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arXiv · 1509.02601

On the $O_\beta$-hull of a planar point set

Carlos Alegría-Galicia·David Orden·Carlos Seara·Jorge Urrutia
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Abstract

We study the $O_\beta$-hull of a planar point set, a generalization of the Orthogonal Convex Hull where the coordinate axes form an angle $\beta$. Given a set $P$ of $n$ points in the plane, we show how to maintain the $O_\beta$-hull of $P$ while $\beta$ runs from $0$ to $\pi$ in $O(n \log n)$ time and $O(n)$ space. With the same complexity, we also find the values of $\beta$ that maximize the area and the perimeter of the $O_\beta$-hull and, furthermore, we find the value of $\beta$ achieving the best fitting of the point set $P$ with a two-joint chain of alternate interior angle $\beta$.

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Carlos Alegría-Galicia, David Orden, Carlos Seara, Jorge Urrutia. 2015-09-09. On the $O_\beta$-hull of a planar point set. https://doi.org/10.1016/j.comgeo.2017.06.003

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