Convex Hull of Planar H-Polyhedra

Axel Simon; Andy King

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arXiv · cs/0405089

Convex Hull of Planar H-Polyhedra

Axel Simon·Andy King

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Abstract

Suppose $ $ are planar (convex) H-polyhedra, that is, $A_i \in \mathbb{R}^{n_i \times 2}$ and $\vec{c}_i \in \mathbb{R}^{n_i}$. Let $P_i = \{\vec{x} \in \mathbb{R}^2 \mid A_i\vec{x} \leq \vec{c}_i \}$ and $n = n_1 + n_2$. We present an $O(n \log n)$ algorithm for calculating an H-polyhedron $ $ with the smallest $P = \{\vec{x} \in \mathbb{R}^2 \mid A\vec{x} \leq \vec{c} \}$ such that $P_1 \cup P_2 \subseteq P$.

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Axel Simon, Andy King. 2004-05-24. Convex Hull of Planar H-Polyhedra. https://arxiv.org/abs/cs/0405089

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