Games use segment intersection tests all the time, for everything from line of sight to checking whether a bullet hit a monster. This is the most complicated of the four AABB tests, and is commonly known as a slab test. It finds the time of the line’s intersection with the near and far edges of each axis of the AABB. If they overlap, the segment is intersecting. - Intersection Tests in 2D

see also

• Minkowski sum - What’s the fastest way checking if two moving AABBs intersect?
• Line Segment Intersection
  • Sweep-Line Algorithm for Line Segment Intersection (2/5) | Computational Geometry - Lecture 02
• An Algorithm for Polygon Intersections / HN - describe an algorithm that can compute convex polygon intersections. / method for intersections between axis-aligned rectangles, a function that can determine the intersection of two line segments, as well as a point in polygon test.
• Theory & Practice - Issue 01 - Collision Detection