The intersection of two "k"-DOP's can be computed very similarly to AABBs: for each orientation, you just check the two corresponding intervals of the two DOP's. So, just like DOP's being a generalization of AABBs, the intersection test is a generalization of the AABB overlap test. The complexity of the overlap test of two DOP's is in . This assumes, however, that both DOP's are given with respect to the same set of orientations. If one of them is rotated, this is no longer true. In that case, one relatively easy way to check the two DOP's formula_7 for intersection is to enclose the rotated one, formula_8, by another, smallest enclosing DOP formula_9 that is oriented with respect to the orientations of the first DOP formula_10. The procedure for that is a little bit more complex, but eventually amounts to a matrix vector multiplication of complexity as well.