General collision detection involves checking the distances between every point and every other - that includes between each two points of the same object if the object is flexible, e.g. to stop a man's arm from going through his chest. But if the collision approach direction is known ansd the objects are rigid, it is easier. (The easiest case is between an object and the ground plane in the Poser and Bryce "drop to floor", where the object is moved in Y so that minimum y becomes 0.) Change the coordinates so that the known approach direction is Y. Then make an altitude map of maximum Y for one object and minimum Y for the other object. Then it can be found quickly how far they can approach each other in that direction before they collide.