An optimal online algorithm for halfplane intersection
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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.
Keywordscomputational geometry intersection of halfplanes online algorithm complexity
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