Nuevo algoritmo para la construcción de la envolvente convexa en el plano

Abstract

In this paper we present a new algorithm for finding the convex hull C(P) for P sets of n points in R 2. This problem has been widely studied in computational geometry and has important applications in engineering and other fields of knowledge. The proposed algorithm is based on a directional search of supporting hyperplanes and a variant which includes separating hyperplanes to reduce the number of evaluated points, ignoring the interior ones. The application of the proposed algorithm is illustrated using an example. The complexity of the algorithm obtained is O(max (nv o; nv o)), v o ≤ v ≤ n y v o ≤ v ≤ n, where v is the number of vertices of the convex hull.