Geometric intersection problems

@article{Shamos1976GeometricIP,
  title={Geometric intersection problems},
  author={Michael Ian Shamos and Dan Hoey},
  journal={17th Annual Symposium on Foundations of Computer Science (sfcs 1976)},
  year={1976},
  pages={208-215}
}
  • M. Shamos, Dan Hoey
  • Published 25 October 1976
  • Computer Science, Mathematics
  • 17th Annual Symposium on Foundations of Computer Science (sfcs 1976)
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… 
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