An Efficient Convex Hull Algorithm Using Affine Transformation in Planar Point Set

Abstract

When trying to find the convex hull (CH) of a point set, humans can neglect most non-vertex points by an initial estimation of the boundary of the point set easily. The proposed CH algorithm imitates this characteristic of visual attention, starts by constructing an initial convex polygon (ICP), and measures the width and length of ICP through a shape estimation step. It then maps the point set into the new one by an affine transformation and makes most of the new points exist in a new initial convex polygon (NICP) which approximated to a regular convex polygon. Next, it discards the interior points in NICP by an inscribed circle and processes the remaining points outside NICP by Quickhull. Finally, the algorithm outputs the vertex set of CH. Two theorems are also proposed to solve an unconstrained optimization problem instead of the iteration method. Compared with four popular CH algorithms, the proposed algorithm can generate CH much faster than them and achieve a better performance.