Planar Convex Hull Range Query and Related Problems
نویسندگان
چکیده
We consider the planar convex hull range query problem. Let P be a set of points in the plane. We preprocess these points into a data structure such that given an orthogonal range query, we can report the convex hull of the points in the range in O(log n + h) time, where h is the size of the output. The data structure uses O(n log n) space. This improves the previous bound of O(log n+h) time and O(n log n) space. Given a range query, it also supports extreme points in a given direction, tangent queries through a given point, and line-hull intersection queries on the points in the range in time O(log n) for each orthogonal query and O(log n) time for each additional query on that range. These problems have not been studied before.
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