I wanted to say, its Separating Axis Test, not Theorem.

You'd use SAT on non moving polygons (2D), although you can extend it to cope with relative linear motion.

http://elancev.name/oliver/2D%20polygon.htm#tut3

Don't use GJK in 2D, I found its actually slower than simply brute forcing SAT.

Another technique you can use is Minkowski Difference, which shrinks one object down to a point and 'grows' the other by the shape of the first. Then you test the combined object against the point which is a lot easier - this gives you penetration distance and normal. I find this tool is conceptually very useful for approaching new collision detection problems; easier to visualise than SAT.

For moving and rotating polygons (and polyhedrons) you can use Conservative Advancement to find the exact time and point of contact.

http://www.continuousphysics.com/BulletContinuousCollisionDetection.pdf

You can read more about these techniques in this blog post which I wrote a while back:

http://www.wildbunny.co.uk/blog/2011/04/20/collision-detection-for-dummies/

Hope that helps!

Cheers, Paul.

I wanted to say, its Separating Axis Test, not Theorem.

You'd use SAT on non moving polygons (2D), although you can extend it to cope with relative linear motion.

2D polygon-based collision detection and response: Tutorial 3 - Extending further for fast moving objects

Don't use GJK in 2D, I found its actually slower than simply brute forcing SAT.

Another technique you can use is Minkowski Difference, which shrinks one object down to a point and 'grows' the other by the shape of the first. Then you test the combined object against the point which is a lot easier - this gives you penetration distance and normal. I find this tool is conceptually very useful for approaching new collision detection problems; easier to visualise than SAT.

For moving and rotating polygons (and polyhedrons) you can use Conservative Advancement to find the exact time and point of contact.

Continuous Collision Detection and Physics

You can read more about these techniques in this blog post which I wrote a while back:

Collision detection for dummies

Hope that helps!

Cheers, Paul.