box.
Intersect two AABB.
Check each axis. If no overlap in axis then boxes to not intersect.
If all axis overlap then they intersect.
Intersect AABB and plane.
Intersec Sphere vs AABB
Dynamic AABB Tree - 2013