Short-Cuts on Star, Source and Planar Unfoldings

When studying a 3D polyhedron, it is often easier to cut it open and atten in on the plane. There are several ways to perform this unfolding. Standard unfoldings which have been used in literature include Star Unfoldings, Source Unfoldings, and Planar Unfoldings, each diering only in the cuts that are made. Note that every unfolding has the property that a straight line between two points on this unfolding need not be contained completely within the body of this unfolding. This could potentially lead to situations where the above straight line is shorter than the shortest path between the corresponding end points on the polyhedron. We call such straight lines short-cuts. The presence of short-cuts is an obstacle to the use of unfoldings for designing algorithms which compute shortest paths on polyhedra. We study various properties of Star, Source and Planar Unfoldings which could play a role in circumventing this obstacle and facilitating the use of these unfoldings for shortest path...

• Type: Conference
• Year: 2004
• Where: FSTTCS
• Authors: Vijay Chandru, Ramesh Hariharan, Narasimha M. Krishnakumar
• Keywords: FSTTCS 2004, Planar Unfolding, Shortest Path, Source Unfolding