Reducing the Number of Points on the Convex Hull Calculation Using the Polar Space Subdivision in E2

Abstract

A convex hull of points in E2 is used in many applications. In spite of low computational complexity O(h logn) it takes considerable time if large data processing is needed. We present a new algorithm to speed up any planar convex hull calculation. It is based on a polar space subdivision and speed up known convex hull algorithms of 3,7 times and more. The algorithm estimates the central point using 10% of the data, this point is taken as the origin for the polar subdivision. The space subdivision enables a fast and very efficient reduction of the given points, which cannot contribute to the final convex hull. The proposed algorithm iteratively approximates the convex hull, leaving only a small number of points for the final processing, which is performed using a algorithm. Non-eliminated points are then processed by a selected standard convex hull algorithm. The algorithm is simple and easy to implement. Experiments proved numerical robustness as well.