An efficient improvement of gift wrapping algorithm for computing the convex hull of a finite set of points in $\mathbb {R}^{n}$

Abstract

In this paper, we present an efficient improvement of gift wrapping algorithm for determining the convex hull of a finite set of points in $\mathbb {R}^{n}$ space, applying the best restricted area technique inspired from the Method of Orienting Curves (this method was used successfully in computational geometry by An and Trang in Numerical Algorithms 59, 347–357 (2012), Optimization 62, 975–988 (2013)). The numerical experiments on the sets of random points in two- and three-dimensional space show that the running time of our algorithm is faster than the gift wrapping algorithm and the newest modified one.