A plane-sweep algorithm for finding a closest pair among convex planar objects

Given a set of geometric objects a closest pair is a pair of objects whose mutual distance is smallest. We present a plane-sweep algorithm which finds a closest pair with respect to any Minkowski metric, 1#<=#t #<=##infinity#, for planar configurations consisting of n (possibly intersecting) compact convex objects such as line segments, circular discs and convex polygons. For configurations of line segments or discs the algorithm runs in asymptotically optimal time O(nlogN). For a configuration of n convex polygons with a total of N edges it finds a closest pair with respect to the Euclidean metric L"2 in time O(nlogN) if each polygon is given by its vertices in cyclic orderSIGLEAvailable from TIB Hannover: RO 7057(1993,1) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman