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arXiv · 1707.00826

Supporting Ruled Polygons

Nicholas J. Cavanna·Marc Khoury·Donald R. Sheehy
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Abstract

We explore several problems related to ruled polygons. Given a ruling of a polygon $P$, we consider the Reeb graph of $P$ induced by the ruling. We define the Reeb complexity of $P$, which roughly equates to the minimum number of points necessary to support $P$. We give asymptotically tight bounds on the Reeb complexity that are also tight up to a small additive constant. When restricted to the set of parallel rulings, we show that the Reeb complexity can be computed in polynomial time.

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Nicholas J. Cavanna, Marc Khoury, Donald R. Sheehy. 2017-07-04. Supporting Ruled Polygons. https://arxiv.org/abs/1707.00826

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