Convex Hull of Planar H-Polyhedra

Details Convex Hull of Planar H-Polyhedra Convex Hull of Planar H-Polyhedra

2004-05-24

arxiv.org/abs/cs/0405089v1

International Journal of Computer Mathematics, 81(4):259-271, 2004

Computer Science

Computational Geometry

Scientific paper

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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