The big issue with intersections of convex objects is that there might be infinitely many intersection points (two cubes lying on top of each other). This creates a multitude of numerical issues. I worked on this topic extensively for a DEM software where you need to calculate a lot of these interactions with extremely high precision (overlaps between objects are usually < 1% of the bounding radius) and since it's not computer graphics but engineering you really need stability and performance. That was a real tough challenge involving lots of identifying limiting scenarios during large simulations but it works quite nicely now [0].