Non convex polygonal objects in 3 space are much harder from a computational point of view. If we have two terrains with the same vertical direction, Chazelle et al. We allow preprocessing of the obstacles and we answer on line intersection queries in sublinear time. In the worst case we would have a linear number of simplex obstacle pairs to consider. B. Chazelle and D.P. Dobkin.
Detection is easier than computation .
P and Q intersect. If this is not true there is no intersection polygon to construct and the intersection then is either a line segment, a point, or the empty set. In order to simplify the description of the algorithm and to prevent the essential aspects from drowning in a sea of detail we further assume that no three vertices in P Q are collinear and all vertices in P Q are distinct. This implies that if P and Q intersect then so do their interiors. Detection is easier than computation .