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Journal of Computer Science and Technology

, Volume 15, Issue 3, pp 295–299 | Cite as

An optimal online algorithm for halfplane intersection

  • Wu Jigang 
  • Ji Yongchang 
  • Chen Guoliang 
Article
  • 93 Downloads

Abstract

The intersection ofN halfplanes is a basic problem in computational geometry and computer graphics. The optimal offline algorithm for this problem runs in timeO(N logN). In this paper, an optimal online algorithm which runs also in timeO(N logN) for this problem is presented. The main idea of the algorithm is to give a new definition for the left side of a given line, to assign the order for the points of a convex polygon, and then to use binary search method in an ordered vertex set. The data structure used in the algorithm is no more complex than array.

Keywords

computational geometry intersection of halfplanes online algorithm complexity 

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References

  1. [1]
    Megiddo N. Linear time algorithm for linear programming inR 3 and related problems.SIAM J. Comput., 1983, 12(4): 759–776.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    Preparata F P, Shamos M I. Computational Geometry: An Introduction (Chinese version). Beijing: Science Press, 1990, pp. 357–402.Google Scholar
  3. [3]
    Preparata F P, Muller D E. Finding the intersection ofn half-spaces in timeO(n logn).Theoretical Computer Science, 1979, 8(1): 45–55.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    Milgram M S. Does a point lie inside a polygon?J. Comput. Phys., 1989, 84(1): 134–144.zbMATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    Kleinberg J M. Online search in a simple polygon. InProceedings of the Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, ACM, New York, 1994, pp. 8–15.Google Scholar
  6. [6]
    Frederickson G N, Rodger S. A new approach to the dynamic maintenance of maximal points in plane.Discrete Comput. Geometry, 1990, 51(4): 365–374.CrossRefMathSciNetGoogle Scholar
  7. [7]
    Manocha D, Krishnan S. Algebraic pruning: A fast technique for curve and surface intersection.Computer Aided Geometric Design, 1997, 14(9): 823–845.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Science Press, Beijing China and Allerton Press Inc. 2000

Authors and Affiliations

  • Wu Jigang 
    • 1
    • 2
  • Ji Yongchang 
    • 3
  • Chen Guoliang 
    • 3
  1. 1.Department of Computer ScienceYantai UniversityYantaiP.R. China
  2. 2.Department of Computer Science and TechnologyUniversity of Science and Technology of ChinaHefeiP.R. China
  3. 3.National High Performance Computing CenterUniversity of Science and Technology of ChinaHefeiP.R. China

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