S-hull: a fast radial sweep-hull routine for Delaunay triangulation

TL;DR

The paper introduces S-hull, a fast O(nlog(n)) algorithm for 2D Delaunay triangulation that uses a radial sweep-hull method combined with triangle flipping, outperforming q-hull in empirical tests.

Contribution

It presents a novel radial sweep-hull algorithm for Delaunay triangulation, improving speed over existing methods like q-hull.

Findings

Runs in approximately half the time of q-hull on random data

Achieves non-overlapping triangulation through radial sorting

Final triangle flipping ensures Delaunay property

Abstract

A new O(nlog(n)) algorithm is presented for performing Delaunay triangulation of sets of 2D points. The novel component of the algorithm is a radially propagating \emph{sweep-hull} (sequentially created from the radially sorted set of 2D points, giving a non-overlapping triangulation), paired with a final triangle flipping step to give the Delaunay triangluation. In empirical tests the algorithm runs in approximately half the time of q-hull for 2D Delaunay triangulation on randomly generated point sets.