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arXiv · 2209.06020

Rectilinear Convex Hull of Points in 3D

Pablo Pérez-Lantero·Carlos Seara·Jorge Urrutia
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Abstract

Let $P$ be a set of $n$ points in $\mathbb{R}^3$ in general position, and let $RCH(P)$ be the rectilinear convex hull of $P$. In this paper we obtain an optimal $O(n\log n)$-time and $O(n)$-space algorithm to compute $RCH(P)$. We also obtain an efficient $O(n\log^2 n)$-time and $O(n\log n)$-space algorithm to compute and maintain the set of vertices of the rectilinear convex hull of $P$ as we rotate $\mathbb R^3$ around the $z$-axis. Finally we study some properties of the rectilinear convex hulls of point sets in $\mathbb{R}^3$.

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Pablo Pérez-Lantero, Carlos Seara, Jorge Urrutia. 2022-09-13. Rectilinear Convex Hull of Points in 3D. https://doi.org/10.1007/978-3-030-61792-9_24

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