If you need to think about it try to do it on the outside
 Specified by p_{min}and p_{max}.
 Center c = (p_{min}+p_{max})/2.
 Size s = p_{max}  p_{min}.
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.
Reference
