A Convexity Measurement for Polygons
J. Zunic, Paul L. Rosin · 2002
Convexity estimators are commonly used in the analysis of shape. In this paper we define and evaluate a new easily computable measure of convexity for polygons. Let P be an arbitrary polygon. If 7 ) (P, c) denotes the perimeter in the sense of l metrics of the polygon obtained by the rotation of P by angle c with the origin as the center of the applied rotation, and if 7)2 (R(P, c)) is the Euclidean perimeter of the minimal rectangle R(P, c) having the edges parallel to coordinate axes which includes such a rotated polygon P, then we show that C(P) defined as C(P) = min 7)2(R(P,c)) a C[0,2rr] 7)1 (P, c) can be used as an estimate for the convexity of P. Several desirable properties of C (P) are proved, as well.