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 .
Proceedings of the Twelfth Annual ACM Symposium on Theory of Computing. If the chains do not intersect then we need only keep the leftmost of the two chains. There are many different algorithms for detecting or avoiding collisions of convex objects. B. Chazelle and D. P.Dobkin. Detection is easier than computation .