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.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Megiddo N. Linear time algorithm for linear programming inR 3 and related problems.SIAM J. Comput., 1983, 12(4): 759–776.
Preparata F P, Shamos M I. Computational Geometry: An Introduction (Chinese version). Beijing: Science Press, 1990, pp. 357–402.
Preparata F P, Muller D E. Finding the intersection ofn half-spaces in timeO(n logn).Theoretical Computer Science, 1979, 8(1): 45–55.
Milgram M S. Does a point lie inside a polygon?J. Comput. Phys., 1989, 84(1): 134–144.
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.
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.
Manocha D, Krishnan S. Algebraic pruning: A fast technique for curve and surface intersection.Computer Aided Geometric Design, 1997, 14(9): 823–845.
Author information
Authors and Affiliations
Additional information
This work is supported by PH.D. Foundation of State Education Department of China.
WU Jigang was born in April, 1963. He received the B.S. degree in computational mathematics from Lanzhou University in 1983, and studied some M.S. degree courses in Southeast University in 1984. He was Assistant Professor, lecturer successively in Lanzhou University from 1983 to 1993. He is an Associate Professor in Yantai University and a doctoral candidate in computer science and technology at University of Science and Technology of China. His current research interests include parallel computing, theorem of algorithm, computational geometry and artificial intelligence.
JI Yongchang was born in May, 1971. He received the B.S. degree in computer science from Anhui University in 1993, the M.S. degree in parallel computing from University of Science and Technology of China in 1996, and the Ph.D. degree in 1998. His research interests include parallel computational models, design and analysis of algorithm.
CHEN Guoliang was born in June, 1938. He is a Professor and Ph.D. advior in high performance parallel computing at University of Science and Technology of China. He is the director of the National High Performance Computing Center at Hefei. His interests include parallel computing, computer architecture and computational geometry.
Rights and permissions
About this article
Cite this article
Wu, J., Ji, Y. & Chen, G. An optimal online algorithm for halfplane intersection. J. Comput. Sci. & Technol. 15, 295–299 (2000). https://doi.org/10.1007/BF02948817
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02948817