A divide-and-conquer algorithm for computing 4-dimensional convex hulls

Abstract

This paper contains a description an algorithm for computing four dimensional convex hulls of point sets using the divide-and-conquer paradigm. The algorithm features minimal asymptotic time and memory complexity with respect to the size of its input point set. It is based upon a fully-dual four-dimensional boundary representation (BREP) data structure called Hexblock, also developed by the author, which was inspired by Guibas' and Stolfi's quadedge data structure.