1976/10/01 by Michael Ian Shamos, Dan Hoey · 2 citations
Computer Science · Mathematics · Engineering · #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #Robotic Path Planning Algorithms #Intersection (aeronautics) #Plane (geometry) #Line segment #Line (geometry) #Simplex algorithm #Computational geometry #Combinatorics #Simple (philosophy) #Linear programming #Simplex #Mathematics #Algorithm #Computer science #Geometry #Engineering
paper · doi:10.1109/sfcs.1976.16
openalex publication_date 1976/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
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 it 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 is on obtaining upper and lower bounds and relating these results to other problems in computational geometry.