Collision detection that behaves

Add collision handling to my game. Entities are <rectangles / circles>:
<paste the entity shape and movement code>

- Detection: <AABB / circle> overlap, with the maths explained.
- Resolution: move on X, resolve, then move on Y, resolve. Not both
  at once — I know that causes sticking to walls while falling.
- Report which side the collision happened on, so I can tell landing
  on a platform from hitting its underside.
- Handle fast-moving objects passing through thin walls between
  frames. Tell me whether that's a real risk at my speeds before
  adding anything for it.

Keep detection separate from response, so I can reuse detection for
triggers and pickups that don't push anything.