| Dynamic Planar Convex Hull (2002) | |||||||||||||||||
Abstract | |||||||||||||||||
| In this paper we determine the computational complexity of the dynamic convex hull problem in the planar case. We present a data structure that maintains a finite set of n points in the plane under insertion and deletion of points in amortized O(log n) time. The space usage of the data structure is O(n). The data structure supports extreme point queries in a given direction, tangent queries through a given point, and queries for the neighboring points on the convex hull in O(log n) time. The extreme point queries can be used to decide whether or not a given line intersects the convex hull, the tangent queries to determine whether a given point is inside the convex hull. | |||||||||||||||||
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