Your scene will have bounding boxes that will never collide. The first rule of real-time applications is only calculate what is essential. If a bounding box can never collide with another, then do not test them for collisions. The axis-aligned bounding box approach gives a good first check for a collision. It is fairly low in the computational hit apart from one major flaw; graphics cards are increasingly able to do all the transformations, relieving the processor of this computationally expensive work. The maximum and minimum vertex bounding box approach is rather reliant on the processor doing the transformation work, so that you can derive the world values for maximum and minimum values for the character’s bounding box in world coordinates. You can get around this problem by having a fixed bounding box that you transform using the graphics hardware matrix which you can get from OpenGL after setting up the camera location. You can then use this matrix to transform just the two vertices in the fixed bounding box.