2012/05/04 by Itoh, Jin-ichi, O'Rourke, Joseph, Vilcu, Costin
#52B10 #Computational Geometry (cs.CG) #F.2.2 #FOS: Computer and information sciences #G.2
paper · doi:10.48550/arxiv.1205.0963
We extend the notion of a source unfolding of a convex polyhedron P to be based on a closed polygonal curve Q in a particular class rather than based on a point. The class requires that Q "lives on a cone" to both sides; it includes simple, closed quasigeodesics. Cutting a particular subset of the cut locus of Q (in P) leads to a non-overlapping unfolding of the polyhedron. This gives a new general method to unfold the surface of any convex polyhedron to a simple, planar polygon.