A Rectilinearity Measurement for Polygons

Abstract

In this paper we define a function $ \mathcal{R} $ (P) which is defined for any polygon P and which maps a given polygon P into a number from the interval (0, 1]. The number $ \mathcal{R} $ (P) can be used as an estimate of the rectilinearity of P . The mapping $ \mathcal{R} $ (P) has the following desirable properties: any polygon P has the estimated rectilinearity $ \mathcal{R} $ (P) which is a number from (0,1]; $ \mathcal{R} $ (P) =1 if and only if P is a rectilinear polygon, i.e., all interior angles of P belong to the set π/2, 3π/2; inf $ \mathcal{R} $ (P) = 0, where Π denotes the set of all polygons; p ∈ II a polygon’s rectilinearity measure is invariant under similarity transformations. A simple procedure for computing $ \mathcal{R} $ (P) for a given polygon P is described as well.