A rectilinearity measurement for polygons

Abstract

In this paper we define a function 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 R(P) can be used as an estimate of the rectilinearity of P. The mapping R(P) has the following desirable properties: – any polygon P has the estimated rectilinearity R(P) which is a number from (0, 1]; – 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 P∈Π R(P) = 0, where Π denotes the set of all polygons; – a polygon’s rectilinearity measure is invariant under similarity transformations. A simple procedure for computing R(P) for a given polygon P is described as well.