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- W2981019968 abstract "We study the following range searching problem: Preprocess a set $P$ of $n$ points in the plane with respect to a set $mathcal{O}$ of $k$ orientations % , for a constant, in the plane so that given an $mathcal{O}$-oriented convex polygon $Q$, the convex hull of $Pcap Q$ can be computed efficiently, where an $mathcal{O}$-oriented polygon is a polygon whose edges have orientations in $mathcal{O}$. We present a data structure with $O(nk^3log^2n)$ space and $O(nk^3log^2n)$ construction time, and an $O(h+slog^2 n)$-time query algorithm for any query $mathcal{O}$-oriented convex $s$-gon $Q$, where $h$ is the complexity of the convex hull. Also, we can compute the perimeter or area of the convex hull of $Pcap Q$ in $O(slog^2n)$ time using the data structure." @default.
- W2981019968 created "2019-10-25" @default.
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- W2981019968 date "2019-10-19" @default.
- W2981019968 modified "2023-09-27" @default.
- W2981019968 title "Polygon Queries for Convex Hulls of Points" @default.
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