Discrete & Computational Geometry
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 ℘ to a simple (nonoverlapping) planar polygon: cut along one shortest path from each vertex of ℘ toQ, and cut all but one segment of Q.
Unfolding, Star unfolding, Convex polyhedra, Quasigeodesics, Quasigeodesic loops, Shortest paths
Itoh, Jin-ichi; O'Rourke, Joseph; and Vîlcu, Costin, "Star Unfolding Convex Polyhedra via Quasigeodesic Loops" (2010). Computer Science: Faculty Publications, Smith College, Northampton, MA.