an upper bound for min-max angle of polygons

Let s be a set of n points in the plane, ∇(s) the set of all simple polygons crossing s, γp the maximum angle of polygon p ∈ ∇(s) and θ = minp∈∇(s)γp . in this paper, we prove that θ ≤ 2π − 2π 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 θ and prove that this is tight for r = 1.