How do physics engines like Box2D detect and respond to collisions between arbitrary polygons?

Question

I've always wondered how collision detection like this was achieved, and I've always wondered what the response would be. Do they perform line-line intersection tests for each line making up the two polygons? If it'd make the question any more specific, how does Box2D handle this?

Answer 1

2D collisions with non-rectangular shapes are often detected using the Separating Axis Theorem (tutorial here). Look it up, there are a lot of good articles on the subject.

Box2D uses it as part of the solution for their collision system, for a more in-depth view read their manual.