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arXiv · 2407.01633

A New Construction of Forests with Low Visibility

Kirill Kashkan
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Abstract

A set of points with finite density is constructed in $\mathbb{R}^d$, with $d\geq2$, by adding points to a Poisson process such that any line segment of length $O\left(\varepsilon^{-(d-1)}\ln\varepsilon^{-1}\right)$ in $\mathbb{R}^d$ will contain one of the points of the set within distance $\varepsilon$ of it. The constant implied by the big-$O$ notation depends on the dimension only.

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Kirill Kashkan. 2024-06-29. A New Construction of Forests with Low Visibility. https://arxiv.org/abs/2407.01633

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