Determining polygon intersection and containment

Question

I have a set of simple (no holes, no self-intersections) polygons, and I need to check that they don\'t intersect each other (one can be entirely contained in another; that is o

Answer 1

Determining whether none of the polygons intersect can be done in O(n*log(n)) by applying the Shamos-Hoey algorithm. Depending on what the Shamos-Hoey algorithm returns, a polygon P_i contains polygon P_j if any vertex from Pj is inside Pi which is done in O(n) for two polygons.