# Convex Hull for Planar H-Polyhedra

Simon, Axel, King, Andy (2004) Convex Hull for Planar H-Polyhedra. International Journal of Computer Mathematics, 81 (3). pp. 259-271. ISSN 0020-7160. (doi:10.1080/00207160310001650034)

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http://dx.doi.org/10.1080/00207160310001650034

## Abstract

Suppose $\langle A_i, \vec{c}_i \rangle$ are planar (convex) H-polyhedra, that is, (unknown variable A_i) \in \mathbb{R}^{n_i \times 2}$and$\vec{c}_i \in \mathbb{R}^{n_i}$. Let (unknown variable P_i) = \{ \vec{x} \in \mathbb{R}^2 \mid A_i\vec{x} \leq \vec{c}_i \}$ and (unknown variable n) = n_1 + n_2$. We present an (unknown variable O)(n \log n)$ algorithm for calculating an H-polyhedron $\langle A, \vec{c} \rangle$ with the smallest (unknown variable P) = \{ \vec{x} \in \mathbb{R}^2 \mid A\vec{x} \leq \vec{c} \}$such that (unknown variable P)_1 \cup P_2 \subseteq P$.

Item Type: Article 10.1080/00207160310001650034 A General Works Faculties > Sciences > School of Computing > Programming Languages and Systems Group Andy King 12 Dec 2013 15:56 UTC 29 May 2019 11:39 UTC https://kar.kent.ac.uk/id/eprint/37534 (The current URI for this page, for reference purposes)