Star Unfolding Convex Polyhedra via Quasigeodesic Loops

TL;DR

This paper introduces a novel method for unfolding convex polyhedra into a plane using quasigeodesic loops, generalizing previous point-based approaches and ensuring non-overlapping planar unfoldings.

Contribution

It extends star unfolding techniques to quasigeodesic loops, providing a new general method for convex polyhedron surface unfolding.

Findings

Unfolds convex polyhedra into simple polygons without overlap.

Uses shortest paths from vertices to quasigeodesic loops for cuts.

Generalizes star unfolding from points to loops.

Abstract

We extend the notion of star unfolding to be based on a 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 (non-overlapping), planar polygon: cut along one shortest path from each vertex of P to Q, and cut all but one segment of Q.