Orthogonal dissection into few rectangles
Computational Geometry
2025-01-08 v2
Abstract
We describe a polynomial time algorithm that takes as input a polygon with axis-parallel sides but irrational vertex coordinates, and outputs a set of as few rectangles as possible into which it can be dissected by axis-parallel cuts and translations. The number of rectangles is the rank of the Dehn invariant of the polygon. The same method can also be used to dissect an axis-parallel polygon into a simple polygon with the minimum possible number of edges. When rotations or reflections are allowed, we can approximate the minimum number of rectangles to within a factor of two.
Cite
@article{arxiv.2206.10675,
title = {Orthogonal dissection into few rectangles},
author = {David Eppstein},
journal= {arXiv preprint arXiv:2206.10675},
year = {2025}
}
Comments
18 pages, 8 figures. This version adds results on dissection with rotations and reflections