Convex Hull of Planar H-Polyhedra
<|reference_start|>Convex Hull of Planar H-Polyhedra: Suppose $<A_i, \vec{c}_i>$ 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 $<A, \vec{c}>$ with the smallest $P = \{\vec{x} \in \mathbb{R}^2 \mid A\vec{x} \leq \vec{c} \}$ such that $P_1 \cup P_2 \subseteq P$.<|reference_end|>
@article{simon2004convex,
    title={Convex Hull of Planar H-Polyhedra},
    author={Axel Simon and Andy King},
    journal={International Journal of Computer Mathematics, 81(4):259-271, 2004},
    year={2004},
    archivePrefix={arXiv},
    eprint={cs/0405089},
    primaryClass={cs.CG}
}