Geometric Intersection Problems

Date of Original Version



Working Paper

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All Rights Reserved

Abstract or Description

We develop optimal algorithms for forming the intersection of geometric objects in the plane and apply them to such diverse problems as linear programming, hidden-line elimination, and wire layout. Given N line segments in the plane, finding all intersecting pairs requires O(N2) time. We give an O(N log N) algorithm to determine whether any two intersect and use i t to detect whether two simple plane polygons intersect. We employ an O(N log N) algorithm for finding the common intersection of N half-planes to show that the Simplex method is not optimal. The emphasis throughout i s On obtaining upper and lower bounds and relating these results to other problems in computational geometry.