@article {
author = {Asaeedi, Saeed and Didehvar, Farzad and Mohades, Ali},
title = {An Upper Bound for Min-Max Angle of Polygons},
journal = {Mathematics Interdisciplinary Research},
volume = {8},
number = {3},
pages = {247-260},
year = {2023},
publisher = {University of Kashan},
issn = {2538-3639},
eissn = {2476-4965},
doi = {10.22052/mir.2023.246534.1363},
abstract = {Let $S$ be a set of $n$ points in the plane, $\nabla(S)$ the set of all simple polygons crossing $S$, $\gamma_P$ the maximum angle of polygon $P \in \nabla(S)$ and $\theta =min_{P\in\nabla(S)} \gamma_P$. In this paper, we prove that $\theta\leq 2\pi-\frac{2\pi}{r.m}$ where $m$ and $r$ are the number of edges and inner points of the convex hull of $S$, respectively. We also propose an algorithm to construct a polygon with the upper bound on its angles. Constructing a simple polygon with the angular constraint on a given set of points in the plane can be used for path planning in robotics. Moreover, we improve our upper bound on $\theta$ and prove that this is tight for $r=1$.},
keywords = {Min-max angle,Upper bound,Sweep arc,Simple polygonization,Computational geometry},
url = {https://mir.kashanu.ac.ir/article_113991.html},
eprint = {https://mir.kashanu.ac.ir/article_113991_5f60217ec36459aeb0d0cbd4eb6fb175.pdf}
}