An Algorithm for Finding Convex Hulls of Planar Point Sets

TL;DR

This paper introduces a novel convex hull algorithm for planar points that efficiently discards interior points, sorts remaining points, and constructs the hull using recursive quadrilaterals, offering faster computation at the expense of higher space usage.

Contribution

The paper proposes a new convex hull algorithm that improves speed by discarding interior points early and using recursive quadrilaterals, differing from traditional methods.

Findings

Faster convex hull computation compared to three popular algorithms.

Effective discarding of interior points during preprocessing.

Increased space complexity due to data structures used.

Abstract

This paper presents an alternate choice of computing the convex hulls (CHs) for planar point sets. We firstly discard the interior points and then sort the remaining vertices by x- / y- coordinates separately, and later create a group ofquadrilaterals (e-Quads) recursively according to the sequences ofthe sorted lists of points. Finally, the desired CH is built based on a simple polygon derived from all e-Quads. Besides the preprocessing for original planar point sets, this algorithm has another mechanism of discarding interior point when form e-Quads and assemble the simple polygon. Compared with three popular CH algorithms, the proposed algorithm can generate CHs faster thanthe three but has a penalty in space cost.