I have a pools like game and I'm struggling with balls bouncing at corners. In more general terms: a circle moving towards the corner of a rectangle. In frame n it doesn't overlap yet, in frame n+1 it does overlap. I need a new velocity vector and a new position for frame n+1. I think I've got the mathematics for it right, but it is very complicated and I'm looking for simplifications to keep frame rate high. Any ideas?

Perhaps I wasn't clear enough. The circle hits the corner of the rectangle from outside. If it would hit both walls successively, it should actually hit the imaginary extensions of the walls. Doing this it wouldn't hit the actual corner at all.

edit:
On the game field there are inner corners, too. I treat them just like you suggested, by successive hits on both walls. I don't even notice exact hits, where I would need the 45 degree wall. Using floats in coordinates and velocities take care of that there are never exact hits.

As I said, I think I know how it happens in real physics, I shall return to that. In my approximation I simply do this: when the circle would overlap I create a vector from the corner to the centre of the overlapped circle and add this vector to the velocity vector. Then I move the overlapped circle along this new vector just so much that it won't overlap. Then I draw it. It behaves almost correct, but not quite. It sometimes gets more velocity from the bounce, instead of loosing velocity.

edit:
Ok, here's the hard way explained, almost.