This is usually where physics gets messy. It's all fun and games until someone suggests that maybe all objects are not perfectly convex, such as... the game level? There is convex decomposition, yes, but I'm not totally convinced that's a silver bullet. Convex decomposition is awfully complicated, and requires heavy preprocessing. It's definitely a good idea in many cases, but there will always be raw triangles. Convex decomposition or not, you need some sort of mid-phase, finding which triangles/primitives collide with a specific object. A lot of work has been put into this, and I think most people today agree that a quantized, binary AABB tree is the ideal solution. What's interesting here is how people usually query these AABB trees. The output from the broad phase is a list of pairs with overlapping bounding volumes. These pairs are then processed one by one, and in the case of a triangle mesh, the mid-phase is engaged to find the relevant triangles/primitives
A game technology blog with focus on physics. I'm the co-creator of mobile games Smash Hit, PinOut, Does not Commute, Granny Smith, Beyondium and Sprinkle. Twitter handle: @tuxedolabs