Usefulness of angle-sweep over line-sweep
The sweeping approach is a powerful paradigm for solving 2-dimensional problems. There are problems which have been solved in the literature by sweeping an arrangement of lines by a vertical line across the plane. We have introduced in this paper another sweeping technique, called the angle-sweep technique. We have shown that the angle-sweep technique can successfully be applied to solve problems which have traditionally been solved by sweeping an arrangement of lines by a vertical line across the plane. We have demonstrated this by tackling three different problems. These problems are the maximum gap problem [Asano90a, Comer82], the uniform density problem [Comer82] and the k-belt problem [Edelsbrunner86].The proposed algorithms are simple. They use simple data structures. Their running times match the best running times reported in the literature for these problems. Moreover, in most of the cases the proposed algorithms for the maximum gap and the uniform density problems are shown to be better than the existing algorithms in the worst case.
KeywordsLine Segment Convex Hull Root Node Extreme Point Computational Geometry
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