On the shape of a set of points in the plane

ACKNOWLEDGMENT The authors express their appreciation for numerous constructive suggestions, which led to improvements on various phases of the manuscript, to Dr. A high performance multiple data rate burst modem for satellite packet communication, " EASCON Conference Record, Nov. 198 1. A microprocessor-based PSK modem for packet transmission over satellite channels, " IEEE Truns. Abstract-A generalization of the convex hull of a finite set of points in Akl and Toussaint [ 11, for instance, discuss the relevance the plane is introduced and analyzed. This generalization leads to a family of straight-line graphs, " o-shapes, " which seem to capture the intuitive of the convex hull problem to pattern recognition. By notions of " fine shape " and " crude shape " of point sets. It is shown that identifying and ordering the extreme points of a point set, a-shapes are subgraphs of the closest point or furthest point Delaunay the convex hull serves to characterize, at least in a rough triangulation. Relying on this result an optimal O(n log n) algorithm that way, the " shape " of such a set. Jarvis [9] presents several constructs o-shapes is developed. algorithms based on the so-called nearest neighbor logic that compute what he calls the " shape " of a finite set of I. INTR~DUOTION points. The " shape, " in Jarvis' terminology, is a notion T HE efficient construction of convex hulls for finite sets of points in the plane is one of the most exhaustively examined problems in the rather young field often referred to as " computational geometry. " Part of the motivation is theoretical in nature. It seems to stem from the fact that the convex hull problem, like sorting, is easy to formulate and visualize. Furthermore, the convex hull problem, again like sorting, plays an important role as a component of a large number of more complex problems. Nevertheless, much of the work on convex hulls is motivated by direct applications in some of the more practical branches of computer science. made concrete by the algorithms that he proposes for its construction. Besides this lack of any analytic definition, the inefficiency of Jarvis' algorithms to construct the " shape " is a striking drawback. More recently, Fairfield [6] introduced a notion of the shape of a finite point set based on the closest point Voronoi diagram of the set. He informally links his notion of shape with …