CS 268 : Geometric Algorithms
نویسنده
چکیده
Given a polygonal subdivision of the plane and some query point, we would like to know which region (or edge or vertex) contains it. In one dimension, the problem reduces to locating a query point in a subdivision of the line into intervals, and is easily solved by binary search. We will look for a method to extend the idea of binary search into two dimensions. Given a subdivision with m edges, we would like a method which will use O(m) preprocessing time and achieve O(log m) query time using O(m) space. The algorithm we will discuss below employs two nested binary searches and is based on monotone polygonal lines called separators. For more details on this algorithm, see [1].
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CS 268 : Geometric Algorithms Handout
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