A Straightforward Preprocessing Approach for Accelerating Convex Hull Computations on the GPU

TL;DR

This paper introduces a GPU-based preprocessing method that filters out interior points by using extreme points to form a convex polygon, significantly accelerating convex hull computations with speedups of 4x to 6x.

Contribution

The paper presents a simple, efficient GPU preprocessing technique that discards interior points using extreme points, improving convex hull computation speed.

Findings

Achieves 4x to 6x speedup over non-preprocessed methods

Discards over 99% of input points in most tests

Effective for large point sets in convex hull calculations

Abstract

An effective strategy for accelerating the calculation of convex hulls for point sets is to filter the input points by discarding interior points. In this paper, we present such a straightforward and efficient preprocessing approach by exploiting the GPU. The basic idea behind our approach is to discard the points that locate inside a convex polygon formed by 16 extreme points. Due to the fact that the extreme points of a point set do not alter when all points are rotated in the same angle, four groups of extreme points with min or max x or y coordinates can be found in the original point set and three rotated point sets. These 16 extreme points are then used to form a convex polygon. We check all input points and discard the points that locate inside the convex polygon. We use the remaining points to calculate the expected convex hull. Experimental results show that: when employing the proposed preprocessing algorithm, it achieves the speedups of about 4x ~5x on average and 5x ~ 6x in the best cases over the cases where the proposed approach is not used. In addition, more than 99% input points can be discarded in most experimental tests.