Unfolding Convex Polyhedra via Quasigeodesic Star Unfoldings

TL;DR

This paper introduces a novel method for unfolding convex polyhedra into planar polygons using quasigeodesic loops, expanding the traditional star unfolding concept based on points.

Contribution

It generalizes star unfoldings by using quasigeodesic loops instead of points, providing a new approach to unfold convex polyhedra.

Findings

Method produces simple planar polygons from convex polyhedra

Shortest paths to quasigeodesic loops are used for unfolding

Applicable to any convex polyhedron

Abstract

We extend the notion of a star unfolding to be based on a simple quasigeodesic loop Q rather than on a point. This gives a new general method to unfold the surface of any convex polyhedron P to a simple, planar polygon: shortest paths from all vertices of P to Q are cut, and all but one segment of Q is cut.