Computing pseudotriangulations via branched coverings

TL;DR

This paper introduces an efficient algorithm for computing pseudotriangulations of convex bodies using advanced visibility complex theory and branched coverings, with applications to specific bitangent line segments.

Contribution

It extends visibility complex theory to branched coverings and presents a novel algorithm for pseudotriangulation of convex bodies from chirotopes.

Findings

Algorithm efficiently computes pseudotriangulations.

Extends visibility complex theory to branched coverings.

Addresses pseudotriangulation with specified bitangent segments.

Abstract

We describe an efficient algorithm to compute a pseudotriangulation of a finite planar family of pairwise disjoint convex bodies presented by its chirotope. The design of the algorithm relies on a deepening of the theory of visibility complexes and on the extension of that theory to the setting of branched coverings. The problem of computing a pseudotriangulation that contains a given set of bitangent line segments is also examined.