Generating empty convex polygon randomly from a subset of given point set

Abstract

In computational geometry, problem of generating random geometric objects are very interesting and extensively studied problems. In this paper we propose a new algorithm to generate an empty convex polygon from a subset of given point set. Let S ¼ {p1; p2;…; pn} be the given point set lying in ℝ2. The proposed algorithm generates a random empty convex polygon consisting of k vertices in S. In preprocessing phase we compute Convex Hull Layers CL(S) in O(n log n) time. By using the visibility relationship in Convex Layers, the proposed algorithm generates a random empty convex polygon in O(log n + k) time which is improved over the existing solution for this problem.