Towards the computation of the convex hull of a configuration from its corresponding separating matrix

TL;DR

This paper explores algorithms for computing the convex hull of a point configuration using separating line data, providing solutions for small hulls and directions for larger ones.

Contribution

It introduces an algorithm for convex hulls of size 3 and offers partial methods and insights for larger convex hulls based on separating matrix data.

Findings

Algorithm for convex hull of size 3

Partial algorithm for larger convex hulls

Directions for future research on convex hull computation

Abstract

In this paper, we cope with the following problem: compute the size of the convex hull of a configuration C, where the given data is the number of separating lines between any two points of the configuration (where the lines are generated by pairs of other points of the configuration). We give an algorithm for the case that the convex hull is of size 3, and a partial algorithm and some directions for the case that the convex hull is of size bigger than 3.