Detecting the intersection of convex objects in the plane

Numerous applications require intersection detection. Many algorithms have been developed for telling whether two convex polygons intersect. We have revised and generalized one such algorithm to allow us to detect in C log n operations the intersection of two convex planar regions with piecewise curved boundaries, where n represents the number of curved segments. The constant C depends strictly upon the complexity of the n curved segments. The algorithms presented here have been implemented and details of their implementation are included.