The computation of the intersection staircase can be done using a list of the rectangles r (t') decreasingly ordered according to the y-coordinate of their upper boundaries. For each rectangle r (t') we check if it intersects the diagonal of r (t) and does not belong to P(t) ⋃ Q(t) ⋃ R (t). If the right boundary of the last element of the actual intersection staircase is also intersected by the upper boundary of r (t') or if the last element of the intersection staircase ends above r (t'), r (t') is appended to the list of the intersection staircase.