Catching Polygons
Computational Geometry
2022-01-05 v1
Abstract
Consider an arrangement of lines intersecting the unit square. There is some minimum scaling factor so that any placement of a rectangle with aspect ratio with must non-transversely intersect some portion of the arrangement or unit square. Assuming the lines of the arrangement are axis-aligned, we show the optimal arrangement depends on the aspect ratio of the rectangle. In particular, the optimal arrangement is either evenly spaced parallel lines or an evenly spaced grid of lines. We present the precise aspect ratios of rectangles for which each of the two nets is optimal.
Cite
@article{arxiv.2201.01286,
title = {Catching Polygons},
author = {Bradley McCoy and Eli Quist and Anna Schenfisch},
journal= {arXiv preprint arXiv:2201.01286},
year = {2022}
}