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December 1984 (vol. 33 no. 12)
pp. 1072-1101
D.T. Lee, Department of Electrical Engineering and Computer Science, Northwestern University
We survey the state of the art of computational geometry, a discipline that deals with the complexity of geometric problems within the framework of the analysis of algorithms. This newly emerged area of activities has found numerous applications in various other disciplines, such as computer-aided design, computer graphics, operations research, pattern recognition, robotics, and statistics. Five major problem areas?convex hulls, intersections, searching, proximity, and combinatorial optimizations?are discussed. Seven algorithmic techniques?incremental construction, plane-sweep, locus, divide-and-conquer, geometric transformation, prune-and-search, and dynamization?are each illustrated with an example. A collection of problem transformations to establish lower bounds for geo-metric problems in the algebraic computation/decision model is also included.
Index Terms:
proximity, Algebraic computation tree, analysis of algorithms, combinatorial optimization, computational complexity, computational geometry, convex hull, divide and conquer, dynamization, geometric transformation, plane sweep
Citation:
D.T. Lee, F.P. Preparata, "Computational Geometry?A Survey," IEEE Transactions on Computers, vol. 33, no. 12, pp. 1072-1101, Dec. 1984, doi:10.1109/TC.1984.1676388
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