School of Computing

Convex Hull of Planar H-Polyhedra

Axel Simon and Andy King

International Journal of Computer Mathematics, 81(4):182-196, March 2004.

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$.

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Bibtex Record

@article{1754,
author = {Axel Simon and Andy King},
title = {{C}onvex {H}ull of {P}lanar {H}-{P}olyhedra},
month = {March},
year = {2004},
pages = {182-196},
keywords = {determinacy analysis, Craig interpolants},
note = {},
doi = {},
url = {http://www.cs.kent.ac.uk/pubs/2004/1754},
    publication_type = {article},
    submission_id = {14141_1070879968},
    journal = {International Journal of Computer Mathematics},
    volume = {81},
    number = {4},
    publisher = {Taylor & Francis},
}

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