Authors | سعید آسعیدی,فرزاد دیدهور,علی محدث |
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Journal | Mathematics Interdisciplinary Research |
IF | ثبت نشده |
Paper Type | Full Paper |
Published At | 2023-04-06 |
Journal Grade | Scientific - research |
Journal Type | Electronic |
Journal Country | Iran, Islamic Republic Of |
Journal Index | ISC |
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 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 $r=1$.
tags: Min-Max Angle, Upper Bound, Sweep Arc, Simple Polygonization, Computational Geometry