New measure for the rectilinearity of polygons

Jovisa Zunic; Paul L. Rosin

doi:10.1117/12.453591

24 November 2002 A new measure for the rectilinearity of polygons

Jovisa Zunic, Paul L. Rosin

Proceedings Volume 4794, Vision Geometry XI; (2002) https://doi.org/10.1117/12.453591
Event: International Symposium on Optical Science and Technology, 2002, Seattle, WA, United States

Abstract

A polygon Pis said to be rectilinear if all interior angles of P belong to the set {π/2, 3π/2}. In this paper we establish the mapping R(P)=(π/(π-2x√2))⊗(max_α∈[0,2π] ((P₁(P,α)/√2⊗P₂(P))-((2√2)/π)) where P is an arbitrary polygon, P₂(P) denotes the Euclidean perimeter of P, while P₁(P,α) is the perimeter in the sense of l₁ metrics of the polygon obtained by the rotation of P by angle α with the origin as the center of the applied rotation. It turns out that R(P) can be used as an estimate for the rectilinearity of P. Precisely, 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; - inf_p∈II R(P) = 0, where II denotes the set of all polygons - a polygon's rectilinearity measure is invariant under similarity transformations. The proposed rectilinearity measure can be an alternative for the recently described measure R₁(P)¹. Those rectilinearity measures are essentially different since there is no monotonic function f, such that f(R₁(P))= R(P), that holds for all P ∈ II. A simple procedure for computing R(P) for a given polygon P is described as well.

Citation Download Citation

Jovisa Zunic and Paul L. Rosin "A new measure for the rectilinearity of polygons", Proc. SPIE 4794, Vision Geometry XI, (24 November 2002); https://doi.org/10.1117/12.453591

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